Invalidating Validity

[John Powell]

Invalidating Validity-1

POWELL:
I promised to give arguments indicating that so-called "valid deductive arguments" aren't really valid in the way usually claimed. Here I go. First, let me quote what the various logical terms mean. I will assume that Copi and Cohen "Introduction to Logic" 11th edition (copyright 2002) represents the consensus view of introductory logic teachers on these issues.

COPI & COHEN Glossary / Index:
Argument:
Any group of propositions of which one is claimed to follow from the others, which are regarded as providing support or grounds for the truth of that one, <snipped page numbers>

Deduction:
One of the two major types of argument traditionally distinguished, the other being induction. A deductive argument claims to provide conclusive grounds for its conclusion; if it does so it is valid, if it does not it is invalid, <snipped page numbers>

Induction:
One of the two major types of argument traditionally distinguished, the other being deduction. An inductive argument claims that its premisses give only some degree of probability, but not certainty, to its conclusion, <snipped page numbers>

Valid:
A deductive argument whose premisses, if they were all true, would provide conclusive grounds for the truth of its conclusion, is said to be valid. Validity is a formal characteristic; it applies only to arguments, as distinguished from truth, which applies to propositions, <snipped page number>

Modus Ponens (M.P.):
One of the nine elementary valid argument forms; a rule of inference according to which, if the truth of the hypothetical premiss is assumed, and the truth of the antecedent of that premiss is also assumed, we may conclude that the consequent of that premiss is true. Symbolized as: p =) q , p, therefore q, <snipped page numbers>

Modus Tollen (M.T.):
One of the nine elementary valid argument forms; a rule of inference according to which, if the truth of the hypothetical premiss is assumed, and the falsity of the consequent of that premiss is also assumed, we may conclude that the antecedent of that premiss is false. Symbolized as p =) q, ~q, therefore ~p, <snipped page numbers>

COPI & COHEN (pg. 42-43):

1.7 Deduction and Validity

Every argument makes the claim that its premisses provide grounds for the truth of its conclusion. Indeed, that claim is the mark of an argument. But there are two major classes of arguments: deductive and inductive. These two classes differ fundamentally in the way in which their conclusions are supported by their premisses. In this section we give a brief account of deduction.

A deductive argument makes the claim that its conclusion is supported by its premisses conclusively. In contrast, an inductive argument does not make such a claim. If, in interpreting a passage, we judge that such a claim is being made, we treat the argument as deductive; if we judge that such a claim is not being made, we treat it as inductive. Since every argument either makes this claim of conclusiveness or does not, every argument is either deductive or inductive.

When an argument makes the claim that its premisses (if true) provide irrefutable grounds for the truth of its conclusion, that claim will be either correct or not correct. If it is correct, that argument is valid. If it is not correct (that is, if the premisses when true fail to establish the conclusion irrefutably), that argument is invalid.

For logicians, therefore, the term validity is applicable only to deductive arguments. To say that a deductive argument is valid is to say that it is not possible for its conclusion to be false if its premisses are true. Thus we define "validity" as follows: A deductive argument is valid when, if its premisses are true, its conclusion must be true.

Every deductive argument makes the claim that its premisses guarantee the truth of its conclusion, but not all deductive arguments live up to that claim. Deductive arguments that fail to do so are invalid.

COPI & COHEN (pg. 43-44)

1.8 Induction and Probability

Inductive arguments do not claim that their premisses, even if true, support their conclusions with certainty. They make a weaker but nonetheless important claim that their premisses support their conclusions with probability, which always falls short of certainty. What was said above about validity and invalidity therefore does not apply to inductive arguments: Inductive arguments are neither valid nor invalid. ^47

- - - - - begin footnote

Note 47: In everyday speech the terms "valid" and "invalid" have taken on much wider and looser meanings. One hears it said, for example, that a fine motion picture "makes a valid statement," or that some emotional response to an act or event is a "valid reaction," and so forth. English is beautifully rich. But as logicians we use the terms valid and invalid far more narrowly; they indicate nothing more than the success, or lack of success, of a deductive argument in making its claim that if the premisses are true its conclusion must be true.

- - - - - - end footnote

We can still evaluate them [inductive arguments, added by Powell] of course. Indeed, the appraisal of inductive arguments is one of the leading tasks of scientists in every sphere. The premisses of an inductive argument provide some support for its conclusion, and the higher the level of probability the premisses confer on the conclusion, the greater the merit of the argument. In general, we say that inductive arguments may be "better" or "worse," "weaker" or "stronger," and so on. But even when the premisses are all true and provide very strong support for the conclusion, in an inductive argument the conclusion is never certain.

<snipped comments about where different techniques are treated in the text>

The difference between inductive and deductive arguments is deep. Because an inductive argument can yield no more than some degree of probability for its conclusion, it is always possible that additional information will strengthen or weaken it. Newly discovered facts may cause us to change our estimate of the probabilities, and thus may lead us to judge the argument to be better (or worse) than we thought it was. In the world of inductive argument - - - even when the conclusion is thought to be very highly probable - - - all the evidence is never in. It is this possibility of new data, perhaps conflicting with what was believed earlier, that keeps us from asserting that any inductive conclusion is absolutely certain.

Deductive arguments, on the other hand, cannot gradually become better or worse. They either succeed or do not succeed in exhibiting a compelling relation between the premisses and conclusion. The fundamental difference between deduction and induction is revealed by this contrast. If a deductive argument is valid, no additional premisses could possibly add to the strength of that argument. For example, if all humans are mortal, and if Socrates is human, we may conclude without reservation that Socrates is mortal - - - and that conclusion will follow from those premisses no matter what else may be true in the world, and no matter what other information may be discovered or added. If we come to learn that Socrates is ugly, or that angels are immortal, or that cows give milk, neither those findings nor any other findings can have any impact on the validity of the original argument.

In the case of every valid deductive argument, the conclusion that follows with certainty from its premisses follows from an enlarged set of premisses with the same certainty, regardless of the nature of the additional premisses. If an argument is valid, nothing in the world can make it more valid; if a conclusion is validly inferred from some set of premisses, nothing can be added to that set to make that conclusion follow more strictly, or more logically, or more validly.

But this is not true of inductive arguments, in which the relationship claimed between premisses and conclusion is much less strict and different in kind.

<snipped some examples>

A deductive argument is one whose conclusion is claimed to follow from its premisses with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case. In sharp contrast, an inductive argument is one whose conclusion is claimed to follow from its premisses only with probability, this probability being a matter of degree and dependent upon what else may be the case.

Inductive arguments do not always acknowledge explicitly that their conclusions are inferred only with some degree of probability. On the other hand, the mere presence of the word "probability" within an argument is no sure indication that the argument is inductive. This is so because there are some strictly deductive arguments about probabilities themselves *

- - - - - - begin footnote

Note *: If, for example, we learn that the probability of three successive heads in three tosses of a coin is 1/8, we may infer deductively that the probability of getting at least one tail in three tosses of the coin is 7/8.

- - - - - - end footnote


POWELL:
Now, I'll add a few dictionary definitions.

Merriam-Webster On-Line Dictionary:
Main Entry: de·duc·tion
Pronunciation: di-'d&k-sh&n, dE-
Function: noun
Date: 15th century
1 a : an act of taking away <deduction of legitimate business expenses>
b : something that is or may be subtracted <deductions from his taxable
income>
2 a : the deriving of a conclusion by reasoning; specifically : inference in which the conclusion about particulars follows necessarily from general or universal premises -- compare INDUCTION
b : a conclusion reached by logical deduction

Main Entry: in·duc·tion
Pronunciation: in-'d&k-sh&n
Function: noun
Date: 14th century
1 a : the act or process of inducting (as into office)
b : an initial experience : INITIATION c : the formality by which a civilian is inducted into military service
2 a (1) : inference of a generalized conclusion from particular instances -- compare DEDUCTION 2a
(2) : a conclusion arrived at by induction
b : mathematical demonstration of the validity of a law concerning all the positive integers by proving that it holds for the integer 1 and that if it holds for an arbitrarily chosen positive
integer k it must hold for the integer k+1 -- called also mathematical induction
3 : a preface, prologue, or introductory scene especially of an early English play
4 a : the act of bringing forward or adducing (as facts or particulars)
b : the act of causing or bringing on or about
c : the process by which an electrical conductor becomes electrified when near a charged body, by which a magnetizable body becomes magnetized when in a magnetic field or in the magnetic flux set up by a magnetomotive force, or by which an electromotive force is produced in a circuit by varying the magnetic field linked with the circuit
d : the inspiration of the fuel-air charge from the carburetor into the combustion chamber of an internal combustion engine e : the sum of the processes by which the fate of embryonic cells is determined and morphogenetic differentiation brought about


POWELL:
In the next posts of the same title I will give my arguments.

John Powell

[John Powell]

Invalidating Validity-2
Dialetheism Argument

POWELL:
The first argument I will present is based on the possible existence of true contradictions and the possible failure of the Law of Non-Contradiction.

http://plato.stanford.edu/entries/dialetheism/

PLATO STANFORD:
Stanford Encyclopedia of Philosophy

Dialetheism

A dialetheia is a true contradiction, a statement, A, such that both it and its negation, ~A, are true. Hence, dialeth(e)ism is the view that there are true contradictions. Dialetheism opposes the so-called Law of Non-Contradiction (LNC) (sometimes also called the Law of Contradiction): for any A, it is impossible for both A and ~A to be true. Since Aristotle's defence [sic] of the LNC, the Law has been orthodoxy in Western philosophy. Nonetheless, there are some dialetheists in the history of Western Philosophy. Moreover, since the development of paraconsistent logic in the second half of this century, dialetheism has now become a live issue once more.


POWELL:
The fact that some philosophers are seriously considering the possibility that A and ~A could both be true will serve as my first argument that so-called "valid deductive arguments" are not valid in the way usually claimed.

Let's use Modus Ponens as our first example.

1) If p then q
2) p
3) therefore, q

Now, let p = A and q = ~A (not A)

4) If A then ~A
5) A
6) therefore, ~A

Modus Ponens indicates this inference should be valid, since the argument form is supposed to be valid. However, there are problems. If premiss 2, A, is true then the conclusion should also be A, but by the Law of Non-Contradiction, ~A can't then be true. The LNC, however, was thrown out the window with this contradictory substitution. Anyway, if you allow for dialetheism to be true then you can get weird results.

Now, consider Modus Tollens:

7) If p then q
8) ~q
9) therefore, ~p

As before, let p = A and q = ~A

This results in

10) If A then ~A
11) ~ (~A)
12) therefore, ~A

If ~(~A) is the same as A then Modus Tollens looks identical to Modus Ponens with this substitution.

The point is that if dialetheism is true then neither M.P. nor M.T. are known to be a valid inferences because you can no longer rely on the conclusion being true or noncontradictory because if the premisses are true then there could be contradictions.

Let's consider some "real life" examples so one doesn't falsely assume this is just word games. I'll mention 3 from science and then a couple of more common ones from the natural language.

Example 1: Is the classical Law of Conservation of Matter true? Is the classical Law of Conservation of Energy true? Or, is E = mc^2 true? Today, we'd say that E=mc^2 is true, but when Einstein first proposed it there was an apparent contradiction.

Example 2. Is light a particle or a wave? Are things like electrons particles or waves?

Example 3. Are physical quantities quantized (come in discrete bundles) or not? Quantum Mechanics assumes yes. General Relativity assumes no. Which is it?

Example 4: A "couple" (2 or 3?), a few (3 to 4?), and many (more than 4?).

Example 5: "Like" and "love." Women will often pressure a man to say he "loves" her, when the man may want to say he only "likes her," perhaps "a lot." Some of these men perhaps want to avoid having to defend themselves when they don't "show your love" to her satisfaction.

Example 6: "Dislike" and "hate." It's more common to hear something like "I dislike him so much that I hate him." However, it's linguistically possible to have someone meaningfully say: "I don't dislike him. I hate him."

Example 7: "Hungry" and "Starving." This is similar to the dislike / hate example. Let's look at this one a little more in detail.

These two terms are sometimes used synonymously and sometimes they are not, even by the same person. When they aren't treated as synonyms then "hungry" usually means something like "feeling hunger pains" and "starving" means "very hungry" or perhaps even "hunger so bad that damage to organs or death of the complete organism is imminent." The idea is that on a "hunger" spectrum, the word "hungry" goes from barely feeling hunger pains up to where damage to organs or even death is imminent, and "starving" covers the more extreme forms of hunger.

For discussion sake, let's assume that hunger level 0 is neutral, neither hungry nor full. Hunger levels up to 50 are "hungry" and above 50 are "starving" with level 100 death by starvation. Negative levels of hunger are feeling satisfied to feeling full.

Now, one could think of "starving" as a kind of hunger that's from level 50 to 100. Therefore, "starving" is a kind of "hungry". On the other hand, one could think of "starving" as distinct from "hungry" since "hungry" only goes up to hunger level 50. In other words, "starving" is not "hungry."

Given that introduction, consider the following syllogism.

13) If Jack is starving then Jack is hungry.
14) Jack is starving.
15) therefore, Jack is hungry.

This argument may be valid if "starving" means "very hungry." In other words, if starving isn't just normal hunger, but strong hunger. This argument could be saying semantically that if Jack is "very hungry" then Jack is "hungry."

However, if "starving" and "hungry" are considered as exclusive of each other, in which "starving" is level 50-100 while "hungry" is level 0-50, then things could be different.

A person hearing the argument above might initially accept premiss 13 as true, but by the time he gets to the conclusion, the same person could have switched to the other distinction between hungry and starving, so the conclusion wouldn't necessarily follow.

The logician might strongly assert that IF premisses 13 and 14 are true then 15 MUST be true, but that's not necessarily the case since the moments that the truth values of premisses 13 and 14 are considered are not necessarily the same moment that the truth value of the conclusion 15 is considered. One must assign truth values to 13, 14, and 15 simultaneously to have a chance of the argument being valid. There is a relativistic problem with this procedure that I'll treat in a later argument.

Now, getting back to the problem of allowing contradictions.

What is the solution to make these arguments really valid? One way might be to just disallow propositions which violate the LNC. Based on what I've read on Internet sites, I think this is how most logicians handle the problem. Probably Copi and Cohen do the same thing, but I'll have to get to that part. However, doing this would mean that so-called valid deductive arguments could only be valid for a restricted range of possible substitutions. That would make so-called valid deductive arguments merely statistical again.

An example of such an excluded substitution would be a decisional conditional like:

16) If the President wins re-election then I will eat my hat.

Even if the President were to win re-election that would not necessarily mean that I would eat my hat. This is a promise, not a logically binding relationship. A truth value cannot be reliably assigned to the conditional until the President wins re-election and I eat my hat or the last possible moment transpires that I could possibly fulfill my promise, but failed to.

Including modal terms like "necessarily," "probably," and "possibly" in the conditionals could also cause problems.

A similar, but more cumbersome solution is to add a premiss which explicitly disallows contradictory substitutions into the logical forms. Let's apply it to M.P.

17) LNC is true and Dialetheism is false (or something to that effect)
18) If p then q
19) p
20) therefore, q

This revised M.P. might be valid, but you can't be sure that any given substitution is sound because dialetheism might be true and the LNC might be false. It is not necessarily the case that dialetheism is false and LNC is true. Who knows what future ideas philosophers will come up with?

Consider again the words of Copi and Cohen:

COPI and COHEN::
If an argument is valid, nothing in the world can make it more valid; if a conclusion is validly inferred from some set of premisses, nothing can be added to that set to make that conclusion follow more strictly, or more logically, or more validly.


POWELL
It appears that no one can know whether the so-called deductively valid arguments, such as M.P. and M.T., really are valid or not because we don't know if dialetheism will turn out to be true.

The point is that neither the classically valid Modus Ponens or Modus Tollens with only two premisses are certain of being valid. In order to be MORE assured that the inferences are valid one must add a LNC premiss. The inferences of the original M.P. and M.T. are suspect because of the possibility that dialetheism could be true and LNC could be false. The revised Modus Ponens + LNC assumption (and M.T. + LNC) might be valid, but that's still questionable. At least the revised M.P. appears to be MORE valid than the original Modus Ponens. However, this "matter of degree" defeats it as well since deductively valid arguments aren't supposed to be matters of degree, but all or nothing. Consider,

COPI and COHEN:
A deductive argument is one whose conclusion is claimed to follow from its premisses with absolute necessity, this necessity not being a matter of degree and not depending in any way on whatever else may be the case.

In sharp contrast, an inductive argument is one whose conclusion is claimed to follow from its premisses only with probability, this probability being a matter of degree and dependent upon what else may be the case.


POWELL:
It appears to me that so-called valid deductive arguments are subject to matters of degree. Perhaps arguments like M.P. and M.T. have worked flawlessly for most logicians for thousands of years, but new knowledge reveals that they actually need additional explicit premisses or implicit restrictions to be more sure that they are valid. This makes them appear more like what Copi and Cohen call inductive arguments, those for which the inference is less than 100% certain.

Therefore, due to the dialetheism argument, so-called deductively valid arguments are really just statistical arguments with nearly 100% certainty that the inference is correct if the premisses are true.

John Powell

[John Powell]

Invalidating Validity-3
Ambiguity of Language Argument

POWELL:
In the previous argument, I tried to show that so-called valid deductive arguments (specifically Modus Ponens and Modus Tollens) aren't really valid as advertised because the possible failure of the Law of Non-Contradiction or the truth of Dieletheism (the possibility that A and not A could both be true) makes knowledge of the inference uncertain. In this second argument, I will use the ambiguity of language to argue that deductively valid arguments aren't really valid as advertised.

Let's use the classical deductively valid argument

1) All men are mortal
2) Socrates is a man
3) therefore, Socrates is mortal

How do you know the Socrates in premiss 2 is the same as the Socrates in the conclusion 3? You don't. Maybe the Socrates in premiss 2 is the philosopher, but the one in the conclusion 3 is an immortal angel also named Socrates. You could have two true premisses, but the conclusion is not true. Therefore, this classically valid argument is not really valid as advertised.

The natural language does not insist that every time you use a word it has exactly the same meaning. Numbers are probably least subject to this variability.

Consider some other examples I am critical of.

http://www.unc.edu/~theis/phil20/arguments.html

PHIL 20:
Example 1:
Premise 1 St. Paul is a city in Minnesota.
Premise 2 Last week I was in St. Paul.
------------
Conclusion Therefore, last week I was in Minnesota.

This is a good argument. It is valid and since the premises are true, it is also sound.


POWELL
I don't think this is valid because there could easily be more than one place named St. Paul in the world.

PHIL 20:
Example 2:
Premise 1 I am the star player on Carolina's basketball team
Premise 2 Everyone on Carolina's basketball team is over 7 feet tall.
------------
Conclusion Therefore, I am over 7 feet tall

This is a valid argument, but since the premises are false, it is not sound.


POWELL:
I don't believe this is even a valid argument because the "Carolina basketball team" mentioned in both premiss 1 and 2 could be different ones. Both North and South Carolina could easily have more than one basketball team.

Let me make up an argument.

4) All the players on Carolina's basketball team are black men.
5) Jane is on Carolina's basketball team
6) therefore, Jane is a black man

I'm confident that the author of PHIL 20 would consider this to be a valid deductive argument. In other words, that if premiss 4 and 5 are true then conclusion 6 must be true, cannot be false. However, PHIL 20 would probably think that it's an unsound argument since a person named Jane is unlikely to be on a basketball team composed entirely of black men.

Now, imagine an alien, Xz206yl, is listening in on a conversation between Jack and Jill as they watch basketball on T.V.

Jack asks, "Are all the players on Carolina's basketball team black men?"

Jill truthfully says,"Yes."

Xz206yl translates those words into its own language.

There is heard a click, but basketball is still being presented on the T.V. Unknown to Xz206yl, Jack just changed the channel to a game being played by the Women's Carolina Basketball team.

"Hey isn't that Jill playing on the Carolina basketball team?" Jack asks.

"Yes," Jill truthfully says.

Xz206yl translates these words.

Is Xz206yl justified in concluding that it must absolutely be true that Jane is a black man if the statements were truthfully spoken and the translation was correct? No. Given the limited information, we shouldn't criticize Xz206yl for concluding that Jill is probably a black man, but Xz206yl would be unjustified in concluding that it must be an absolutely correct inference even though the argument follows a so-called valid deductive form.

The inference that Jane is a black man does not follow from this possible dialogue.

Let's consider another example, more dialogue.

Eve: "I'm starving. Can we hurry up and order?"

Adam: "Sure"

Jack, a poor man walks up. "I bet you're hungry. Could you people help out a starving poor man? Aren't you starving?"

Eve: "No, but I'm really hungry."

The point here is that in normal conversation Eve could both claim to be starving and, yet, deny that she's starving. Language allows that kind of freedom. Because of that you can't be sure that the words used in so-called deductive arguments always refer to exactly the same thing in all premisses and in the conclusion.

Different people have different meanings for the same words and even the same person changes their understanding of the meanings of the same words as they gain more experience. Words like "man" and "mortal" will have a slightly different meaning to every single person. Furthermore, what you "see" as "green" may be different than what my visual system perceives.

Useful communication between human beings and of a person with his own mind is possible because humans are reasonably similar in physical characteristics and experiences and, so, there is reasonably close overlap in understanding and the meanings of words tend to change slowly with time compared with the life span of the communicators. The concepts for numbers, like 1, 2, etc. may be the least subjective or changeable, however even here there is some variation. To the Hebrews, for example, the number "7" may have meant more things than just this many: I I I I I I I.

Logicians try to invent logical languages that satisfy their logical rules, their axioms and their theorems. Natural languages like English do not necessarily follow those rules.

Because of the ambiguity of language, so-called deductively valid arguments really aren't valid as advertised. The words in various parts of the argument could mean different things to different people and even to the same person at different times.

What is the solution to overcome this ambiguity of language problem and to make the so-called valid deductive argument valid as advertised? I don't think there is a solution. You can't force the definitions of words to be understood identically by everyone or even by the same person from moment to moment. There is no way to be absolutely certain that any two people have exactly the same understanding for the same word. In fact, it is more sensible to expect that two people or the same person at different times will have a slightly different understanding for what any certain word means.

Therefore, due to the ambiguity of language argument, so-called valid deductive arguments are just statistical arguments in which the conclusion is nearly 100% certain if the premisses are true.

John Powell

[John Powell]

Invalidating Validity-4
Nonconservation of Identity Argument

POWELL:
In the first argument to show that so-called deductively valid arguments aren't valid as advertised, I used Dialetheism. In the second argument I used the ambiguity of language. In this argument I will use the nonconservation of identity.

Again, let's use the classical deductively valid argument

1) All men are mortal
2) Socrates is a man
3) therefore, Socrates is mortal

Because of the nature of our physical existence, the atoms which comprise our body keep changing over time. You are not the same being you were a moment before. At each moment you will have a slightly different assortment of particles in different energy states. Because human beings are very similar to what they were a second before, they have a concept of conservation of identity, but it's only approximately true on short time scales.

You imagine, for example, that the apple you saw a second ago is the same one you see now, but that's only approximately true. If you watch the apple long enough you won't want to eat it because it will change, it will decompose. Likewise, if you watch Socrates long enough he will die and decompose. Human beings and apples are very much like clouds which form, change, but eventually dissipate to make something else.

Therefore, even if the Socrates in premiss 2 is the same "person," as we say, as the Socrates in the conclusion (we're not talking about Socrates the philosopher and Socrates the angel anymore), it still can't really be exactly the same entity because of this problem. The Socrates from one moment to the next is so similar in attributes that you can have very high (but not absolute) confidence that a typical time interval is irrelevant.

Therefore, due to the nonconservation of identity argument, so-called deductively valid arguments are really just statistical arguments with nearly 100% certainty that the inference is correct if the premisses are true.

The solution to make these arguments valid? What you must do is to consider the truth value of the premisses and the conclusion at the exact same instant so there is no time for a change of state. Since people can usually only think about one thing at the same time, this would probably require more than one observer to accomplish. The validity of the inference could only be determined after their notes were compared and it was clear they had considered the truth value
simultaneously.

That will bring up perhaps my most complicated argument, the problem of simultaneity.

John Powell

[John Powell]

Invalidating Validity-5
Simultaneity or Special Relativity Argument

POWELL:
Again, let's use the classical deductively valid argument

1) All men are mortal
2) Socrates is a man
3) Therefore, Socrates is mortal

In the ambiguity of language problem, we've considered that "man" might mean different things in different parts of the argument or the man Socrates might not be the Angel Socrates. In the Nonconservation of identity problem we've considered the fact that nothing material is ever the same if a time interval is involved. The new problem has to do with simultaneity. In order to know that the argument is sound you must test the truth value of all the premisses and the conclusion at the exact same instant. Otherwise, absolute certainty is destroyed. Things change over time.

For example, consider that premiss 1 is proposed 2000 some odd years ago, premiss 2 applies both then, now, and into the future, but conclusion 3 applies to the year 3001 A.D. on the day that Jesus Christ finally gets around to "quickly" coming back to Earth and turning men like Socrates into immortal angel men. The argument may have appeared to be valid 2000 years ago and continued to appear to be valid up to 3001 A.D.. However, once Socrates, the man, is resurrected and immortalized then the argument is unsound, because premiss 1 at that moment becomes false.

The point is that if you consider the premisses at a different time than the conclusion, then it's not valid, the conclusion is no longer certain of being true even if the premises were true when you measured them.

Consider another example, one I made up.

4) All of Jack's brothers are in the house.
5) Bill is one of Jack's brothers.
6) Therefore, Bill is in the house.

Logic teachers, I believe, would consider this to be a valid argument. They would consider that if premiss 4 and 5 are true then conclusion 6 must also be true. However, if Bill is on the way out the door there could be a problem. The logician can check premiss 4 as true and premiss 5 as true, but by the time he considers the conclusion 6, Bill may have left the house and premiss 4 is no longer true. Thus, the logician might go back and erase the "truth" check of premiss 4 and so the conclusion doesn't have to be true.

Now, what do you do during the second that Bill is in the doorway in which part of his body is in the house and part out? You could define him as "in the house" when more of his body is on the house side of some defined plane than outside that plane. Fine. This just helps to show that the logician may not be able to consider the truth value of 4 and then 6 before Bill has moved from being inside to outside the house or vice versa. Premiss 5 changes too slowly in truth value here to need to worry about it unless Bill is near death.

In other words, if you check mark the premisses as true, you can't be sure that the conclusion will be true when you get around to considering it. You have to check mark them all simultaneously.

Some logicians might try to avoid the check marking exercise as needless. However, what do they mean that some proposition is true that at other times could be false if it's not based on a truth-determination that occurs at some location in space at some moment of time?

So, again, one MUST consider the truth values of the premisses and conclusion simultaneously or close enough to simultaneous according to the time scale at which the truth values might change.

The problem, however, is that simultaneous measurements in one reference frame will not be simultaneous in a reference frame moving relative to it. This is something Einstein explained in his Special Theory of Relativity. Before I apply the principle to dethroning so-called valid deductive arguments, let me explain the simultaneity problem.

Imagine Jack is on the ground, while Jill is on a train car standing exactly at the center of the car. As measured by Jack, at the instant that Jill passes Jack, a bolt of lightning strikes both the front and the rear of the train car Jill is on leaving scorch marks on both the tracks and on the train car. Jack measures the time for the light flashes to reach him. They arrive at the same instant. He measures the distance between the marks on the tracks and finds that he was exactly at the center. Therefore, Jack will judge that the two flashes struck at exactly the same instant of time some fraction of a second before he saw the flashes.

Jill, however, is moving relative to Jack. If Jack measures the flashes to be simultaneous then Jill will receive the light flash from the front of her train car before she receives the flash from behind. Yet, she will measure herself to be exactly at the center of the train car. She, therefore, will conclude that the flash that happened at the front of the car occurred before the flash at the rear, since the signal reached her first, yet she was at the center.

The classical solution would be to claim that Jill is really moving and Jack is not, and to assume that information of things can travel infinitely fast. However, motion is all relative to the observer and the fastest information can travel is at the speed of light. There is no known experiment that can show that it is really Jack who is stationary and Jill who is moving. The constant and limited speed of light helps to produce this problem. In fact, an observer moving with the Sun might measure both Jack and Jill to be moving in the same direction, but at different speeds. You can't claim that the flashes really were simultaneous just because that's what Jack obtained. All observers in non-accelerating reference frames have equal claim to such things.

The conclusion Einstein came up with is that what is simultaneous to Jack won't be simultaneous to someone moving relative to Jack (such as Jill).

Simultaneity is not a constant of the universe, it's NOT invariant to relative motion.

Now, how does that apply to determining the validity of deductive arguments?

The problem with determining the truth value of the premisses and conclusion of an argument is that it will only be valid for people stationary with respect to the truth testers. People who are moving will judge that the measurements were not done simultaneously and, therefore, the validity claim is not justified. This only becomes a serious problem when the truth values can change rapidly and people are moving near the speed of light, so one can say in practice that the validity of such arguments is approximately correct. However, that destroys it completely, because it's all or nothing for so-called valid arguments.

Therefore, due to the relativistic problem of simultaneity, so-called deductively valid arguments are really just statistical arguments in which the conclusions are virtually (but not exactly) 100% probable of being true if the premisses are true.

John Powell

[John Powell]

Invalidating Validity-6
Modal Argument

POWELL:
Since posting these arguments to the II Errancy Annex, I have come up with an additional argument, the modal argument. I will place it before what used to be my final argument.

It is argued by modal logicians that the following conditional would be incorrect:

1) If p then necessarily q

Modal logicians argue that the problem is that it is not necessarily the case that q be true by itself. In some possible worlds or situations, q might be false. Therefore, a possible resulting conclusion "therefore, necessarily q" would be false. At most it would necessarily be the case that the conditional was true. So, modal logicians argue, the conditional should be worded in the following way:

2) Necessarily (if p then q)

A problem, however, is whether q would be certain to be true if this were used in a M.P. type argument. If q isn't certain or necessarily true in this situation then the argument fails to satisfy what is meant by a valid deductive argument. One cannot conclude with absolute confidence that q is true even if premise 1 and 2 were true because q is not certain to be true because it's not necessarily true. The conclusion q could be false.

It is my current opinion that what logicians really mean by Modus Ponens is probably something more like the following:

3) If (in the possible world w, p) then (in w, necessarily q).
4) In the possible world w, p.
5) therefore, in w, necessarily q.

Perhaps because this is too cumbersome for the translation of arguments from a natural language, the "world w" and "necessarily" parts are omitted. I think this should be clarified in introductory logic texts.

My argument here then, is that because introductory logic texts, like Copi & Cohen do not make this modal / possible world correction clear early on, sufficiently explicit, the conventional wording of the M.P. argument does not satisfy the necessary conditions to be valid. Because of this, one could not be certain that the conclusion would be true even if the premises were true. One can only justifiably claim that the conclusion is very likely to be true if the premises are true.

John Powell

[Butters]

Uh, John, you need to put the book down and go outside and take a little walk.:smile:

[John Powell]

Invalidating Validity-7
Measurement Error Argument

POWELL:
Although I'm giving this as my last argument, it was actually the first one I used for myself. Based on my scientific training, I intuitively felt there had to be a problem with so-called deductively valid arguments. How can anyone be perfectly justified in claiming to know for absolutely certain much of anything? Any measurement has some error associated with it. How can you be perfectly justified in feeling sure that the conclusion will be true even if the premisses were true? Logicians appeared to be saying you are perfectly justified in feeling absolutely certain, but what I had learned about science did not support that position. Things once thought by virtually everyone to be absolutely certain like the Earth is the center of the universe, Euclid's geometry, our concepts of space and time, Classical mechanics, etc., have been shown to be less than certain or plainly wrong.

Let me ask a simple question that attempts to cut right to the point between "certain" valid deductive arguments and "probably true" inductive arguments.

What's the difference between an inference that is 100% certain and one that is only
99.999999999999999999999999999999999999999999% certain (add as many 9's as you want)?

To Copi and Cohen, 100% certain would be deductively valid, while the other would be inductively strong or something like that.

You might call this tiny distinction "a quibble," but that's all you need to dethrone deductively valid arguments as they are advertised in introductory logic texts.

There is a conceptual difference between 100% and virtually 100%, I'll admit, but there is probably no measurement that can distinguish them. When one speaks of "certainty," as in a deductively valid argument, it's only "close to absolute certainty."

There is not a huge difference between what Copi and Cohen term "deductive" and "inductive" since all such arguments are statistical. The question is one of degree. So-called valid deductive arguments are really just those with virtually 100% certainty, while the so-called inductive argument are less certain than that.

Therefore, due to the measurement error problem, so-called deductively valid arguments are really just statistical arguments with nearly 100% certainty that the inference is correct if the premisses are true.

If the difference between these kinds of arguments is merely whether the certainty is virtually 100% probable or less than that, then the basis for distinguishing them as "deductive" and "inductive" is weakened considerably. They might as well all be called "statistical arguments." Actually, they might as well just be called "arguments" because it's not helpful to characterize some arguments as statistical if there are none which are not. It would be like speaking of male men if there are no other kind.

The terms "deductive" and "inductive" could be used, instead, to refer to "going from the general to the specific" and "going from the specific to the general" respectively, as scientists and mathematicians and dictionaries and even some logicians use those terms.

I propose the following term changes.

Deductive argument:
An argument in which a conclusion about a specific case is inferred from a general principle.

Inductive argument:
An argument in which a conclusion about a general principle is inferred from one or more specific cases.

Valid argument:
An argument in which the statistical inference is virtually 100% certain. The conclusion would be virtually certain of being true if the premises were true. Note that very little, if anything, is absolutely certain.

Strong argument:
An argument in which the statistical inference is more than 50% probable, but less than virtually 100% certain. The conclusion would be probably true if the premises were true.

Weak argument:
An argument in which the statistical inference is less than 50% probable. The conclusion would be probably false if the premises were true.

Sound argument:
A valid argument in which the premises are all true. The conclusion is virtually certain of being true because the argument is valid and the premises are true.

Cogent argument:
A strong argument in which the premises are all true. The conclusion is probably true since the argument is strong and the premises are true.

Did I persuade anyone to accept that so-called deductively valid arguments aren't valid as advertised? Any comments?

If I failed to persuade you to doubt that so-called valid deductive arguments are the certain inferences they're claimed to be, maybe the fact that philosophers are debating these issues will motivate you to reconsider. Here's one example I came across when I was searching for details on modus ponens and modus tollens:

http://www.bu.edu/wcp/Papers/Logi/LogiDagl.htm

I didn't read the whole article or the references, but the mere fact that the issue is being debated by philosophers was enough to convince me that the strong claims of introductory logic texts and teachers concerning valid deductive arguments were probably overstated.

This is the last of the Invalidating Validity-x set of initial posts.

John Powell

[John Powell]

Butters:
Uh, John, you need to put the book down and go outside and take a little walk.:smile:


POWELL:
Right.

I need these arguments posted so that from now on when I might claim that so-called valid deductive arguments are not the certain things they are claimed to be then any rebuttal to my assertion that does not directly rebut my specific arguments or does not point to a source that properly responds to my arguments then I can justifiably reply with:

"That's an argument by assertion, appeal to authority, and / or appeal to ignorance."

John Powell

[psychopath]

John -

This is a subject I may be interested in discussing, but I (and presumably most others) simply don't have the time to wade through several full length posts. Could you maybe give a brief summary of one, some, or all of your arguments, or direct us to one in particular? Thanks.

[John Powell]

psychopath

John -

This is a subject I may be interested in discussing, but I (and presumably most others) simply don't have the time to wade through several full length posts. Could you maybe give a brief summary of one, some, or all of your arguments, or direct us to one in particular? Thanks.


POWELL:
Certainly. I'll try.

I posted a series of 6 separate (but sometimes related) arguments that allege to demonstrate that so-called valid deductive arguments are not the "certain" things that introductory logic texts claim they are.

The arguments briefly are the following:

A1. Dialetheism argument.
Because dialetheism may be true, namely that true contraditions might exist, one cannot be absolutely certain that the conclusion of an argument of a so-called valid form such as M.P. is true even if the premises were true. One would have to add a premise "LNC is true" to be valid.

A2. Ambiguity of Language argument.
Because the meanings of words differ from person to person and even with the same person from moment to moment, one cannot be absolutely certain that the conclusion of a so-called valid deductive argument is true even if the premises were true. The meaning might change between the assigning of truth values to the premises and the conclusion. There appears to be no solution to this problem.

A3. Non-conservation of Identity argument.
Because physical things are only approximately the same from moment to moment, one cannot be absolutely certain that the conclusion of a so-called valid deductive argument that refers to them is true even if the premises were true, unless perhaps the truth values of premises and conclusion are determined simultaneously.

A4. Simultaneity argument.
Due to relativity, simultaneous events in one reference frame won't be simultaneous in another. In order to be certain that a time-variable argument is valid, the premises and conclusion must be assigned truth values simultaneously. However, if that is successful in one reference frame it will only be approximately successful in reference frames moving relative to it. Consequently, one cannot be absolutely certain that the conclusion will be true in your reference frame even if the premises are true in your reference frame.

A5. Modal argument.
Because arguments of the form

If p then necessarily q
p
therefore, necessarily q

are what are implied by M.P., but are deemed by modal logicians to be incorrect, one cannot be certain that q is true even if the premises were true. One cannot justifiably say "necessarily q" except perhaps if one uses the possible world w formulation.

A6. Measurement error argument.
Since there is no measurable difference between a conclusion that is 100% certain (deductive) and one that is 99.99999999...% certain (inductive) then to make the distinction is ill-advised. So many things have turned out to be wrong that were previously thought to be certain (such as geocentrism) that one cannot be absolutely certain that what logicians claim about valid deductive arguments is true.

Conclusions:

C1. So-called valid deductive arguments are really just statistical arguments such that the conclusions are very close to being certainly true if the premises were true, not certain of being true, as advertised by introductory logic texts.

C2. "Deductive" and "inductive" should not be distinguished as to the relative certainty of the conclusion as is done by modern introductory logic texts, but according to the historical distinctions (general to specific or vice versa) still used by mathematicians and scientists and some philosophers.

I hope this helps.

John Powell

[psychopath]

A1. Dialetheism argument.
Because dialetheism may be true, namely that true contraditions might exist, one cannot be absolutely certain that the conclusion of an argument of a so-called valid form such as M.P. is true even if the premises were true. One would have to add a premise "LNC is true" to be valid.

In other words:

1. If dialetheism has any possibility of being true, conclusions drawn via M.P. are not 100% certain.

2. Dialetheism has a possibility of being true.

3. Conclusions drawn via M.P. are not 100% certain.

The thing is, you're using an argument of the modus ponens form (though you don't explicitly frame it as such) in an attempt to show the uncertainty of modus ponens. If your conclusion here happens to be true, then it follows that that conclusion itself may be false, and that conclusions drawn via M.P. ARE perhaps 100% certain, since it was arrived it through the use of M.P. So I'm not sure what this argument accomplishes.

A6. Measurement error argument.
Since there is no measurable difference between a conclusion that is 100% certain (deductive) and one that is 99.99999999...% certain (inductive) then to make the distinction is ill-advised. So many things have turned out to be wrong that were previously thought to be certain (such as geocentrism) that one cannot be absolutely certain that what logicians claim about valid deductive arguments is true.

But if it is impossible to achieve absolute certainty due to human fallibility, error, etc., then there can be no certainty in your conclusion that deductive arguments are not 100% certain. It follows, then, that they may be.

It seems, I think, that similar objections could be raised to all of your arguments.

[John Powell]

PSYCHOPATH:
The thing is, you're using an argument of the modus ponens form (though you don't explicitly frame it as such) in an attempt to show the uncertainty of modus ponens.


POWELL:
Perhaps I'm using an inductive argument, similar in form to the one you posted but with "probably" implied in the conclusion.

PSYCHOPATH:
If your conclusion here happens to be true, then it follows that that conclusion itself may be false, and that conclusions drawn via M.P. ARE perhaps 100% certain, since it was arrived it through the use of M.P. So I'm not sure what this argument accomplishes.


POWELL:
It should justify a rational person to doubt that so-called valid deductive arguments are the absolutely certain things advertised in introductory logic texts even if one can't phrase a sound deductive argument that proves this to be true.

PSYCHOPATH:
But if it is impossible to achieve absolute certainty due to human fallibility, error, etc., then there can be no certainty in your conclusion that deductive arguments are not 100% certain. It follows, then, that they may be.


POWELL:
Exactly. I might be wrong, but so might all the logicians who disagree with me, who claim that so-called valid deductive arguments are the certain things they are advertised to be. Don't you agree, Psychopath?

PSYCHOPATH:
It seems, I think, that similar objections could be raised to all of your arguments.


POWELL:
Perhaps, but the arguments are not identically the same.

You bring up good points, Psychopath. I admit that I might be wrong.

Q1) However, which is more likely?

A) That I'm wrong and that valid deductive arguments are the "perfect" things they are made out to be, that one can be ABSOLUTELY CERTAIN WITHOUT ANY DOUBT WHATSOEVER that the conclusions will be ABSOLUTELY NECESSARILY true, that they ABSOLUTELY CANNOT be false if the premises are true

or

B) That I'm right and so-called valid deductive arguments don't quite muster to that absolute level of perfection?

What do you think, psychopath?

There, I just used an inductive argument to tear deductive arguments down to size.

If you think valid deductive arguments do satisfy that absolute level of perfection, Psychopath, then my next two questions to you are

Q2) What is the sound deductive argument proving that position?

and, if you produce what you think is such an argument, then

Q3) How do you absolutely know that particular argument is sound, that the premises are absolutely true and the inference is valid in the absolute way advertised?

John Powell

[Brian]

Hello John!

Let's use Modus Ponens as our first example.

1) If p then q
2) p
3) therefore, q

Now, let p = A and q = ~A (not A)

4) If A then ~A
5) A
6) therefore, ~A

This is a fascinating point. Mathematics has in its arsenol a way to prove things indirectly called the Reducio ad Absurdum. The prove is of this form...

Prove: A
Assume:~A
~A-->B
But we know from an outside theorum or definition that ~B is true. Therefore, by MT we have ~~A, and conclude A. QED.

There is another form of this proof that is used often, but some do not consider valid. It looks like this...

Prove: A
Assume:~A
~A-->B
B-->~B
Therefore, A. QED?

The difference between the 2 forms is that ~B is derived independantly from the proof in example 1, and ~B is derived within the proof in example 2.

I would submit that B-->~B is never valid, and is of the form of many paradoxes like "Barber" and "Lier." So to try and discredit MT or MP by starting off with A-->~A is dubious. Also, it can be shown that A-->~A asserts ~A as being true. All of this violates LC, but not because MT is not valid, but because A-->~A is not valid.

Sincerely,

Brian

[John Powell]

POWELL:
Brian, don't these "proofs" assume the Law of Non-Contradiction is true, that Dialetheism is false? If that axiom were false wouldn't these cease to be "proofs"?

Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right?

BRIAN:
I would submit that B-->~B is never valid, . . .


POWELL:
Do you have a proof for this assertion (preferably what you think is a sound deductive argument) that doesn't assume LNC? What about the "real life" counter-examples I gave?

Can you prove LNC is true?

John Powell

[Butters]

John, I was just kidding you, As I can see that you have spent quite a long time thinking about this.

I must agree with you, even using logical arguments we cannot be 100% sure of anything being "true". This is a favorite argument of theologians. Is the law of contradiction always valid?
Are all events causal? etc.? I think it is important to show that we cannot KNOW this with100% certainty, as not to stop searching for a way to prove these ideas with 100% certainly. However, we cannot discount that adhering to these axioms is the only workable method we have for some sense of our world.

Take causality for example. Some like to claim that events are not casual. We cannot PROVE that they are, with 100% accuracy, but where does that leave us. As ALL events APPEAR to be casual, and that we can explain events and make future predictions by assuming causality, it only makes sense to ASSUME it is true, until it is PROVED otherwise, or until another method comes along that is more useful. Unfortunately for theists, the answer, God did it, also cannot be PROVEN, but beyond that, is not as useful, in fact it's not useful at all.

I believe the state of metaphysics and logic today are analogous to the discovery of Newtonian laws. These laws also only stated unproven axioms. They worked quite well (and still do) to make sense of our world. It should also be noted, that these laws were not "replaced" by a more complete understanding of physics, but were subsumed by them. So while the were not complete, they were "true" enough to be useful.

Almost forgot my favorite axiom,

One good observation is worth more than a centuray of bad philosophy.

[Brian]

Hello Gentlemen!

Brian, don't these "proofs" assume the Law of Non-Contradiction is true, that Dialetheism is false? If that axiom were false wouldn't these cease to be "proofs"?

Yes, they certainly do assume LC to bre true, and therefore Dialetheism false. Your second question is interesting. If Dialetheism was true, how could you know LC is false?

Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right?

As implied in my last question, if you deny LC how can you infer anything? The point is, LC is a non-proven necessary precondition for intelligibility. Without LC, you and I could not have this conversation. In other words, the impossibility of the contrary precludes Dialetheism from being correct.

Do you have a proof for this assertion (I would submit that B-->~B is never valid)...that doesn't assume LNC?

I really was not very accurate here. I should have said that B-->~B has the same proving force as A-->A, i.e. none. Also, B-->~B has been show to lead to ~B-->B, which in turn leads to B-->~B, and then ad infinitum. It is of the form of the "Liar" and "Barber" paradoxs. These all assume LC, and that is why they are considered paradoxes.

Can you prove LNC is true? No. In order to prove it, you would need to assume it. It is a necessary presupposition for intelligibilty. You could validly argue that the world around us cannot be explained apart from assuming LC. Every person assumes LC and does not live without doing so. Because every person must necessarily assume LC, then LC by necessity must be valid.

Sincerely,

Brian

[John Powell]

POWELL:
To Butters.

Butters:

John, I was just kidding you, As I can see that you have spent quite a long time thinking about this.


POWELL:
I have come to the conclusion that when people say one thing that can be taken as negative and then later say "I was just kidding" what they really mean is "I mostly meant what I said, but I didn't mean for you to take it quite as negatively as you did."

For example,

Wife: "Do you like my new hairstyle."
Husband: "It looks weird."
Wife (frowns):
Husband: "Just Kidding. I think it looks great."

What I suspect really happened in this kind of dialogue is that the husband really did think the new hairstyle was weird, but he didn't intend that comment to cause as much displeasure to his wife, so he "took his words back" and replaced them with an exaggeration, if not lie, about his true judgment.

Some people think I sometimes over analyze things. They're probably right.

BUTTERS:
I must agree with you, even using logical arguments we cannot be 100% sure of anything being "true". This is a favorite argument of theologians. Is the law of contradiction always valid?

Are all events causal? etc.? I think it is important to show that we cannot KNOW this with100% certainty, as not to stop searching for a way to prove these ideas with 100% certainly. However, we cannot discount that adhering to these axioms is the only workable method we have for some sense of our world.


POWELL:
Perhaps it's the best method we have, but sometimes the world doesn't cooperate because there are things that appear to be dialetheias. People express them in their natural language. Scientists seem to see them, but then seek non-contradictory explanations for them.

BUTTERS:
Take causality for example. Some like to claim that events are not casual.


POWELL:
As in "casual relationships"?

BUTTERS:
We cannot PROVE that they are, with 100% accuracy, but where does that leave us. As ALL events APPEAR to be casual {causal}, and that we can explain events and make future predictions by assuming causality, it only makes sense to ASSUME it is true, until it is PROVED otherwise, or until another method comes along that is more useful.


POWELL:
I'm largely in agreement.

However, rather than saying "it only makes sense to ASSUME it is true," I would say "generally, it is more wise to assume it is true than to not," For normal circumstances, one would be expected to have greater success (therefore it would be more wise) by assuming LNC than not. However, in the cases of dealing with apparent dialetheias (such as wave particle duality, or GR vs. QM) and in the special case of discussing the issue of whether LNC might be false then it could be useful (therefore wise) to temporarily consider that the LNC could be violated.

BUTTERS:
Unfortunately for theists, the answer, God did it, also cannot be PROVEN, but beyond that, is not as useful, in fact it's not useful at all.


POWELL:
I agree with the "spirit" of your position, Butters, but I think you are exaggerating. I would delete "in fact it's not useful at all" unless you clarify the "what purpose" it's not useful for. Apparently, it is useful in some way to theists to supply that explanation because that's what they do.

BUTTERS:
I believe the state of metaphysics and logic today are analogous to the discovery of Newtonian laws. These laws also only stated unproven axioms. They worked quite well (and still do) to make sense of our world. It should also be noted, that these laws were not "replaced" by a more complete understanding of physics, but were subsumed by them. So while the were not complete, they were "true" enough to be useful.


POWELL:
Modern physics replaced classical physics in certain regimes, specifically phenomena having to do with the very fast, the very massive, and the very tiny. Modern physics did not, except in perhaps rare circumstances, replace classical physics in the more normal regimes that classical physics gave and still gives reasonably correct answers for. This is primarily because classical physics is easier to explain and simpler to use, so it is preferred where it can be justifiably applied.

I like the sentiment you are expressing. I wish more philosophers agreed with you.

Unfortunately, I see a strong resistance from philosophers to what I consider to be a rational, logical, scientific way of dealing with this issue. Perhaps their resistance is due to the perception that to accept these ideas as true or likely true would be for philosophy to surrender to science as the superior method of truth determination, as the superior logic.

Galileo and other early scientists knocked the Aristotelian philosophers of their day down to size. Although science came from philosophy, in fact early scientists called themselves natural philosophers partly to gain prestige, scientists have gradually voluntarily disowned themselves from their eccentric parent, philosophy. Although there is a philosophy and a language of science, it is not considered a subfield of philosophy or language. Science uses philosophical logic, language, and mathematics to try to determine cause and effect, to understand the physical universe around us.

Philosophers tried to recover after the repeated thrashings from scientists, partly by incorporating some of the scientific ideas, such as the usefulness of non-deductive forms of logic. Perhaps philosophers have misled themselves to think they've regained the cherished position as the supreme authority of truth. Maybe they need a new wake up call that the real king of the hill of truth is still science.

To too many philosophers, valid deductive arguments are not subject to the limitations you and I agree are there. Anyone who argues otherwise must, in too many of their minds, be arguing in a circle, must be trying to use valid deductive arguments to prove that valid deductive arguments can't prove anything. Or, trying to use contradictory statements to prove that contradictory statements are possible. Or, using language to communicate the idea that language cannot communicate ideas.

They too often don't see that this isn't necessarily the case.

They are too often so caught up in the ideal world of the semantics of their creation, in the artificial logical language they have invented, they don't realize as well as scientists generally do that the real universe is not bound to have the features language gives to it.

Just because the mind can conceive of a thing doesn't mean it can exist outside the mind.

BUTTERS:
Almost forgot my favorite axiom,

One good observation is worth more than a centuray of bad philosophy.


POWELL:
I agree with the sentiment, but it's probably an exaggeration unless "is" is replaced with "can be." An observation that is barely on the positive side of being good, is not necessarily "worth more" in all senses of the term than lots of philosophy that is barely on the negative side.

Science means "knowledge." Philosophy, on the other hand, means "love of wisdom." I sometimes think of it as the "love of ideas," too often their own experimentally unsupported ones.

I look forward to the day that scientists no longer receive Ph.D.'s, but something like D.S.'s (Doctor of Science), and scientists agree to rename their credentials. Until then, we Ph.D.'s will have to display what our universities thought were the appropriate designations.

John Powell.
Ph.D., Physics and Astronomy.

[John Powell]

POWELL:
To Brian.

BRIAN:
Hello Gentlemen!


POWELL:
Hello, Brian.

POWELL:
Brian, don't these "proofs" assume the Law of Non-Contradiction is true, that Dialetheism is false? If that axiom were false wouldn't these cease to be "proofs"?

BRIAN:
Yes, they certainly do assume LC to bre true, and therefore Dialetheism false. Your second question is interesting. If Dialetheism was true, how could you know LC is false?


POWELL:
Please quote the "second question" where I asked "If Dialetheism is true, how could you know LC is false?" I don't think that's what my question was. However, it is a good question after all.

If "I am hungry" is a true statement for J then how could you know that the statement "I am not hungry" is not a true statement? You can't know that for sure. Just ask him. I'm J.

J could justifiably (by the rules of natural language) say one and then the other in either order and both statements could be true, are not necessarily false unless, perhaps, you assume a certain man-made logical principle applicable to artificial logical languages is true. Natural language statements allow for dialetheias like this. The universe appears to have dialetheias. Just because an artificial logical language defines them away doesn't make them go away.

POWELL:
Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right?


POWELL:
I don't think you answered my question, Brian. Let me ask it again. Please reply with something like "No", "Yes, because" or "Neither, because."

Q: Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right?

My answer is "No." By the way, when I use "absurd" below the same applies to me. Just because I think something you claim is absurd doesn't necessarily mean it's false. What it partly means is that I feel confident that you are wrong and I am right.

BRIAN:
As implied in my last question, if you deny LC how can you infer anything?


POWELL:
It depends on how you define "infer."

You seem to be assuming that only mental processing that assumes LNC allows inferences, deriving logical conclusions based on premises. If you define "infer" such that the LNC is an essential part then, probably no, you probably cannot infer things without it. However, if you define "infer" such that the LNC is not an essential part then maybe you could. People often come to conclusions based on modes of thinking considered "illogical" by logicians. What's new?

BRIAN:
The point is, LC is a non-proven necessary precondition for intelligibility.


POWELL:
Absurd. People communicate frequently and apparently "intelligibly" even when using apparent dialetheias. Here are two for you to consider.

"God is love." Assuming you're a Bible believer, is this a true statement? Are you obligated to explain to atheists such as myself the apparent contradiction that an imaginary entity is actually a human emotion based on the evolutionary drive to reproduce?

Here's another one for you to explain.

"One is not three. God is one God. God, the Father is God. God, the Son is God. God, the Holy Spirit is God. The Father is not the Son. The Father is not the Holy Spirit. The Son is not the Holy Spirit. God is three Gods."

BRIAN:
Without LC, you and I could not have this conversation.


POWELL:
Absurd. You apparently are confusing absolute "understanding" or something like that with a state of understanding less than that. It may be impossible for a mortal to perfectly understand a true dialetheia, but that probably does not necessarily mean that enough can't be understood when discussing an apparent dialetheia to satisfy some goal of utility.

BRIAN:
In other words, the impossibility of the contrary precludes Dialetheism from being correct.


POWELL:
Then should I take it you can supply a sound deductive argument for that position that does not assume LNC? If it appears impossible to supply such an argument, what justified reason do you have to believe it? Is it by an inductive argument (it has seemed to work in the past, so it probably will work in the future), an appeal to authority (experts say this is what we should believe), an appeal to ignorance (I can't think of a way this could work so it must be false), wishful thinking, or what?

POWELL:
Do you have a proof for this assertion (I would submit that B-->~B is never valid)...that doesn't assume LNC?

BRIAN:
I really was not very accurate here. I should have said that B-->~B has the same proving force as A-->A, i.e. none.


POWELL:
Absurd.

A --> A apparently is a valid deductive argument by the conventional rules of logic. If A is true then it is my understanding that A is necessarily true, cannot be false, by the law of identity. However, this is probably not necessarily the case in the natural language. The natural language is not bound to obey the rules logicians apply to their artificial languages.

B --> ~B appears to be an invalid inference in the artificial language of logic that assumes LNC. The natural language allows for that inference.

Furthermore, one can probably CREATE a logical language where A --> A is true (assume Law of Identity) but A --> ~A is not necessarily false (do not assume Law of Non-Contradiction). Whether this is a useful language would be a separate question.

You don't seem to realize, Brian, that the "rules of logic" are an invention of man. The universe is not bound to obey those rules any more than it's bound to obey the laws and theories of nature as we think we understand them. We observe the universe and write up our descriptions and make up our explanations and we call those well-observed descriptions and well-supported explanations "laws" and "theories" of nature. As scientists, we judge the correctness of these laws and theories on whether our imagination, what we think we have observed and have understood, closely matches what we and others seem to observe in repeated, carefully designed experiments and observations.

BRIAN:
Also, B-->~B has been show{n} to lead to ~B-->B, which in turn leads to B-->~B, and then ad infinitum.


POWELL:
So what? It has also been shown that two straight lines in Euclidean geometry never intersect. Does that mean that two straight lines in a curved geomerty or in the universe never intersect?

BRIAN:
It is of the form of the "Liar" and "Barber" paradoxs {sic}. These all assume LC, and that is why they are considered paradoxes.


POWELL:
Is it possible to create an artificial language in which those conclusions do not follow?

So what if they are paradoxes. That doesn't necessarily mean they are false. The www.dictionary.com definition for paradox: A seemingly contradictory statement that may nonetheless be true.

POWELL:
Can you prove LNC is true?

BRIAN
No. In order to prove it, you would need to assume it.


POWELL:
THANK YOU!

BRIAN:
It is a necessary presupposition for intelligibilty {sic}.


POWELL:
Absurd. Humans appear to be able to speak and think intelligibly without necessarily assuming LNC.

BRIAN:
You could validly argue that the world around us cannot be explained apart from assuming LC. Every person assumes LC and does not live without doing so.


POWELL:
I respectfully disagree. Humans often make statements and appear to hold to beliefs that seem to violate LNC. Would you like me to give you some examples? One of the purposes of taking logic in school is to reduce the frequency of this.

BRIAN:
Because every person must necessarily assume LC, then LC by necessity must be valid.


POWELL:
Why must they necessarily assume LC? You seem to think it's because otherwise nothing is intelligible, nothing makes sense. The frequency of contradictory-type thinking in humans appears to contradict your claim. According to modal logic, what happens to be true, must be possible to be true, and cannot be necessarily false.

"Making sense," Brian, is not the absolute thing you seem to think. It's a relative thing. Some things make more sense than others. As we learn more, certain propositions might make more sense or less sense than the last time we thought about them. Humans often deal with this kind of problem.

BRIAN:
Sincerely,

Brian


POWELL:
Good comments, Brian!

John Powell

[Butters]

"POWELL:
I have come to the conclusion that when people say one thing that can be taken as negative and then later say "I was just kidding" what they really mean is "I mostly meant what I said, but I didn't mean for you to take it quite as negatively as you did."

I don't know how you took it, but I didn't mean for you to take it as negativly as you could have!

'They are too often so caught up in the ideal world of the semantics of their creation, in the artificial logical language they have invented, they don't realize as well as scientists generally do that the real universe is not bound to have the features language gives to it.

Just because the mind can conceive of a thing doesn't mean it can exist outside the mind."

EXACTLY.

[John Powell]

POWELL:
I have come to the conclusion that when people say one thing that can be taken as negative and then later say "I was just kidding" what they really mean is "I mostly meant what I said, but I didn't mean for you to take it quite as negatively as you did."

BUTTERS:
I don't know how you took it, but I didn't mean for you to take it as negativly as you could have!


POWELL:
:thumb:

POWELL:
'They are too often so caught up in the ideal world of the semantics of their creation, in the artificial logical language they have invented, they don't realize as well as scientists generally do that the real universe is not bound to have the features language gives to it.

Just because the mind can conceive of a thing doesn't mean it can exist outside the mind."

BUTTERS:
EXACTLY.


POWELL
:thumb:

John Powell

[Brian]

Hello John!

If "I am hungry" is a true statement for J then how could you know that the statement "I am not hungry" is not a true statement? You can't know that for sure. Just ask him. I'm J.

John, do you know what the law of non-contradiction says? Basically it says something cannot be A and ~A at the same time and in the same relationship. John is hungry. What do you mean by this? Is your body telling you by the grumbles in your stomach that it wants food? If so, it would be appropriate to say that John is A. However, what if you meant something different? That is, what if you were hungry for affection, but not hungry for food? Could you say, “I am hungry and I am not hungry” at the same time and it not be contradictory? Sure. You are using the same words, but you are using them in a different sense. So, LC recognizes equivocation. However, if you say that you are hungry for food, and not hungry for food at the same time and in the same relationship, this is nonsense. It is not rational, and you violate LC.

The universe appears to have dialetheias.

I assume you mean by a dialetheias, that a contradiction does exist. To say that the universe “appears” to have them is a bad argument. David Hume had it correct. As a result of his materialistic, naturalist philosophy he concluded that science has no basis whatsoever to expect uniformity in nature. Science cannot tell us anything about reality in an absolute sense. Being that you are a physicist, you must feel the pressure of this point. Take the Grand Unification Theory for example. Even if science were to come up with an equation that unified the forces, would they ever be able to use it? That is, they would need to know in an absolute sense the state of the universe at a particular time. The Heisenberg (sp?) Uncertainty Principle has demonstrated that this impossible. The point is, time after time, what science has said to be true changes. Just look at the major changes since the Hubble telescope. I am sure you are far more able to speak to this than I am. It is the nature of the beast. So, when we “see” for instance the duality of light (i.e. particle–wave), can we conclude a dialetheias? No way! It is far more prudent to be skeptical of our lack of observational ability and information.

Q: Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right?

This is a hard question. For you to ask it, and for me to answer it, LC must be assumed. So maybe my word “dubious” was not the right word. Maybe I should have said that it is impossible to reject LC. You may say you do, but by even uttering those very words of denial, you assume LC. John, with all due respect, I do not believe you understand the implications of LC.

You seem to be assuming that only mental processing that assumes LNC allows inferences, deriving logical conclusions based on premises. If you define "infer" such that the LNC is an essential part then, probably no, you probably cannot infer things without it. However, if you define "infer" such that the LNC is not an essential part then maybe you could. People often come to conclusions based on modes of thinking considered "illogical" by logicians.

All people are inconsistent. Because people are inconsistent that does not make inconsistencies “logical”. John, LC is a precondition to intelligibility. That means, there is NO intelligibility apart from it. If you deny LC, how can communication take place? If you deny LC, who cares how you define “infer?” Anybody can do with it what they want because there is no LC to violate! Over and over, you assume LC in trying to deny it. You can never get away from it….ever! The denial of LC is not rational. If LC is not valid, then what did I just say? I just said LC is valid…no wait, I said LC in not valid…, no wait, I just said the Queen has yellow teeth…no wait, I just said E=MC^2. Get it? Without LC, NOTHING is intelligible.

"God is love." Assuming you're a Bible believer, is this a true statement? Are you obligated to explain to atheists such as myself the apparent contradiction that an imaginary entity is actually a human emotion based on the evolutionary drive to reproduce?

This is supposed to be an example of an apparent dialetheias. Notice how you assumed the definition of love? (Parenthetically, it is interesting to note that you could not even define “love” without assuming LC.) You define love as being “the evolutionary drive to reproduce.” Is love a univocal term? What if I said I loved ice cream? Does that mean I want to “get it on” with a banana split? Sorry for the crude example. Once again, LC recognizes that terms are used in more than one-way - something cannot be A and ~A at the same time and in the same relationship. “God is love” and “love is the evolutionary drive to reproduce” are not necessarily incompatible. Love changes meanings between the sentences.

Your example concerning the Trinity fails as well. God is one in essence, and 3 in persons. This does not violate LC. If it said God is one in being and 3 in being, or God is one in person and three in person, then there would be an apparent violation. The formulation of the Trinity recognizes the distinction between “person” and “being.”

Then should I take it you can supply a sound deductive argument for that position that does not assume LNC? If it appears impossible to supply such an argument, what justified reason do you have to believe it?

This is an interesting question. We all have presuppositions. These presuppositions are not provable. One such presupposition is the law of LC. So, I cannot prove it. However, I can justify my belief in it by saying that the contrary is impossible. However, I have already said this before and am just repeating myself.

BRIAN: I really was not very accurate here. I should have said that B-->~B has the same proving force as A-->A, i.e. none. POWELL: Absurd. A --> A apparently is a valid deductive argument by the conventional rules of logic.

You need to read my posts more closely. I did not say that A-->A is not a valid implication. I just said that it has no proving force! Big difference. If I assume A, and then draw the implication A from A, what have I done? Nothing. Have I “proved” my assumption by this valid inference? No way! My point was that B-->~B has the same proving force as A-->A.

You don't seem to realize, Brian, that the "rules of logic" are an invention of man.

Hmmmm…I see the rules of logic as a reflection of the way God thinks. Presuppositions – you got ‘em, and I got ‘em!

Humans often make statements and appear to hold to beliefs that seem to violate LNC. Would you like me to give you some examples? One of the purposes of taking logic in school is to reduce the frequency of this.

Absolutely! The point is, these are inconsistencies. They cannot in a consistent way live as if LC were not valid. John, you can argue against this all you want, but every word you utter supports my case. Let’s try to assume that with the next question LC is not valid. Please give me the answer.

In a materialistic, naturalistic universe, how can you account for the universal, invariant, immaterial law of non-contradiction?

Good luck!

Brian

[John Powell]

BRIAN:
Hello John!


POWELL:
Hellow Brian.

POWELL:
“ If "I am hungry" is a true statement for J then how could you know that the statement "I am not hungry" is not a true statement? You can't know that for sure. Just ask him. I'm J. ”

BRIAN:
John, do you know what the law of non-contradiction says?
Basically it says something cannot be A and ~A at the same time and in the same relationship.


POWELL:
I knew that already. In the natural language you need the "in the same relationship" caveat, but it is probably unnecessary when you use logical variables like A and ~A. Whatever A is, then ~A is the logical negation of that.

Although the caveat may solve your logical problem, it doesn't solve your physical problem. It appears this condition of "same relationship," meaning "absolutely exactly the same relationship in all the minute details" is physically impossible to produce in our universe. Since things change as time passes, so do relationships.

Logic works, logic is useful, because things change slowly, relationships are fairly consistent on the time scales of human interaction.

BRIAN:
John is hungry. What do you mean by this? Is your body telling you by the grumbles in your stomach that it wants food? If so, it would be appropriate to say that John is A. However, what if you meant something different? That is, what if you were hungry for affection, but not hungry for food? Could you say, “I am hungry and I am not hungry” at the same time and it not be contradictory? Sure. You are using the same words, but you are using them in a different sense. So, LC recognizes equivocation.


POWELL:
This may be logical language equivocation, Brian, but not necessarily natural language equivocation. This might be an error in CONVERTING natural language statements to the artificial language of logic.

You seem to fail to appreciate, Brian, the likely fact that every time you use a word it's likely to have a slightly different sense. In science we understand this as dealing with factors that might vary, but not "significantly." In communicating effectively, the question would be something like "is the meaning of that term in this context likely to be close enough to the meaning I've been using elsewhere that I can assume the meanings are identically the same, to satisfy my current needs?" To the degree that the answer to this question is "yes" one's confidence in the definitions is strong. When this fails then people try to come to agreement on definitions.

BRIAN:
However, if you say that you are hungry for food, and not hungry for food at the same time and in the same relationship, this is nonsense. It is not rational, and you violate LC.


POWELL:
You may be arguing in a circle. Please present your valid deductive argument supporting this position that includes the term "same relationship." I suspect that you will see that to make the argument valid you will have to define "same relationship" in such a way that it proves only what you assume.

If you won't come up with the argument, I may try.

POWELL:
“ The universe appears to have dialetheias. ”

BRIAN:
I assume you mean by a dialetheias, that a contradiction does exist. To say that the universe “appears” to have them is a bad argument. David Hume had it correct. As a result of his materialistic, naturalist philosophy he concluded that science has no basis whatsoever to expect uniformity in nature.


POWELL:
Absurd.

It's my understanding that because one cannot be absolutely certain of the "Uniformity of Nature Principle" that one cannot be absolutely certain that science will work. In other words, science is not provable using a deductive argument. However, that does NOT mean that there is no rational, sensible, logical basis for accepting science. Science is justified using statistical arguments.

Do you reject science, Brian? Why not? According to what you claim Hume concluded, you have no logically valid justification to accept science as true. Do you expect the Sun to rise tomorrow? Why? According to Hume, since it's possible that the Sun does not exist tomorrow, you have no logically valid justification to believe that the Sun will rise tomorrow.

What you need to realize, Brian, is that sound deductive arguments are not the supremely wonderful things philosophers seem to think they are.

BRIAN:
Science cannot tell us anything about reality in an absolute sense.


POWELL:
Then, I would submit that neither can anyone else.

BRIAN:
Being that you are a physicist, you must feel the pressure of this point. Take the Grand Unification Theory for example. Even if science were to come up with an equation that unified the forces, would they ever be able to use it? That is, they would need to know in an absolute sense the state of the universe at a particular time. The Heisenberg (sp?) Uncertainty Principle has demonstrated that this impossible. The point is, time after time, what science has said to be true changes.


POWELL:
Who said change for the better is bad? Are you saying that philosophy hasn't changed? Are you saying that religious notions haven't changed? I submit that in the face of new information science changes faster than philosophy which changes faster than religion and that this "willingness to change" is an indication of the proper ordering of the methodologies from better to worse.

I had a Sunday School teacher once who criticized science compared with religion, but used the ironic example of improving clock speeds on computers.

BRIAN:
Just look at the major changes since the Hubble telescope. I am sure you are far more able to speak to this than I am. It is the nature of the beast. So, when we “see” for instance the duality of light (i.e. particle–wave), can we conclude a dialetheias? No way! It is far more prudent to be skeptical of our lack of observational ability and information.


POWELL:
Can't you accept on at least a provisional basis that such things might be dialetheias? Or, are you compelled, like giving a statement of religious faith, to logically deny that they are real dialetheias, but due to current ignorance, must be treated as such?

POWELL:
“ Q: Just because you consider rejection of the LNC and support of Dialetheism to be "dubius" does not necessarily infer "false," right? ”

BRIAN:
This is a hard question. For you to ask it, and for me to answer it, LC must be assumed. So maybe my word “dubious” was not the right word. Maybe I should have said that it is impossible to reject LC.


POWELL:
Fair enough. I should have checked the spelling.

BRIAN:
You may say you do, but by even uttering those very words of denial, you assume LC. John, with all due respect, I do not believe you understand the implications of LC.


POWELL:
Perhaps.

POWELL:
“ You seem to be assuming that only mental processing that assumes LNC allows inferences, deriving logical conclusions based on premises. If you define "infer" such that the LNC is an essential part then, probably no, you probably cannot infer things without it. However, if you define "infer" such that the LNC is not an essential part then maybe you could. People often come to conclusions based on modes of thinking considered "illogical" by logicians. ”

BRIAN:
All people are inconsistent. Because people are inconsistent that does not make inconsistencies “logical”.


POWELL:
Correct, unless we define the words so that it is logical.

BRIAN:
John, LC is a precondition to intelligibility.


POWELL:
Perhaps if you define "intelligibility" a certain way, but I don't think that's the case if you use the word close to the way I use it.

BRIAN:
That means, there is NO intelligibility apart from it. If you deny LC, how can communication take place?


POWELL:
How can communication take place in which there is complete ambiguity of meaning, only logical contradictions? In that case, maybe you couldn't. This is not what a rejection of LNC requires, however. A rejection of the LNC or support of dialetheism allows for SOME logical contradictions.

Furthermore, as you said in exaggeration "All people are inconsistent." The fact that they appear to communicate intelligibly even with that evident lack of the LNC suggests that the LNC is not essential to intelligible communication. Some consistency is required, perhaps, but not not necessarily consistency at the level of the LNC.

BRIAN:
If you deny LC, who cares how you define “infer?”


POWELL:
I care. I suspect there are others.

BRIAN:
Anybody can do with it what they want because there is no LC to violate!


POWELL:
I assume you mean "can justifiably do" since people are able to do lots of things that aren't justifiable, even redefining words to suit their own contradictory needs. I'm not sure your conclusion follows. It's similar to the theist argument that if morals aren't from God, aren't "objective" in the way they think they must be, then there would be no good reason for people to be moral.

BRIAN:
Over and over, you assume LC in trying to deny it.


POWELL:
I think you are confusing absolute agreement with LNC, Brian, with approximate agreement. I can communicate with you assuming the LNC is true for the vast majority of my comments, yet deny it in specific cases.

BRIAN:
You can never get away from it….ever! The denial of LC is not rational. If LC is not valid, then what did I just say?


POWELL:
We can sometimes go to it . . . sometimes. The acceptance of dialetheism is rational (associated with or requiring the use of the mind). If the possibility of dialetheism is statistically strong, then what will you write?

Now, Brian, tell me honestly. Although you may be confused as to what I meant by the words in response to your question, did I not communicate anything of intelligibility? Was it completely unintelligible?

I tried to replace your "A's" which you believe to be true statements with "~A's" which I believe to be true statements.

BRIAN:
I just said LC is valid…no wait, I said LC in not valid…, no wait, I just said the Queen has yellow teeth…no wait, I just said E=MC^2. Get it? Without LC, NOTHING is intelligible.


POWELL:
I read what you just wrote, Brian, and felt like I understood you well enough. Did you understand what you were writing just now or was it completely inintelligible to you?

POWELL:
“ "God is love." Assuming you're a Bible believer, is this a true statement? Are you obligated to explain to atheists such as myself the apparent contradiction that an imaginary entity is actually a human emotion based on the evolutionary drive to reproduce? ”

BRIAN:
This is supposed to be an example of an apparent dialetheias. Notice how you assumed the definition of love? (Parenthetically, it is interesting to note that you could not even define “love” without assuming LC.) You define love as being “the evolutionary drive to reproduce.” Is love a univocal term? What if I said I loved ice cream? Does that mean I want to “get it on” with a banana split? Sorry for the crude example. Once again, LC recognizes that terms are used in more than one-way - something cannot be A and ~A at the same time and in the same relationship. “God is love” and “love is the evolutionary drive to reproduce” are not necessarily incompatible. Love changes meanings between the sentences.


POWELL:
Aren't there many cases of this problem, Brian? How do you know, then whether the terms satisfy your logical condition that they be used in "the same relationship?" How would you ever know? It appears to me that to do logic, you ASSUME they are being used in the same way and proceed from there.

BRIAN:
Your example concerning the Trinity fails as well. God is one in essence, and 3 in persons. This does not violate LC. If it said God is one in being and 3 in being, or God is one in person and three in person, then there would be an apparent violation. The formulation of the Trinity recognizes the distinction between “person” and “being.”


POWELL:
Good enough for now. Let's not get into a debate about the trinity here.

POWELL:
“ Then should I take it you can supply a sound deductive argument for that position that does not assume LNC? If it appears impossible to supply such an argument, what justified reason do you have to believe it? ”

BRIAN:
This is an interesting question. We all have presuppositions. These presuppositions are not provable. One such presupposition is the law of LC. So, I cannot prove it. However, I can justify my belief in it by saying that the contrary is impossible.
However, I have already said this before and am just repeating myself.


POWELL:
So, Brian, you can logically justify believing something is true by SAYING that the contrary is impossible. Is that your position? Perhaps you'd rather use an appeal to authority rather than an argument by assertion.

POWELL:
“ BRIAN: I really was not very accurate here. I should have said that B-->~B has the same proving force as A-->A, i.e. none.

POWELL: Absurd. A --> A apparently is a valid deductive argument by the conventional rules of logic. ”

BRIAN:
You need to read my posts more closely. I did not say that A-->A is not a valid implication. I just said that it has no proving force! Big difference.


POWELL:
And, what would that difference be, Brian? Were you aware that I have posted my argument (presented in the philosophy section) that M.P., when assumed to be merely valid is essentially a circular argument?

If you were to accept that the premise "A" is true, would you be persuaded to accept that the conclusion "A" is true? Can you think of a kind of argument that has more "proving" or "persuasive" force than one that satisifies the law of identity?

Can you supply a valid deductive argument that does not essentially assume what it concludes to be true?

BRIAN:
If I assume A, and then draw the implication A from A, what have I done? Nothing. Have I “proved” my assumption by this valid inference? No way! My point was that B-->~B has the same proving force as A-->A.


POWELL:
You seem to be equivocating on terms, Brian. You say "valid," but you seem to be speaking about "sound." Valid arguments do NOT prove the truth of their conclusions. They argue that *IF* the premises happened to be true *THEN* the conclusion to that valid argument would have to be true, could not be false. On the other hand, sound arguments argue that the premises ARE true and the argument is valid so the conclusion is true, cannot be false.

You should consider the following to be a valid deductive argument, since it follows the M.P. form, but the conclusion, you will agree, is false.

1. If dogs fly then snakes sing opera.
2. dogs fly
3. therefore, snakes sing opera.

This argument does not PROVE that snakes sing opera, right?

In similar manner the valid, not sound, argument "If A then A" does not prove A, it only argues that if the premise A happens to be true then the conclusion A would have to be true, could not be false.

POWELL:
“ You don't seem to realize, Brian, that the "rules of logic" are an invention of man. ”

BRIAN:
Hmmmm…I see the rules of logic as a reflection of the way God thinks. Presuppositions – you got ‘em, and I got ‘em!


POWELL:
Fair enough for now.

POWELL:
“ Humans often make statements and appear to hold to beliefs that seem to violate LNC. Would you like me to give you some examples? One of the purposes of taking logic in school is to reduce the frequency of this. ”

BRIAN:
Absolutely! The point is, these are inconsistencies. They cannot in a consistent way live as if LC were not valid. John, you can argue against this all you want, but every word you utter supports my case. Let’s try to assume that with the next question LC is not valid. Please give me the answer.


POWELL:
Remember, Brian, the LNC indicates that it is never allowed for contradictions at all, anywhere, anytime, at any minute level. When I deny that, I can be saying that there are contradictions in some places at some times even if at a relatively insignificant level. The measurable difference between a universe where LNC is true and only approximately true may be very slight.

BRIAN:
In a materialistic, naturalistic universe, how can you account for the universal, invariant, immaterial law of non-contradiction?


POWELL:
Reply 1: :yipee:

Reply 2: Complex question. The question assumes that the LNC is true which I was supposed to assume wasn't the case. I claim that LNC is not the universal, invariant thing you seem to think it is. It is a very useful axiom, however. There are notable, but rare counter-examples evident in the physical universe. More frequent counter-examples exist in the minds and words of rational (i.e. thinking) human beings. Denial of LNC is not necessarily a denial of a less universal version, the Law of "Almost always there are no contradictions."

Reply 3: At the non-materialistic, non-naturalistic spirit world, how can we account for the occasional existence of dialetheia?

BRIAN:
Good luck!

Brian


POWELL:
How did I do?

John Powell.

[Brian]

Hello John! :smile:

It appears this condition of "same relationship," meaning "absolutely exactly the same relationship in all the minute details" is physically impossible to produce in our universe.

Naw. That is not what it means. I am a professor at BYU. I am not a professor at BYU. Professorship at BYU might look very different. One might be an Astronomer, another might be a linguist. Yet, will still have a contradiction.

According to what you claim Hume concluded, you have no logically valid justification to accept science as true.

Our senses are generally reliable. Therefore, Science can be generally reliable.

Can't you accept on at least a provisional basis that such things might be dialetheias?

I have given you my justification for assuming LC. I have also pointed out that Science is often wrong. So let me ask you, what is more reasonable, beliving in contradictions because science has come up with something it cannot explain, or beliving in LC because of its consistency inspite of Sciences inability to explain something?

How can communication take place in which there is complete ambiguity of meaning, only logical contradictions? In that case, maybe you couldn't. This is not what a rejection of LNC requires, however. A rejection of the LNC or support of dialetheism allows for SOME logical contradictions.

This is where you are mistaken. You can arbitrarily choose to ignore LC when it soots you if you want. However, it is completely arbitrary and you would have to allow someone else to do the same. What if you were driving down the road, would you want someone to arbitrarily choose the a red light is a green light? You cannot live this way. It is interesting to note that LC precludes an arbitrary use of it. It is an all or nothing proposition.

I care. I suspect there are others.

Why would you care if it ok to ignore LC? Perhaps you care because you can't ignore LC.

I can communicate with you assuming the LNC is true for the vast majority of my comments, yet deny it in specific cases.

This is an arbitrary choice you are making. You can choose to go against that which is true. However, it does not make it not true. Deep down you know you can't deny LC. Frankly, I can't understand why you would want to? MAybe you realize that if LC is a universal invariant immaterial law, then your world view cannot account for it. Perhaps that is what is motiviating this discussion?

The acceptance of dialetheism is rational (associated with or requiring the use of the mind)

Wow. How would you define irrational? Is it something not associated with the mind? Whatever.

So, Brian, you can logically justify believing something is true by SAYING that the contrary is impossible.

It is not an assertion. Every human being necessarily assumes LC. Living contrary to LC is impossible. If it is not, explain how it is not. The evidence for my position is the world around you. Just take a look!

You seem to be equivocating on terms, Brian.

You need to go back and read my posts more carefully. No equivocation taking place.

Remember, Brian, the LNC indicates that it is never allowed for contradictions at all, anywhere, anytime, at any minute level. When I deny that, I can be saying that there are contradictions in some places at some times even if at a relatively insignificant level. The measurable difference between a universe where LNC is true and only approximately true may be very slight.

The is NO basis for your claim. If LC does not apply all of the time, then it does not apply at all. The field of Quantum Mechanics is not the empirical foundation you should want to use to deny LC. Again, wouldn't it seem far more reasonable to say that we just do not understand what we are seeing, rather than denying LC? John, you are an educated man. This whole line of thinking seems so bizarre.

How did I do?

You did well. you have a great sense of humor. By the way, now that we are assuming LC once more, my question was when do you think the Jazz will get a point guard? :brow:

Thanks for the conversation. I think I will be moving on.

Sincerely,

Brian

[nomad]

i like the concepts of newtonian vs. einsteinian physics. so let's go from there.

a couple of those objections (i think 2 and 3) look like traditional fallacies of equivocation. that is a good place to start, and probably the right attitude to dealing with all of them.

as you already know, everything has assumptions. and it's no surprise that using a syllogism has assumptions too, such as LNC. even statements have assumptions... are the statements

P1: The sum of the angles in a triangle is always 180 degrees.
P2: 3 + 5 = 10

true or false? most people would answer 'true' for P1 and 'false' for P2, but of course this is because of basic assumptions most people hold - there are non-euclidian geometries for which P1 is false, and if i was a programmer in 1970 working in octal, then P2 would be, in fact, true. so in fact, the difficulties are not because it is incorrect to attempt to postulate, but that a postulate may itself have 'hidden assumptions' that have to be made clear for a truth or falsehood to show itself.

many times people who cannot agree on what seem like solid arguments fall to this trap... they are really disagreeing with each other's premises based on unspoken assumptions. this seems similar to what you are saying?

fallacies are similar, and i believe most fallacies (which occur in text) can be rewritten as a syllogism exposing the error:

P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority.
C: Tillamook butter is the best tasting.

ok, this is a fallacy, but we can only dismiss it as a fallacy currently. let's rewrite it:

P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority on basketball.
P4: John is an authority on butter.
C: Tillamook butter is the best tasting.

now, it is an actually valid argument - but not sound, since P4 is false. we have converted an improper and fallacious syllogism to a valid but unsound syllogism we can work with.=

ok, so we all know that LNC is an assumption for a syllogism, and sometimes it appears to not be true. so we end up (like you said) where if we can accept LNC as an assumption for the syllogism, we can accept the syllogism as perfectly valid.

the nice thing is that like the above, i believe that MOST syllogisms can be turned from an invalid syllogism to a valid syllogism simply by making the assumptions explicit, by adding caveats to the premises.

this takes care of everything so far except the dialethias. however, i think we still have to prove they exist in the real world. let's look at your examples, and see if there are any unspoken assumptions behind the apparent contradiction, which might remove the contradiction, or if the problem goes away when properly constrained:

the first example is the law of conservation of matter, and the law of conservation of energy. and the apparent contradiction. as you have noted, there is no contradiction any more; we just had insufficient knowledge. so this is only an 'apparent' dialethia, not a true one.

and, i might add, because of assumptions which were not even know... these laws work because there is no matter to energy conversions. so, if you add this as a constraint, then the laws work, and there is no dialethia. if you remove it as a constraint, then you are attempting to use a law outside the scope in which it is defined (though, the scope was not known when the laws were first proposed, as no one knew matter and energy could transmute).

2 and 3 might be problems with modelling - as you already know (or at least as i understand it), science deals with what things ARE only on a surface level... it deals much more with how things WORK. if an atom, or a cell, were some kind of optical illusion, and didn't really look the way we thought they do, it would be OK because our models work, they work the way we expect them to.

2 (light as wave vs. particle) i'm not sure is a contradiction... what we really mean is that light ACTS like a wave sometimes, and like a particle sometimes. neither is a complete description. what we have is another case of #1. if
A = 'Light acts like a wave'
and
B = 'Light acts like a particle',
i do not see in this case that B = ~A, anymore than 'my shirt is red' and 'my shirt is blue' is a contradiction; when put that way, both could be true. they are not contradictions, they are simply incomplete.

i believe 3 will fall in the same category.

the rest seem like just normal problems with equivocation going between language and symbolism... nothing that can't be cleared up by clarifying your assumptions.

or have i missed it altogether?

[John Powell]

POWELL:
To BRIAN.

BRIAN:
Hello John!


POWELL:
Hello Brian!

POWELL:
It appears this condition of "same relationship," meaning "absolutely exactly the same relationship in all the minute details" is physically impossible to produce in our universe.

BRIAN:
Naw. That is not what it means. I am a professor at BYU. I am not a professor at BYU. Professorship at BYU might look very different. One might be an Astronomer, another might be a linguist. Yet, will still have a contradiction.


POWELL:
Nice try, Brian, but this won't work in the natural language of English.

When you say "professor" do you mean a teacher? I'm technically staff at UVSC, but I don't always correct my students when they call me "professor Powell"? Should I?

When you say "professor" do you mean a full professor or are you including a "sub-professor" (assistant or associate) as a professor? Normally, "sub-professors" are considered professors.

In English you could mean by those words (but you would be encouraging confusion): I am an assistant professor at BYU, but I am not a full professor. Isn't that correct?

In other words. If asked:

Are you a professor at BYU? If you were an assistant professor, you could truthfully answer either yes or no. Yes, you are an assistant professor. No, you are not a full professor.

It is the artificial language of logic that demands that linguistic variables like "professor" have the same meaning in both sentences. Natural languages don't require such a thing.

For example, is a Lt. a Captain? Is a Lt. Coronel a Coronel? Is a Lt. General a General? It is my understanding that Lt. Generals are usually considered generals, but Lt. Coronels are only sometimes considered Coronels, and Lt. (Captains) are never considered Captains.

POWELL:
According to what you claim Hume concluded, you have no logically valid justification to accept science as true.

BRIAN:
Our senses are generally reliable. Therefore, Science can be generally reliable.


POWELL:
Which, in your view, is a more reliable source of truth about our universe, Brian: Philosophy or Science?

POWELL:
Can't you accept on at least a provisional basis that such things might be dialetheias?

BRIAN:
I have given you my justification for assuming LC. I have also pointed out that Science is often wrong.


POWELL:
Is philosophy also often wrong? Was Aristotle right about falling objects? What about the exaggerated claims of introductory logic texts concerning so-called valid deductive arguments? Perhaps it's that scientists are more willing than philosophers to admit when they are wrong.

BRIAN:
So let me ask you, what is more reasonable, beli{e}ving in contradictions because science has come up with something it cannot explain, or beli{e}ving in LC because of its consistency inspite {sic} of Sciences inability to explain something?


POWELL:
Notice that you are using a statistical, rather than a deductive argument, Brian. If it wasn't for scientists, philosophers probably would still be relying exclusively on deductive arguments.

I think it is more reasonable to allow for the possibility of some dialetheias in our universe based upon the physical experiments of scientists and the way people speak using natural language than to reject that based upon the wishes of philosophers for a logical language that doesn't allow such things. What do you think is more reasonable?

If a philosopher says there's nothing illogical about faster than light travel or reverse time travel, should we accept that such things are physically possible?

POWELL:
How can communication take place in which there is complete ambiguity of meaning, only logical contradictions? In that case, maybe you couldn't. This is not what a rejection of LNC requires, however. A rejection of the LNC or support of dialetheism allows for SOME logical contradictions.

BRIAN:
This is where you are mistaken.


POWELL:
How is that? The LNC states something to the effect that "there are no dialethieas." That would be contradicted if there were only one dialetheia, right?

BRIAN:
You can arbitrarily choose to ignore LC when it soots {suits} you if you want. However, it is completely arbitrary and you would have to allow someone else to do the same.


POWELL:
So what? Should I reject the possibility of dialetheias because of ethical considerations?

BRIAN:
What if you were driving down the road, would you want someone to arbitrarily choose the a red light is a green light? You cannot live this way.


POWELL:
Sure I could. Not as efficiently, I would think.

But, so what? Should I reject the possibility of dialetheias because it would make my life more difficult to live if I accepted dialetheias? Should I reject dialetheias due to wishful thinking, because I don't want them to exist?

BRIAN:
It is interesting to note that LC precludes an arbitrary use of it. It is an all or nothing proposition.


POWELL:
That's right. Be aware that absolutes are rarely true.

POWELL:
I care. I suspect there are others.

BRIAN:
Why would you care if it{'s} ok to ignore LC? Perhaps you care because you can't ignore LC.


POWELL:
I'm not "ignoring" LNC, Brian, I'm suggesting that it is not true. I'm suggesting that there might be some dialetheias in the universe. On the other hand, to assume that everything is a dialetheia would be incredibly unwise.

POWELL:
I can communicate with you assuming the LNC is true for the vast majority of my comments, yet deny it in specific cases.

BRIAN:
This is an arbitrary choice you are making. You can choose to go against that which is true. However, it does not make it not true. Deep down you know you can't deny LC.


POWELL:
Are you a mind reader? You are wrong about my "inner" thoughts. As a free agent I can deny whatever I want. Whether I'd be justified in doing so is another question.

BRIAN:
Frankly, I can't understand why you would want to? MAybe you realize that if LC is a universal invariant immaterial law, then your world view cannot account for it. Perhaps that is what is motiviating this discussion?


POWELL:
I hadn't thought of it quite that way. It was more my efforts to put philosophy below science that was the motivation. Certainly, desires to support my current atheism was involved somehow.

POWELL:
The acceptance of dialetheism is rational (associated with or requiring the use of the mind)

BRIAN:
Wow. How would you define irrational? Is it something not associated with the mind? Whatever.


POWELL:
In a sense, yes.

One can think of irrational as bad thinking and rational as thinking (period), but especially good thinking. Notice how natural language definitions do not necessarily obey the LNC rules of the artificial language of logic.

POWELL:
So, Brian, you can logically justify believing something is true by SAYING that the contrary is impossible.

BRIAN:
It is not an assertion. Every human being necessarily assumes LC.

POWELL:
False. People who talk about dialetheism don't seem to make that assumption. I'm not assuming that to be the case. However, to have this conversation, I'm assuming that most things do not contradict in a significant way.

BRIAN:
Living contrary to LC is impossible. If it is not, explain how it is not. The evidence for my position is the world around you. Just take a look!


POWELL:
Is it possible for the mind of man, Brian, to consider that an electron is both a particle and a wave, a wavicle?

Is it possible for the mind of man, Brian, to believe that God is 1 God and God is three Gods at the same time?

Is it possible for the mind of man, Brian, to assume that essentially all daily events are due to the non-supernatural laws of nature and to believe that many of them are due to the supernatural will of God?

Is it possible for the mind of man, Brian, to both "love" something and "dislike" it at the same time? In other words, can someone have feelings of love and dislike at the same time for the same thing?

The universe appears to have some examples of dialetheias. Users of the natural language seem to use dialetheias more than you want to admit.

POWELL:
You seem to be equivocating on terms, Brian.

BRIAN:
You need to go back and read my posts more carefully. No equivocation taking place.


POWELL:
Ok. This was the context.

BRIAN:
If I assume A, and then draw the implication A from A, what have I done? Nothing. Have I "proved" my assumption by this valid inference? No way! My point was that B-->~B has the same proving force as A-->A.

POWELL:
You seem to be equivocating on terms, Brian. You say "valid," but you seem to be speaking about "sound." Valid arguments do NOT prove the truth of their conclusions. They argue that *IF* the premises happened to be true *THEN* the conclusion to that valid argument would have to be true, could not be false. On the other hand, sound arguments argue that the premises ARE true and the argument is valid so the conclusion is true, cannot be false.


POWELL:
Isn't it true Brian that if you believe the premise A is true then one can "prove" to you that the conclusion A is true by virtue of the following argument?:

If A then A.

The purpose of valid deductive arguments is not to prove that the conclusion is true, that's the purpose of sound deductive arguments. The purpose of valid deductive arguments is to prove that IF the premises happened to be true THEN the conclusion would have to be true.

POWELL:
Remember, Brian, the LNC indicates that it is never allowed for contradictions at all, anywhere, anytime, at any minute level. When I deny that, I can be saying that there are contradictions in some places at some times even if at a relatively insignificant level. The measurable difference between a universe where LNC is true and only approximately true may be very slight.

BRIAN:
The{re} is NO basis for your claim. If LC does not apply all of the time, then it does not apply at all. The field of Quantum Mechanics is not the empirical foundation you should want to use to deny LC. Again, wouldn't it seem far more reasonable to say that we just do not understand what we are seeing, rather than denying LC? John, you are an educated man. This whole line of thinking seems so bizarre.


POWELL:
I am rejecting a philosophical position that is based on thought experiments, not physical experiments. Does that seem bizarre to you?

POWELL:
How did I do?

BRIAN:
You did well. you have a great sense of humor. By the way, now that we are assuming LC once more, my question was when do you think the Jazz will get a point guard?


POWELL:
Isn't John Stockton a point guard?

BRIAN:
Thanks for the conversation. I think I will be moving on.

Sincerely,

Brian


POWELL:
I might do the same thing if I were in your shoes.

Thanks for the discussion.

John Powell

[John Powell]

POWELL:
To NOMAD.

NOMAD:
i like the concepts of newtonian vs. einsteinian physics. so let's go from there.

a couple of those objections (i think 2 and 3) look like traditional fallacies of equivocation. that is a good place to start, and probably the right attitude to dealing with all of them.

as you already know, everything has assumptions. and it's no surprise that using a syllogism has assumptions too, such as LNC. even statements have assumptions... are the statements

P1: The sum of the angles in a triangle is always 180 degrees.
P2: 3 + 5 = 10

true or false? most people would answer 'true' for P1 and 'false' for P2, but of course this is because of basic assumptions most people hold - there are non-euclidian geometries for which P1 is false, and if i was a programmer in 1970 working in octal, then P2 would be, in fact, true. so in fact, the difficulties are not because it is incorrect to attempt to postulate, but that a postulate may itself have 'hidden assumptions' that have to be made clear for a truth or falsehood to show itself.


POWELL:
I like your comments. What if one of their assumptions, rather than proof, is that M.P. has the features they claim it has?

My point is the following:

Would you be willing to risk everything in the universe by claiming that the following statement is absolutely true without any reservation whatsoever, without needing additional premises even?

1. All humans are mortal.
2. Socrates is human.
3. therefore, Socrates is mortal.

Logicians like Copi and Cohen seem to think they are justified in saying, "Yes." I think no.

COPI & COHEN pg. 44:
If a deductive argument is valid, no additional premisses could possibly add to the strength of that argument. For example, if all humans are mortal, and if Socrates is human, we may conclude without reservation that Socrates is mortal --- and that conclusion will follow from those premisses no matter what else may be true in the world, and no matter what other information may be discovered or added.

POWELL:
Even if you allow for the assumption of LNC (which is a reasonable one for most purposes), there are other problems, as I indicate in my other proofs.

NOMAD:
many times people who cannot agree on what seem like solid arguments fall to this trap... they are really disagreeing with each other's premises based on unspoken assumptions. this seems similar to what you are saying?


POWELL:
Sort of. It's more like I'm pointing out the assumptions they didn't realize they were making.

I think what's happening is that philosophical innovators create new logical languages or make improvements to old ones, but the philosphical users fail to appreciate the fact that these are man-made linguistic tools. They are "theoretical" languages. They are not how the universe necessarily really is, nor even how natural languages (like English) actually work. As a scientist, this important distinction between theory and experiment is more strictly emphasized. It's as if too many philosophers are believing their ideal forms are more real than the objects in the universe those forms are supposed to be modeling or representing.

NOMAD:
fallacies are similar, and i believe most fallacies (which occur in text) can be rewritten as a syllogism exposing the error:

P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority.
C: Tillamook butter is the best tasting.

ok, this is a fallacy, but we can only dismiss it as a fallacy currently. let's rewrite it:


POWELL:
Based on the wording of your argument this is a valid argument. You said John is an authority, right? I suspect you're confusing the "appeal to authority" fallacy with the "appeal to inappropriate authority" fallacy. I don't blame you for being confused since logicians seem to want to intentionally confuse these and persuade the readers that only one is really a fallacy.

NOMAD:
P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority on basketball.
P4: John is an authority on butter.
C: Tillamook butter is the best tasting.

now, it is an actually valid argument - but not sound, since P4 is false. we have converted an improper and fallacious syllogism to a valid but unsound syllogism we can work with.=


POWELL:
This one is also valid. However, both arguments are unsound because premise P1 is false.

NOMAD:
ok, so we all know that LNC is an assumption for a syllogism, and sometimes it appears to not be true. so we end up (like you said) where if we can accept LNC as an assumption for the syllogism, we can accept the syllogism as perfectly valid.


POWELL:
Yes. If LNC is true then we might be able to accept the argument as valid.

NOMAD:
the nice thing is that like the above, i believe that MOST syllogisms can be turned from an invalid syllogism to a valid syllogism simply by making the assumptions explicit, by adding caveats to the premises.


POWELL:
So what? You could try to turn them into identities too. That would be less work, but it doesn't solve all the problems I outlined. For example, Just because you use the same word twice in the same sentence does not mean it has the same meaning in both places. You might word for word repeat yourself in a sentence, but mean something different each time you say it.

NOMAD:
this takes care of everything so far except the dialethias. however, i think we still have to prove they exist in the real world. let's look at your examples, and see if there are any unspoken assumptions behind the apparent contradiction, which might remove the contradiction, or if the problem goes away when properly constrained:

the first example is the law of conservation of matter, and the law of conservation of energy. and the apparent contradiction. as you have noted, there is no contradiction any more; we just had insufficient knowledge. so this is only an 'apparent' dialethia, not a true one.


POWELL:
On of my points is that for a time one might have been justified in accepting that there was a dialetheia there.

NOMAD:
and, i might add, because of assumptions which were not even know... these laws work because there is no matter to energy conversions. so, if you add this as a constraint, then the laws work, and there is no dialethia. if you remove it as a constraint, then you are attempting to use a law outside the scope in which it is defined (though, the scope was not known when the laws were first proposed, as no one knew matter and energy could transmute).


POWELL:
If you allow for modern physics then you can remove the contradiction. If you don't then there could be a contradiction, right?

NOMAD:
2 and 3 might be problems with modelling - as you already know (or at least as i understand it), science deals with what things ARE only on a surface level... it deals much more with how things WORK. if an atom, or a cell, were some kind of optical illusion, and didn't really look the way we thought they do, it would be OK because our models work, they work the way we expect them to.

2 (light as wave vs. particle) i'm not sure is a contradiction... what we really mean is that light ACTS like a wave sometimes, and like a particle sometimes. neither is a complete description. what we have is another case of #1. if
A = 'Light acts like a wave'
and
B = 'Light acts like a particle',
i do not see in this case that B = ~A, anymore than 'my shirt is red' and 'my shirt is blue' is a contradiction; when put that way, both could be true. they are not contradictions, they are simply incomplete.


POWELL:
That is an acceptable way to look at it, to deny that there is a contradiction and to assume that our understanding is incomplete. However, my point is that alternative philosophical approaches might be justified, such as accepting that light is both a wave and a particle at the same time. To accept that light is a "wavicle" a wave-particle thing might be justified. Which approach to adopt should be decided by correspondence to experiments, utility in terms of mathematical theories, and such things. It should not be decided merely because we don't want there to be dialetheias. Nature is the way it is regardless of what we may want.

A blue shirt could also be a red shirt yes. Therefore, it’s a problem when you try to convert such terms to an artificial logical language. Consider the following logical questions.

Jack and Bob are each wearing a shirt. One has a blue shirt on. The other has a red shirt on. Jack has a blue shirt on. What color is Bob’s shirt?

Which is the correct answer?

1) definitely red.
2) probably red, but possibly blue or red / blue mixed.
3) unknown.
4) something else (please explain)

Next questions: How many shirts is each one wearing and could they be wearing the same shirt? Could Jack and Bob be the same person or a siamese twin?

The point is that the real world and natural language is sometimes a lot more complicated logically then the artificial logical world philosophers create.

NOMAD:
i believe 3 will fall in the same category.

the rest seem like just normal problems with equivocation going between language and symbolism... nothing that can't be cleared up by clarifying your assumptions.

or have i missed it altogether?


POWELL:
I think you're understanding quite well.

John Powell

[psychopath]

I know that my first post to you in this thread was a while back, but I still want to make a few comments.

I'm not going to go point by point, because I pretty much agree with what you're saying.

Logic is an axiomatic system, its most fundamental axiom being that A=A. However, as Godel's Incompleteness Theorem showed, no axiomatic system can be both wholly complete and internally consistent at the same time. So, consider the axiom A=A. Can this statement be proven to be true? Any proof would either involve logic, in which case I'm assuming the system's validity in order to prove its fundamental axiom, or it would involved some proof method outside of logic, in which case whatever I use to prove the truth of the axiom now becomes part of the system, and it must now be proven in and of itself. IOW, at any given time, an axiomatic system contains more true statements than it can possibly prove according to its own defining set of rules.

What you seem to be doing is attacking the axioms of deductive logic; for example, in your dialetheism argument, you are denying the truth of A=A, by saying that it may be possible for A=~A. Of course, you will succeed in this endeavor, because the fundamental axioms of some system are unprovable. Here's a simpler way, in my mind, of denying the LNC:

Me: I deny the LNC.

Other Dude: But by denying it you are affirming its veracity, because that very statement assumes that the LNC is the LNC, and that your denial = your denial, etc. Your statement is contradictory.

Me: But I don't care if I "contradict" myself, because I deny the LNC in the first place!

I guess I would just say that, on a fundamental level, it is possible to argue against deductive arguments in such a fashion, but it doesn't seem like a very practical move at all. If the LNC is not assumed by both parties engaging in communication or a debate, I don't see how anything can be accomplished, becaues anything that is said or written may not be what is said or written.

[John Powell]

POWELL:
To Psychopath. I liked your reply to LNC problems.

PSYCHOPATH:
I'm not going to go point by point, because I pretty much agree with what you're saying.


POWELL:
YES! :yipee:

Part of my point is that introductory logic texts exaggerate the certainty of so-called valid deductive arguments. Arguments in the artificial language of logic might be certain, given the assumptions, but that does not mean that the similar-looking arguments in the natural language (like English), with all the problems of the natural language and problems with the real universe, will be similarly certain.

PSYCHOPATH:
I guess I would just say that, on a fundamental level, it is possible to argue against deductive arguments in such a fashion, but it doesn't seem like a very practical move at all. If the LNC is not assumed by both parties engaging in communication or a debate, I don't see how anything can be accomplished, becaues anything that is said or written may not be what is said or written.


POWELL:
YES! :yipee:

Part of my point is that logic is a special artificial language useful to help determine whether certain statements in the natural language (like English) are correct and certain arguments are valid or whatever. However, just because an argument form in the artificial language of logic is invalid does not mean that an argument in the natural language of the same form is invalid. Sometimes essential information is lost in the "translation." Furthermore, just because a certain statement is "incorrect" in the logical language (e.g., it violates LNC) does NOT mean that the statement in the natural language is false. It's "logically false." It violates the well-respected, powerful rules of logic.

Logic is a tool to understand language and to understand the universe around us. Like mathematics (e.g. Euclidean Geometry) it's an artificial world that might not correspond in all ways to the real universe. It might not be "true" in a correspondence sort of way. To the extent that logic and mathematics "match" the real universe, they are useful to understand the same.

John Powell

[nomad]

POWELL:

I like your comments. What if one of their assumptions, rather than proof, is that M.P. has the features they claim it has?


of course it is. *proof* requires using some sort of logical method. i do not know of *any* logical method that sits on nothing (how do you get to 'logic without logic'?)

fwiw, MP afaik has good grounding in *science* - i.e. MP is assumed in the same way that science works... it is rational (it appeals to 'common sense'), it is empirical (if we assume MP, we can come to sensible conclusions about the world around us), and when we use MP to try to prove other things, those other things generally seem to match what we expect from MP. i don't see this as a wrong assumption.


Would you be willing to risk everything in the universe by claiming that the following statement is absolutely true without any reservation whatsoever, without needing additional premises even?

1. All humans are mortal.
2. Socrates is human.
3. therefore, Socrates is mortal.

Logicians like Copi and Cohen seem to think they are justified in saying, "Yes." I think no.


let's reduce this to:

1. 'p->q' is true
2. p is true
C. q is true

note that even THIS has an assumption, but here i am reducing them to reasonable assumptions for a theoretical language, namely, we both agree on what the symbols mean, what 'is true' means, and that those symbols are defined in the theoretical language such that they cannot change their values, either truth values or what they actually assert.

the logical language has much stricter rules than natural language.

with these caveats, yes, i would risk everything in the universe on this (in fact, i AM risking everything on this, as it's part of my belief in God).

i'll explain why in a minute.

POWELL:

Even if you allow for the assumption of LNC (which is a reasonable one for most purposes), there are other problems, as I indicate in my other proofs.


let's take one of those, the equivocation in time fallacy.
P1: all humans are mortal.
P2: Socrates is human.
C: Socrates is mortal.

You claim that you shouldn't actually trust this, because say 'human' could mean different things in P1 and P2.

i claim we can deal with this by making things explicit:

P1: If X is human, then X is mortal.
P2: Socrates is human.
C: Socrates is mortal.

now, let's assume we did have a fallacy of equivocation in time. if this is true, then we would write this in symbolic form as:

P1: 'if P, then Q' is true.
P2: 'R' is true.
C: ??

it is simply no longer a valid argument.


i believe that the THEORETICAL form CANNOT be violated. however, i would agree that it is fairly easy to write a natural argument that looks valid but isn't. but, for every single one of these arguments, PROPER conversion to the theoretical language, obeying the rules of the theoretical language, and making all assumptions clear that aren't clear, will show all such arguments to be invalid.

in most cases, we do a bit of 'hand-waving', because we can't always establish our assumptions. we can argue about whether 'socrates' means the same in premise 1 or premise 2, but if we had to do that all the time conversations, and both arguments and all kinds of science, would proceed very slowly. most conversations, and contexts in which arguments appear (and arguments DO appear in contexts normally), have a set of implicit assumptions which govern the argument.

occasionally, people will find that i was assuming something in my argument you don't acknowledge to be true; in that base, you may have to examine assumptions. but practically, we don't do that, and we usually understand what that means.


POWELL:

Sort of. It's more like I'm pointing out the assumptions they didn't realize they were making.

I think what's happening is that philosophical innovators create new logical languages or make improvements to old ones, but the philosphical users fail to appreciate the fact that these are man-made linguistic tools. They are "theoretical" languages. They are not how the universe necessarily really is, nor even how natural languages (like English) actually work.


mathematics is ALSO this sort of logical language. it would actually be ridiculous to even talk about mathematics 'matching' the universe - 3 is 3. what is 3? it is nothing, it is a concept. a very useful one, but only an ephemeral mist. but, when we describe the universe in this theoretical language, with much more defined rules than the natural universe, we can say things that, when reflected back into the real universe, turn out to be valid statements.

philosophical languages of logic are no different.


As a scientist, this important distinction between theory and experiment is more strictly emphasized. It's as if too many philosophers are believing their ideal forms are more real than the objects in the universe those forms are supposed to be modeling or representing.


it is no more real, or less real, than mathematics. if i have the newtonian distance equation s = vt, and i say i was traveling in a straight line for 3 seconds at 3m/s, do i have any justification for saying i have moved 9m, which is a result i got by working in a purely theoretical domain?

in one sense, i some agree with you. but i don't see how science is in any way superior. you assert that logic isn't a good predictor of reality because it has unproven assumptions; i argue that science also has an unproven assumption, the law of causality. without LC, science cannot make any meaningful statements about the universe.

you say LC has a better empirical basis than MP? i would disagree.

and also... i could say that science, in one sense, doesn't require anything more than LC. in some sense, you can do some science without MP and without philosophy of any kind... i can assert 'the sun will come every morning', and every morning for a long time i can see if the sun comes up. eventually, i feel confident in my theory that it is real.

but, science in this way is only *descriptive* - it cannot predict anything.

if i remember the story right, einstein discovered that this relativity theory allowed for the existence of black holes. now, this existed in a *purely* theoretical construct - mathematics. but science had never seen one. and the concept was a little repugnant to him as well, iirc. he assumed it must be some problem with his theory, those couldn't *really* exist.

yet today, we know they do exist. this was a prediction out of a purely theoretical context.

an experiment is used to test 'i know X, and i think that because of that if i do Y, then Z must be true, so let's test that'. but predictive science often uses MP itself to show that the conclusions it's reaching are actually the result of its premises. how many studies have been conducted where the conclusions were invalid because of not enough controls, so that they claimed 'we did X and Y always happened, so therefore X must cause Y', when in fact we learn that actually some uncontrolled factor Z that was always present with X was what caused Y, and X was a red herring?


NOMAD:
fallacies are similar, and i believe most fallacies (which occur in text) can be rewritten as a syllogism exposing the error:

P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority.
C: Tillamook butter is the best tasting.

POWELL:
Based on the wording of your argument this is a valid argument. You said John is an authority, right? I suspect you're confusing the "appeal to authority" fallacy with the "appeal to inappropriate authority" fallacy. I don't blame you for being confused since logicians seem to want to intentionally confuse these and persuade the readers that only one is really a fallacy.


ok :) um, i guess i shouldn't have used that one. i tried equivocation above, maybe that will be better. i think actually, from reading through the fallacies again, you may be right, the fault is usually the (normally implicit) transcription of english into theory that is the problem; implicit assumptions do come into play, but usually involving the truth or falsity of the premises...

POWELL:

On of my points is that for a time one might have been justified in accepting that there was a dialetheia there.


it might have been justified, but it would not have been strictly true, true in the sense that it matches the real universe. instead, the assumption was made that LNC is true, and the apparent dialethia was demolished.

note that in a sense, this dialethia is *still* there - if i accept certain simplifying assumptions, then i may use the simpler model, which may still involve the dialethia but which still reflects the real world 'closely enough'.

now, if you are really arguing that there might be times where doing science with the assumption of a dialethia is *useful*, that's different. although i don't have enough experience to see how that would help, and i can't see it myself. can you give some examples?

POWELL:

If you allow for modern physics then you can remove the contradiction. If you don't then there could be a contradiction, right?


i don't think so. i just see that, like the philosophical argument, we aren't seeing all the caveats, there are some implicit assumptions we just don't know we are making.

the law (or theory) came by measurements. perhaps this was the 'missing control' - there is something that was always true, but we did not know it was always true. the law has an implicit assumption ('it is only true in these circumstances'), but we are not aware of them.

now, we find a new case where it doesn't seem to apply. the solution is 1. the theory is wrong 2. find the hidden assumption.

science tends to go with 2. and then the old theory isn't *wrong*, merely incomplete.



POWELL:

That is an acceptable way to look at it, to deny that there is a contradiction and to assume that our understanding is incomplete. However, my point is that alternative philosophical approaches might be justified, such as accepting that light is both a wave and a particle at the same time. To accept that light is a "wavicle" a wave-particle thing might be justified.


see, my objection is that i don't see current logic preventing that. i don't see anything that refuses to accept that light is a 'wavicle'. all we are saying is that we have a MODEL for something which is a wave, and a MODEL for something that is a particle, and sometimes the actions match the wave model, and sometimes the particle model.

what is clear is that it is NEITHER a wave or a particle, in the classic sense of the word; manufacturing a new term, 'wavicle', and then trying to ascertain its properties does not seem out of the domain of current logic.


A blue shirt could also be a red shirt yes. Therefore, it’s a problem when you try to convert such terms to an artificial logical language. Consider the following logical questions.

Jack and Bob are each wearing a shirt. One has a blue shirt on. The other has a red shirt on. Jack has a blue shirt on. What color is Bob’s shirt?

Which is the correct answer?

1) definitely red.
2) probably red, but possibly blue or red / blue mixed.
3) unknown.
4) something else (please explain)


exactly. i have not given you enough information about what i meant by 'my shirt is blue' to make a real answer. that is not the same as not being able to make a real answer:


Next questions: How many shirts is each one wearing and could they be wearing the same shirt? Could Jack and Bob be the same person or a siamese twin?


if i answer all these questions in a way favorable to the argument, do you think you could then tell me what color shirt Bob is wearing? i bet you could. clarify assumptions, don't create dialethias.

this is a very interesting discussion BTW, thanks for posting it...

[John Powell]

POWELL:
I like your comments. What if one of their assumptions, rather than proof, is that M.P. has the features they claim it has?

NOMAD:
of course it is. *proof* requires using some sort of logical method. i do not know of *any* logical method that sits on nothing (how do you get to 'logic without logic'?)


POWELL:
Trial and error. Human experience with what seems to work. I don't think logic came as a packaged set of rules on a stone carved out of a mountain by the finger of God.

NOMAD:
fwiw, MP afaik has good grounding in *science* - i.e. MP is assumed in the same way that science works... it is rational (it appeals to 'common sense'), it is empirical (if we assume MP, we can come to sensible conclusions about the world around us), and when we use MP to try to prove other things, those other things generally seem to match what we expect from MP. i don't see this as a wrong assumption.


POWELL:
When phrased in the non-absolute way you just did, I don't see a problem either. You used the word "generally." If introductory logic books used that kind of language, I would never have had a problem. Compare what you wrote with the extreme language of Copi and Cohen.

COPI AND COHEN:
"For example, if all humans are mortal, and if Socrates is human, we may conclude without reservation that Socrates is mortal ---"

POWELL:
Would you be willing to risk everything in the universe by claiming that the following statement is absolutely true without any reservation whatsoever, without needing additional premises even? . . .

NOMAD:
let's reduce this to:

1. 'p->q' is true
2. p is true
C. q is true

note that even THIS has an assumption, but here i am reducing them to reasonable assumptions for a theoretical language, namely, we both agree on what the symbols mean, what 'is true' means, and that those symbols are defined in the theoretical language such that they cannot change their values, either truth values or what they actually assert.

the logical language has much stricter rules than natural language.

with these caveats, yes, i would risk everything in the universe on this (in fact, i AM risking everything on this, as it's part of my belief in God).


POWELL:
It's one thing to claim that a mathematical equation or theoretical linguistic argument like M.P. using "p" and "q" is correct or incorrect without significant reservation given the assumptions of that artificial language, but it's another thing to claim that the natural language in the same form is correct or incorrect.

For example, 3 + 2 = 5, right? Not necessarily, even if you're using base 10. If you have 3_units1 and 2_units2 then you cannot in general combine them together to get 5_units1 or 5_units2. If the units are "apples" and "oranges" then you cannot add them together correctly to get either apples or oranges. You'd have to reduce them both to "fruit" to be legal. Even if the units are the same they still might not add to be 5. For example, if the two terms are vector quantities of magnitude 3_units1 and 2_units1 then the vector sum won't necessarily be 5_units1 in magnitude. You could safely say that 3 + 2 = 3 + 2, provided you don't switch the units.

I think you are over confident, NOMAD. The explicit assumptions for logic and mathematics are given in the natural language. You cannot be certain even what those assumptions mean or that I have the same understanding of what they mean. The assumptions might be self-contradictory with other assumptions, for example. You could add an assumption that the assumptions are not self-contradictory, but even that doesn't guarantee that this assumption is not self-contradictory.

We use logic and mathematics because they work better than any alternative, not because they are necessarily true.

NOMAD:
i’ll explain why in a minute.

POWELL:
Even if you allow for the assumption of LNC (which is a reasonable one for most purposes), there are other problems, as I indicate in my other proofs.

NOMAD:
let's take one of those, the equivocation in time fallacy.
P1: all humans are mortal.
P2: Socrates is human.
C: Socrates is mortal.

You claim that you shouldn't actually trust this, because say 'human' could mean different things in P1 and P2.


POWELL:
I did not mean to suggest you can't "trust." I think you CAN trust this to a very high degree, just not absolutely trust it in the way introductory logic texts suggest you can.

NOMAD:
i claim we can deal with this by making things explicit:

P1: If X is human, then X is mortal.
P2: Socrates is human.
C: Socrates is mortal.

now, let's assume we did have a fallacy of equivocation in time. if this is true, then we would write this in symbolic form as:

P1: 'if P, then Q' is true.
P2: 'R' is true.
C: ??

it is simply no longer a valid argument.


POWELL:
Yes, that's one way for logicians to deal with it. If Socrates in one part of the argument is not Socrates "in exactly the same sense" in another part then it doesn't match the theoretical model. However, due to my arguments you can't be certain that you will EVER have two Socrates that are ABSOLUTELY EXACTLY THE SAME in the natural language.

What I'm saying is that the categorical argument of Socrates is a highly reliable argument form. Natural arguments put into that form with terms REASONABLY CLOSE to having the same meaning (which is the best we can hope for) will be HIGHLY LIKELY to have a true conclusion.

This, however, makes so-called valid deductive arguments really just statistical arguments with very high reliability.

NOMAD:
i believe that the THEORETICAL form CANNOT be violated. however, i would agree that it is fairly easy to write a natural argument that looks valid but isn't. but, for every single one of these arguments, PROPER conversion to the theoretical language, obeying the rules of the theoretical language, and making all assumptions clear that aren't clear, will show all such arguments to be invalid.


POWELL:
I don't think so.

The following argument form is "denying the antecedent." It is considered an invalid form. However, if one substitutes terms that are considered "equivalents," or one is the definition of the other, such as "husband" and "married man" then a valid argument results.

1'. If J is a husband then J is a married man.
2'. J is not a husband.
3'. therefore, J is not a married man.

The logical claim, I think, is that natural language arguments which follow a valid form in the artificial language can be assured of being valid in the natural language. However, just because a natural language argument matches an "invalid" logical form does not necessarily mean that the natural language argument is invalid. Sometimes important information is lost in the "translation." However, if even in translating you get a valid argument form, you can be assured that the extra information that was dropped won't invalidate it.

NOMAD:
in most cases, we do a bit of 'hand-waving', because we can't always establish our assumptions. we can argue about whether 'socrates' means the same in premise 1 or premise 2, but if we had to do that all the time conversations, and both arguments and all kinds of science, would proceed very slowly. most conversations, and contexts in which arguments appear (and arguments DO appear in contexts normally), have a set of implicit assumptions which govern the argument.


POWELL:
That's fine, NOMAD. What I object to is introductory logic texts exaggerating the confidence one can have in the conclusion being true of a so-called valid deductive argument. I want them to clarify that one can only have very high confidence, that the conclusion is very likely true if the natural language premises of a so-called valid deductive argument are true.

NOMAD:
occasionally, people will find that i was assuming something in my argument you don't acknowledge to be true; in that base, you may have to examine assumptions. but practically, we don't do that, and we usually understand what that means.


POWELL:
Yes.

POWELL:
Sort of. It's more like I'm pointing out the assumptions they didn't realize they were making. . .

NOMAD:
mathematics is ALSO this sort of logical language. it would actually be ridiculous to even talk about mathematics 'matching' the universe - 3 is 3. what is 3? it is nothing, it is a concept. a very useful one, but only an ephemeral mist. but, when we describe the universe in this theoretical language, with much more defined rules than the natural universe, we can say things that, when reflected back into the real universe, turn out to be valid statements.

philosophical languages of logic are no different.


POWELL:
Yes. It's amazing how many times theoretical mathematics has turned out to be "true," or at least useful, in the real world. The same can be said about logic.

The comparison between logic and mathematics is a good one. If introductory logic texts had been more HONEST with their students about these things, I would not have had occasion to complain.

POWELL:
As a scientist, this important distinction between theory and experiment is more strictly emphasized. It's as if too many philosophers are believing their ideal forms are more real than the objects in the universe those forms are supposed to be modeling or representing.

NOMAD:
it is no more real, or less real, than mathematics. if i have the newtonian distance equation s = vt, and i say i was traveling in a straight line for 3 seconds at 3m/s, do i have any justification for saying i have moved 9m, which is a result i got by working in a purely theoretical domain?


POWELL:
Given those assumptions and staying in the artificial world of mathematics, you'd be fine. However, if you actually did the experiment, in which the measurements were (3 +/- 1 s) at (3 +/- 1) m/s then you should not be surprised to get an answer something between about 4 m and 16 m. The real world is not the perfect thing we might write down on paper.

NOMAD:
in one sense, i some agree with you. but i don't see how science is in any way superior.


POWELL:
Science educators also deceive their students to encourage understanding at the appropriate level. However, this is supposed to largely stop in college. Probably without exception, introductory physics students know that classical physics is not the "completely true" thing it was once thought. They have all heard of Einstein and quantum mechanics even if they don't understand them. They know that science has been wrong in the recent past and is improving as time goes on. The teacher freely admits that what the physics student is being taught is not necessarily completely true.

What do introductory logic students learn? They are taught that deductive arguments are those for which you can be ABSOLUTELY CONFIDENT that the conclusion is true if the premises are true. The logic student is not always aware of the major mistakes of logicians of the recent past. The teacher does NOT freely admit that what the logic student is being taught is not necessarily completely true.

NOMAD:
you assert that logic isn't a good predictor of reality because it has unproven assumptions;


POWELL:
That's not what I meant to assert. I meant to assert that the methods of science are significantly superior to the methods of philosophy as a predictor of reality. Philosophy can't pick up on all those methods or it would become a science. To avoid that, it should restrict itself to dealing with questions that can't be determined using the scientific method. Perhaps surprisingly, they are justified in asking questions about the validity of the scientific method itself. However, what philosophy concludes using its "thought experiments" such as what is moral, is not, in general, as reliable as what scientists conclude about the universe using scientific methods.

It is my contention that on general-type questions about the universe, if science doesn't have the answer, no one really does. Math and logic can DEFINE things to be a certain way, but that's not necessarily how the universe really is. Ethics can DEFINE something to be unethical, but that doesn't mean it has the features of badness ascribed to it. A scientific-quality experiment would need to be performed. If a scientific-quality experiment cannot be performed then reliability in the conclusion should be significantly reduced.

NOMAD:
i argue that science also has an unproven assumption, the law of causality. without LC, science cannot make any meaningful statements about the universe.


POWELL:
Fine. The difference is that the assumptions of science are more clearly conceded to their students, I think, than the assumptions of philosophy are conceded to their students.

How many introductory physics students would argue with me about whether the classical laws of physics are valid in all regimes of the physical universe? Few, if any.

How many introductory logic students would argue with me about whether the classical laws of logic are valid in all regimes of the natural language? Quite a lot apparently.

NOMAD:
you say LC has a better empirical basis than MP? i would disagree.


POWELL:
I don't remember saying that. I hadn't thought about comparing their relative empirical basis.

NOMAD:
and also... i could say that science, in one sense, doesn't require anything more than LC. in some sense, you can do some science without MP and without philosophy of any kind... i can assert 'the sun will come every morning', and every morning for a long time i can see if the sun comes up. eventually, i feel confident in my theory that it is real.


POWELL:
You can't do science without M.P. Every conditional has M.P. as a consequence. Science is a sub-branch of philosophy. It's a daughter who has chosen to sever as much as possible those mother-daughter ties.

NOMAd:
but, science in this way is only *descriptive* - it cannot predict anything.

if i remember the story right, einstein discovered that this relativity theory allowed for the existence of black holes. now, this existed in a *purely* theoretical construct - mathematics. but science had never seen one. and the concept was a little repugnant to him as well, iirc. he assumed it must be some problem with his theory, those couldn't *really* exist.

yet today, we know they do exist. this was a prediction out of a purely theoretical context.


POWELL:
I agree with the sentiment, but not the wording. The point is that Einstein's "instint" or "intuition" was possibly wrong. Sometimes math results in things we would not expect, or that we intuitively deny, yet they turn out to be true.

However in the example you chose, Einstein's instinct might have been correct. It can be justifiably argued, I think, that black holes (singularities with event horizons) do not exist in our universe. This is because when such a thing forms then, from our perspective, nothing ever falls within the event horizon, but remains frozen on the event horizon. If, from our perpective far from the black hole, the moment that the event horizon forms from then on it takes an infinite amount of time for anything else to fall within it, then it's plausible to argue that it takes a long time to reach that point. What we have, perhaps, is what I call "asymptotic" black holes, objects which are approaching the theoretical black hole, but never quite reaching it. The theoretical black hole is a mathematical construct similar in some ways to the real exotic specimens we're finding in binary systems and at the centers of galaxies, but may not be the real mccoy. We have to study the specimens to decide.

NOMAD:
an experiment is used to test 'i know X, and i think that because of that if i do Y, then Z must be true, so let's test that'. but predictive science often uses MP itself to show that the conclusions it's reaching are actually the result of its premises. how many studies have been conducted where the conclusions were invalid because of not enough controls, so that they claimed 'we did X and Y always happened, so therefore X must cause Y', when in fact we learn that actually some uncontrolled factor Z that was always present with X was what caused Y, and X was a red herring?


POWELL:
I don't know how often this has happened, but it can happen.

NOMAD:
fallacies are similar, and i believe most fallacies (which occur in text) can be rewritten as a syllogism exposing the error:

P1: If an authority says something is true, it is true.
P2: John says that Tillamook butter is the best tasting.
P3: John, point guard for the Duke Blue Devils, is an authority.
C: Tillamook butter is the best tasting.

POWELL:
Based on the wording of your argument this is a valid argument. You said John is an authority, right? I suspect you're confusing the "appeal to authority" fallacy with the "appeal to inappropriate authority" fallacy. I don't blame you for being confused since logicians seem to want to intentionally confuse these and persuade the readers that only one is really a fallacy.

NOMAD:
ok :) um, i guess i shouldn't have used that one. i tried equivocation above, maybe that will be better. i think actually, from reading through the fallacies again, you may be right, the fault is usually the (normally implicit) transcription of english into theory that is the problem; implicit assumptions do come into play, but usually involving the truth or falsity of the premises...


POWELL:
Perhaps.

POWELL:
On{e} of my points is that for a time one might have been justified in accepting that there was a dialetheia there.

NOMAD:
it might have been justified, but it would not have been strictly true, true in the sense that it matches the real universe. instead, the assumption was made that LNC is true, and the apparent dialethia was demolished.

note that in a sense, this dialethia is *still* there - if i accept certain simplifying assumptions, then i may use the simpler model, which may still involve the dialethia but which still reflects the real world 'closely enough'.

now, if you are really arguing that there might be times where doing science with the assumption of a dialethia is *useful*, that's different. although i don't have enough experience to see how that would help, and i can't see it myself. can you give some examples?


POWELL:
Sure. When you do a diffraction or interference experiment then assume that the electron / photon behaves like a wave while it's moving through the air, but like a particle once it hits somewhere. When you study the energy levels of an atom or molecule assume the quantized assumptions of Quantum Mechanics are true, but when you study cosmology or black holes, assume the non-quantized assumptions of General Relativity are true. When you do physics in the normal regime assume classical mechanics is true, but when you work in the extreme regimes of the very small, the very fast, and the very massive then don't assume that. In other words, do whatever works.

POWELL:
If you allow for modern physics then you can remove the contradiction. If you don't then there could be a contradiction, right?

NOMAD:
i don't think so. i just see that, like the philosophical argument, we aren't seeing all the caveats, there are some implicit assumptions we just don't know we are making.

the law (or theory) came by measurements. perhaps this was the 'missing control' - there is something that was always true, but we did not know it was always true. the law has an implicit assumption ('it is only true in these circumstances'), but we are not aware of them.

now, we find a new case where it doesn't seem to apply. the solution is 1. the theory is wrong 2. find the hidden assumption.

science tends to go with 2. and then the old theory isn't *wrong*, merely incomplete.


POWELL:
We still don't know what the "true" statements are. Science is about approaching "truth," not being there. Philosophy seems to want to bypass that never-reaching position and claim that certain things are already absolutely true.

POWELL:
That is an acceptable way to look at it, to deny that there is a contradiction and to assume that our understanding is incomplete. However, my point is that alternative philosophical approaches might be justified, such as accepting that light is both a wave and a particle at the same time. To accept that light is a "wavicle" a wave-particle thing might be justified.

NOMAD:
see, my objection is that i don't see current logic preventing that. i don't see anything that refuses to accept that light is a 'wavicle'. all we are saying is that we have a MODEL for something which is a wave, and a MODEL for something that is a particle, and sometimes the actions match the wave model, and sometimes the particle model.

what is clear is that it is NEITHER a wave or a particle, in the classic sense of the word; manufacturing a new term, 'wavicle', and then trying to ascertain its properties does not seem out of the domain of current logic.


POWELL:
Perhaps you have a point. However, what are the features of a "wavicle"? It could be thought of as a wave and a particle at the same time. On the other hand, you could claim that it’s a wave when it’s in the air, but a particle when it hits something. It's a mowan, a man/woman at the same time. It behaves like a man when moving, but like a woman when standing. These could be considered contradictions or you could choose to think about them in a non-contradictory way.

Just because we can’t seem to think logically about dialethias doesn’t mean they don’t exist.

POWELL:
A blue shirt could also be a red shirt yes. Therefore, it’s a problem when you try to convert such terms to an artificial logical language. Consider the following logical questions.

Jack and Bob are each wearing a shirt. One has a blue shirt on. The other has a red shirt on. Jack has a blue shirt on. What color is Bob’s shirt?

Which is the correct answer?

1) definitely red.
2) probably red, but possibly blue or red / blue mixed.
3) unknown.
4) something else (please explain)

NOMAD:
exactly. i have not given you enough information about what i meant by 'my shirt is blue' to make a real answer. that is not the same as not being able to make a real answer:

POWELL:
Next questions: How many shirts is each one wearing and could they be wearing the same shirt? Could Jack and Bob be the same person or a siamese twin?

NOMAD:
if i answer all these questions in a way favorable to the argument, do you think you could then tell me what color shirt Bob is wearing? i bet you could. clarify assumptions, don't create dialethias.


POWELL:
I probably could identify bizarre situations. My point is that "probably" is the best answer if one wants to be completely truthful. In common examples, one would expect merely "red" as the answer. Just about anything I claim to be true, I should put "probably" in front of it, but that would be too verbose.

NOMAD:
this is a very interesting discussion BTW, thanks for posting it...


POWELL:
You're welcome. Thanks for your interesting and useful comments.

John Powell

[nomad]

first off, i want to apologize... i appear to have read more into your comments than you meant in several cases, and the fault is clearly mine.

second, just as a summary, it seems that what you are getting at in the end is 'there is NO method that gives an ABSOLUTE proof; the best we can say is 'most likely', or 'statistically valid''. that sort of statement i would agree is warranted; i tend to shy away from absolute statements as well (which my wife sometimes complains about), despite my seeming effervescence below :)

i think i can definitely live with that conclusion.

POWELL:

Trial and error. Human experience with what seems to work. I don't think logic came as a packaged set of rules on a stone carved out of a mountain by the finger of God.


not related to this discussion, but i was curious... what do you believe about how scientific laws came about?

POWELL:

When phrased in the non-absolute way you just did, I don't see a problem either. You used the word &quot;generally.&quot; If introductory logic books used that kind of language, I would never have had a problem.


i think this is the root of your objections, and i can sympathize and agree with this sentiment :)

POWELL:

It's one thing to claim that a mathematical equation or theoretical linguistic argument like M.P. using &quot;p&quot; and &quot;q&quot; is correct or incorrect without significant reservation given the assumptions of that artificial language, but it's another thing to claim that the natural language in the same form is correct or incorrect.


i think we agree on this point.

POWELL:

For example, 3 + 2 = 5, right? Not necessarily, even if you're using base 10. If you have 3_units1 and 2_units2 then you cannot in general combine them together to get 5_units1 or 5_units2. If the units are &quot;apples&quot; and &quot;oranges&quot; then you cannot add them together correctly to get either apples or oranges. You'd have to reduce them both to &quot;fruit&quot; to be legal. Even if the units are the same they still might not add to be 5. For example, if the two terms are vector quantities of magnitude 3_units1 and 2_units1 then the vector sum won't necessarily be 5_units1 in magnitude. You could safely say that 3 + 2 = 3 + 2, provided you don't switch the units.


i would not say this is reasonable, but it is, in fact, strictly true. though it is again not a failure in the mathematics (3 + 2 does, in fact, always equal 5), but in the translations to natural language. but this is your point :)

POWELL:

I think you are over confident, NOMAD. The explicit assumptions for logic and mathematics are given in the natural language.


maybe :) i do see your point - we have to use natural language to communicate to ensure we ARE using the same assumptions. and that language could be flawed, meaning that even in the case where we THINK we are using the same assumptions in our argument, there could be a pathological case where the language still causes a misunderstanding (possibly intentional, but not necessarily). and since we cannot rule out this pathological case, we cannot use absolute language.

and any attempt to get around this sits in natural language, and therefore we come to an unresolvable paradox. from the human's point of view, there is nothing absolute.

well, i guess this is reasonable, i have used it myself: i was once asked by an atheist that if God was true, why didn't He give solid evidence? but there is no such thing. we can argue about if there is a 'reasonable' evidence for God, but there will never be an absolute that will convince everyone.


POWELL:

I want them to clarify that one can only have very high confidence, that the conclusion is very likely true if the natural language premises of a so-called valid deductive argument are true.


maybe not when MP is usually introduced in an introductory text (reasonable simplifications due to pragmatism are fairly normal in introductory texts, we wouldn't want to 'poison the well' this early on), but certainly later on this is a good idea.

POWELL:

Given those assumptions and staying in the artificial world of mathematics, you'd be fine. However, if you actually did the experiment, in which the measurements were (3 +/- 1 s) at (3 +/- 1) m/s then you should not be surprised to get an answer something between about 4 m and 16 m. The real world is not the perfect thing we might write down on paper.


on this i will slightly disagree. i understand the precision was exaggerating to make the position more obvious but two things are clear, the borders were defined using the same standard multiplication and second, as the precision is improved, the measurements should get very close to the theoretical.

actually, this may be a useful model... the concept of precision has not often (if at all) been applied to a logical argument, but maybe it should be. you can't measure it though, which might make it difficult.

POWELL:

Science educators also deceive their students to encourage understanding at the appropriate level. However, this is supposed to largely stop in college.

What do introductory logic students learn? They are taught that deductive arguments are those for which you can be ABSOLUTELY CONFIDENT that the conclusion is true if the premises are true.


putting these two together, maybe this is the source of the problem... i don't know that i've ever even seen an 'advanced logic' class.


POWELL:

That's not what I meant to assert. I meant to assert that the methods of science are significantly superior to the methods of philosophy as a predictor of reality.


possibly. science is certainly better at testing the truth of the assertions made under its umbrella, than those assertions made under philosophy :)


However, what philosophy concludes using its &quot;thought experiments&quot; such as what is moral, is not, in general, as reliable as what scientists conclude about the universe using scientific methods.


i'm not sure that's a meaningful statement. how do we measure its thought experiments against real morality? morality is at its core a different sort of 'thought paradigm' than science. there aren't really any assertions to test. science says 'if you do this, then this other thing happens'; morality says 'you should do this thing, and not the other', and it is the conclusion that is assumed. basically, ethics and science aren't even distant cousins.

philosophical arguments about real universe though, where it 'competes' with science, i would be inclined to agree with you.



It is my contention that on general-type questions about the universe, if science doesn't have the answer, no one really does.


i have a little more faith than you in the outcomes of 'thought' experiments (and a little less in the veracity of that asserted by science), but i do not vary that much and it is, after all, merely my opinion anyways.

POWELL:

I don't remember saying that. I hadn't thought about comparing their relative empirical basis.


sorry, you didn't say that directly. i equated 'science' with LC (because without LC, you can't say anything meaningful about the future, and science really doesn't 'know' anything).

but, really, you get around this by not claiming LC to be absolute... just reasonable, and well-informed believable.

which falls into...

POWELL:

You can't do science without M.P. Every conditional has M.P. as a consequence. Science is a sub-branch of philosophy. It's a daughter who has chosen to sever as much as possible those mother-daughter ties.


i don't think that separation will ever be amputated :) philosophy and science aren't really as far apart as you think, they just work in a different set of propositions :)

POWELL:

I agree with the sentiment, but not the wording. The point is that Einstein's &quot;instint&quot; or &quot;intuition&quot; was possibly wrong. Sometimes math results in things we would not expect, or that we intuitively deny, yet they turn out to be true.

However in the example you chose, Einstein's instinct might have been correct.
some snippage


it sounds like your assertion here is: the theoretical model can go either way, depending on how you look at it. that's fair.


In other words, do whatever works.

These could be considered contradictions or you could choose to think about them in a non-contradictory way.


i think if you put these two thoughts together, you get what i was originally getting at.



Just because we can’t seem to think logically about dialethias doesn’t mean they don’t exist.


so does this mean that God could truly be fully omnipotent after all? ;)

POWELL:

In common examples, one would expect merely &quot;red&quot; as the answer. Just about anything I claim to be true, I should put &quot;probably&quot; in front of it, but that would be too verbose.


that, i think, is reasonable.


thanks again. i have never thought this much about logic before!

[John Powell]

NOMAD:
first off, i want to apologize... i appear to have read more into your comments than you meant in several cases, and the fault is clearly mine.


POWELL:
Surely some of the blame is poor writing on my part. I try hard, but I don't always succeed.

NOMAD:
second, just as a summary, it seems that what you are getting at in the end is 'there is NO method that gives an ABSOLUTE proof; the best we can say is 'most likely', or 'statistically valid''. that sort of statement i would agree is warranted; i tend to shy away from absolute statements as well (which my wife sometimes complains about), despite my seeming effervescence below :)

i think i can definitely live with that conclusion.


POWELL:
Great. :smile:

POWELL:
Trial and error. Human experience with what seems to work. I don't think logic came as a packaged set of rules on a stone carved out of a mountain by the finger of God.

NOMAD:
not related to this discussion, but i was curious... what do you believe about how scientific laws came about?


POWELL:
Same. Trial and error. Same for the math and ethics.

POWELL:
When phrased in the non-absolute way you just did, I don't see a problem either. You used the word "generally." If introductory logic books used that kind of language, I would never have had a problem.

NOMAD:
i think this is the root of your objections, and i can sympathize and agree with this sentiment :)


POWELL:
Great! :smile:

POWELL:
It's one thing to claim that a mathematical equation or theoretical linguistic argument like M.P. using "p" and "q" is correct or incorrect without significant reservation given the assumptions of that artificial language, but it's another thing to claim that the natural language in the same form is correct or incorrect.

NOMAD:
i think we agree on this point.


POWELL:
Great. :smile:

POWELL:
For example, 3 + 2 = 5, right? Not necessarily, even if you're using base 10. If you have 3_units1 and 2_units2 then you cannot in general combine them together to get 5_units1 or 5_units2. If the units are "apples" and "oranges" then you cannot add them together correctly to get either apples or oranges. You'd have to reduce them both to "fruit" to be legal. Even if the units are the same they still might not add to be 5. For example, if the two terms are vector quantities of magnitude 3_units1 and 2_units1 then the vector sum won't necessarily be 5_units1 in magnitude. You could safely say that 3 + 2 = 3 + 2, provided you don't switch the units.

NOMAD:
i would not say this is reasonable, but it is, in fact, strictly true. though it is again not a failure in the mathematics (3 + 2 does, in fact, always equal 5), but in the translations to natural language. but this is your point :)


POWELL:
You're right. As written in the artificial world of math, 3 + 2 = 5. However, this is not always true in the real world.

POWELL:
I think you are over confident, NOMAD. The explicit assumptions for logic and mathematics are given in the natural language.

NOMAD:
maybe :) i do see your point - we have to use natural language to communicate to ensure we ARE using the same assumptions. and that language could be flawed, meaning that even in the case where we THINK we are using the same assumptions in our argument, there could be a pathological case where the language still causes a misunderstanding (possibly intentional, but not necessarily). and since we cannot rule out this pathological case, we cannot use absolute language.


POWELL:
I would revise this ending sentence to say "we cannot absolutely rely on language."

NOMAD:
and any attempt to get around this sits in natural language, and therefore we come to an unresolvable paradox. from the human's point of view, there is nothing absolute.


POWELL:
Right, unless we redefine "absolute truth" to include things like math and logic. Consequently, we should be practical. We should use most what works best.

NOMAD:
well, i guess this is reasonable, i have used it myself: i was once asked by an atheist that if God was true, why didn't He give solid evidence? but there is no such thing. we can argue about if there is a 'reasonable' evidence for God, but there will never be an absolute that will convince everyone.


POWELL:
Yes. To be persuaded I would require solid, good, reasonable evidence, but not absolutely solid evidence. I feel very strongly that if the Mormon God I once believed in really existed then virtually everyone on Earth would have sufficient evidence for them to believe in God. The very existence of rational, educated, ethical atheists is strong evidence to me that the God I once believed in does not exist.

POWELL:
I want them to clarify that one can only have very high confidence, that the conclusion is very likely true if the natural language premises of a so-called valid deductive argument are true.

NOMAD:
maybe not when MP is usually introduced in an introductory text (reasonable simplifications due to pragmatism are fairly normal in introductory texts, we wouldn't want to 'poison the well' this early on), but certainly later on this is a good idea.


POWELL:
Good point.

POWELL:
Given those assumptions and staying in the artificial world of mathematics, you'd be fine. However, if you actually did the experiment, in which the measurements were (3 +/- 1 s) at (3 +/- 1) m/s then you should not be surprised to get an answer something between about 4 m and 16 m. The real world is not the perfect thing we might write down on paper.

NOMAD:
on this i will slightly disagree. i understand the precision was exaggerating to make the position more obvious but two things are clear, the borders were defined using the same standard multiplication . . .


POWELL:
When you said "3 s" and "3 m/s" did you mean 3.0 s and 3.0 m/s or 3.00 s and 3.00 m/s or what? I assumed you meant 3. m and 3. m/s.

NOMAD:
. . . and second, as the precision is improved, the measurements should get very close to the theoretical.


POWELL:
This second point is a good one. If the theory is good then reality (physical measurements) should approach it as the precision of the measurements improve.

NOMAD:
actually, this may be a useful model... the concept of precision has not often (if at all) been applied to a logical argument, but maybe it should be. you can't measure it though, which might make it difficult.


POWELL:
Right. If you could measure it reliably then it would be a science instead of philosophy.

POWELL:
Science educators also deceive their students to encourage understanding at the appropriate level. However, this is supposed to largely stop in college.

What do introductory logic students learn? They are taught that deductive arguments are those for which you can be ABSOLUTELY CONFIDENT that the conclusion is true if the premises are true.

NOMAD:
putting these two together, maybe this is the source of the problem... i don't know that i've ever even seen an 'advanced logic' class.

POWELL:
That's not what I meant to assert. I meant to assert that the methods of science are significantly superior to the methods of philosophy as a predictor of reality.

NOMAD:
possibly. science is certainly better at testing the truth of the assertions made under its umbrella, than those assertions made under philosophy :)

POWELL:
However, what philosophy concludes using its "thought experiments" such as what is moral, is not, in general, as reliable as what scientists conclude about the universe using scientific methods.

NOMAD:
i'm not sure that's a meaningful statement. how do we measure its thought experiments against real morality? morality is at its core a different sort of 'thought paradigm' than science. there aren't really any assertions to test.


POWELL:
There are assertions in morality, I think, but they are very difficult to test. It is this difficulty that suggests that the conclusions of philosophers about philosophy (e.g. morality) are much more subjective than conclusions of scientists about science.

NOMAD:
science says 'if you do this, then this other thing happens'; morality says 'you should do this thing, and not the other', and it is the conclusion that is assumed. basically, ethics and science aren't even distant cousins.


POWELL:
I think you'll see an effort by philosophers over time to make philosophy more scientific in its approach.

NOMAD:
philosophical arguments about real universe though, where it 'competes' with science, i would be inclined to agree with you.


POWELL:
Excellent! :yipee:

POWELL:
It is my contention that on general-type questions about the universe, if science doesn't have the answer, no one really does.

NOMAD:
i have a little more faith than you in the outcomes of 'thought' experiments (and a little less in the veracity of that asserted by science), but i do not vary that much and it is, after all, merely my opinion anyways.


POWELL:
My opinion too.

POWELL:
I don't remember saying that. I hadn't thought about comparing their relative empirical basis.

NOMAD:
sorry, you didn't say that directly. i equated 'science' with LC (because without LC, you can't say anything meaningful about the future, and science really doesn't 'know' anything).

but, really, you get around this by not claiming LC to be absolute... just reasonable, and well-informed believable.

which falls into...

POWELL:
You can't do science without M.P. Every conditional has M.P. as a consequence. Science is a sub-branch of philosophy. It's a daughter who has chosen to sever as much as possible those mother-daughter ties.

NOMAD:
i don't think that separation will ever be amputated :)


POWELL:
Right, "as much as possible. . ." Sometimes philosophy and science converge as philosophers consider the problems of the scientific method and develop logics that are more suitable to scientists.

NOMAD:
philosophy and science aren't really as far apart as you think, they just work in a different set of propositions :)


POWELL:
Perhaps.

Scientists test their ideas against the real universe. Philosophers test their ideas against other ideas they love.

POWELL:
I agree with the sentiment, but not the wording. The point is that Einstein's "instin{c}t" or "intuition" was possibly wrong. Sometimes math results in things we would not expect, or that we intuitively deny, yet they turn out to be true.

However in the example you chose, Einstein's instinct might have been correct.

<some snippage>

NOMAD:
it sounds like your assertion here is: the theoretical model can go either way, depending on how you look at it. that's fair.


POWELL:
Ok.

POWELL:
In other words, do whatever works.

These could be considered contradictions or you could choose to think about them in a non-contradictory way.

NOMAD:
i think if you put these two thoughts together, you get what i was originally getting at.


POWELL:
Ok.

POWELL:
Just because we can’t seem to think logically about dialethias doesn’t mean they don’t exist.

NOMAD:
so does this mean that God could truly be fully omnipotent after all? ;)


POWELL:
Yes, God could be a dialetheia. Possibly yes, probably no.

POWELL:
In common examples, one would expect merely "red" as the answer. Just about anything I claim to be true, I should put "probably" in front of it, but that would be too verbose.

NOMAD:
that, i think, is reasonable.

thanks again. i have never thought this much about logic before!


POWELL:
You're doing great. It's probably that scientific / mathematical background you have.

John Powell

[nomad]

POWELL:

Same. Trial and error. Same for the math and ethics.


well, for ethics at least. but my question was: is it that the universe JUST IS, or do you believe that there is some reason for why scientific laws even exist to be discovered? is the law of causality just another 'useful tool' that could be thrown away if it broke?

i must admit, i've never really understood the basis of science from an atheistic perspective, so i'm taking the opportunity to learn something :)


POWELL:

I would revise this ending sentence to say &quot;we cannot absolutely rely on language.&quot;


works for me. so, if we could communicate without language...


POWELL:

When you said &quot;3 s&quot; and &quot;3 m/s&quot; did you mean 3.0 s and 3.0 m/s or 3.00 s and 3.00 m/s or what? I assumed you meant 3. m and 3. m/s.


ah yes, this is what i get for working in computer science instead of natural science for so long :) ok, i can understand why you assumed +/- 1.

POWELL:

There are assertions in morality, I think, but they are very difficult to test. It is this difficulty that suggests that the conclusions of philosophers about philosophy (e.g. morality) are much more subjective than conclusions of scientists about science.


i'm not sure; a moralist will use arguments with testable outcomes in defense of his position perhaps, but in the end the statement looks something like 'you should not kill in situation X'. there is no outcome to test.

some put moral statements like 'if you do X, Y will happen to you', but we all know that, if you do not include the supernatural, these are not absolute laws. in the end, only the outcome-less form above is really the statements morality makes.

the rest i either agreed with you, or just accepted your opinion without comment.

[John Powell]

POWELL:
Same. Trial and error. Same for the math and ethics.

NOMAD:
well, for ethics at least.


POWELL:
Why not math? Can't you imagine early mathematicians drawing in the sand or on pieces of bark or on walls trying to figure out what works mathematically and what doesn't?

NOMAD:
but my question was: is it that the universe JUST IS, or do you believe that there is some reason for why scientific laws even exist to be discovered? is the law of causality just another 'useful tool' that could be thrown away if it broke?

i must admit, i've never really understood the basis of science from an atheistic perspective, so i'm taking the opportunity to learn something :)


POWELL:
Apparently the law of conservation of mass-energy derives from the fact that in our universe the physical laws are time invariant. Because the laws of our universe do not change from moment to moment something must be conserved from moment to moment. That something is mass-energy.

Also, apparently the law of conservation of linear momentum derives from the fact that in our universe the physical laws are position invariant. Because the laws of our universe do not change from point to point in space something must be conserved from point to point. That something is linear momentum.

If the laws of our universe were not time and space invariant then mass-energy and linear momentum might not be conserved. Perhaps the universe couldn't even exist under such conditions.

The law of causality is a logical condition for change. If there's change there should be a reason for that change, a cause for that. If the universe were unchanging then there would be no use for the law of causality.

POWELL:
I would revise this ending sentence to say "we cannot absolutely rely on language."

NOMAD:
works for me. so, if we could communicate without language...

POWELL:
When you said "3 s" and "3 m/s" did you mean 3.0 s and 3.0 m/s or 3.00 s and 3.00 m/s or what? I assumed you meant 3. m and 3. m/s.

NOMAD:
ah yes, this is what i get for working in computer science instead of natural science for so long :) ok, i can understand why you assumed +/- 1.

POWELL:
There are assertions in morality, I think, but they are very difficult to test. It is this difficulty that suggests that the conclusions of philosophers about philosophy (e.g. morality) are much more subjective than conclusions of scientists about science.

NOMAD:
i'm not sure; a moralist will use arguments with testable outcomes in defense of his position perhaps, but in the end the statement looks something like 'you should not kill in situation X'. there is no outcome to test.


POWELL:
If you can't confirm his predictions, then why should you trust his theory? Testing morality might be like testing preferences. To each his own, maybe.

NOMAD:
some put moral statements like 'if you do X, Y will happen to you', but we all know that, if you do not include the supernatural, these are not absolute laws. in the end, only the outcome-less form above is really the statements morality makes.


POWELL:
An atheist correspondent has argued that ex-members should sue their religions for past donations because the church obtained them under the unsubstantiated guarantee that donations would improve one's position with God now and in the afterlife when the religion has no provable ability to fulfil such a promise.

I prophesy that this will happen for the first time sometime in the next few decades. If the judges are liberal or atheist enough, I suspect that religions will be pressured to resist making extravagant claims about what donations will bring to the giver. They'll likely say things like "it might make you and God happier if you give to us."

NOMAD:
the rest i either agreed with you, or just accepted your opinion without comment.


POWELL:
Interesting points.

John Powell

[nomad]

POWELL:

Why not math? Can't you imagine early mathematicians drawing in the sand or on pieces of bark or on walls trying to figure out what works mathematically and what doesn't?


sort of, for the basic assumptions at least. but a lot of math is definition as well, and definition isn't based on trial and error. 1 + 1 = 2, because that's how we define what 2 means.


POWELL:

Apparently the law of conservation of mass-energy derives from the fact that in our universe the physical laws are time invariant. Because the laws of our universe do not change from moment to moment something must be conserved from moment to moment. That something is mass-energy.

Also, apparently the law of conservation of linear momentum derives from the fact that in our universe the physical laws are position invariant. Because the laws of our universe do not change from point to point in space something must be conserved from point to point. That something is linear momentum.

If the laws of our universe were not time and space invariant then mass-energy and linear momentum might not be conserved. Perhaps the universe couldn't even exist under such conditions.

The law of causality is a logical condition for change. If there's change there should be a reason for that change, a cause for that. If the universe were unchanging then there would be no use for the law of causality.


ok, so these assumptions are your basis for science. do you just accept these assumptions because your experience deems them reasonable, or is there something more than that?

i'm curious, because to a christian, we believe God keeps the universe in order, so we even have a reason to believe in these assumptions. i'm mostly curious as to if there is some similar _base_ assumption that exists for you, or if you are just content to accept certain assumptions and leave it at that.

POWELL:

If you can't confirm his predictions, then why should you trust his theory? Testing morality might be like testing preferences. To each his own, maybe.


it's not a theory, that's sort of the point. there ARE no predictions, just imperatives.

or maybe that is the root... i guess as Christian, it IS supported by a basic imperative - you do not obey what is inside the Christian moral order (that of salvation by faith to most Christians), you do not go to heaven. this is an untestable proposition, but actually i suppose you are right, without backing even an imperative 'lacks teeth'...

we can argue about which courses of action 'minimize pain' or 'maximize happiness', but these two (among a whole plethora of other choices) may lead to a different set of actions, and if we can't even agree on the goal, we're certainly not going to be able to agree on the methods.

POWELL:

An atheist correspondent has argued that ex-members should sue their religions for past donations because the church obtained them under the unsubstantiated guarantee that donations would improve one's position with God now and in the afterlife when the religion has no provable ability to fulfil such a promise.


so this would be like false advertising or something, a right to 'get your money back' so to speak? interesting... obviously i don't agree with it, but it's something i haven't seen before...

[John Powell]

POWELL:
Why not math [coming from trial and error]? Can't you imagine early mathematicians drawing in the sand or on pieces of bark or on walls trying to figure out what works mathematically and what doesn't?

NOMAD:
sort of, for the basic assumptions at least. but a lot of math is definition as well, and definition isn't based on trial and error. 1 + 1 = 2, because that's how we define what 2 means.


POWELL:
The symbolic statement "x + x = xx" can be considered a definition, but the idea of a thing in one hand joined with another thing in the same hand making "two" things in that hand is something that is experienced. If glock balls were to multiply such that every time you brought two similar-sized glock balls together a third would instantly appear then we might have the rule "x + x = xxx" when dealing with glock balls, at least. If nature were to behave quite differently then our math and our logic and our language might be quite different.

POWELL:
Apparently the law of conservation of mass-energy derives from the fact that in our universe the physical laws are time invariant. Because the laws of our universe do not change from moment to moment something must be conserved from moment to moment. That something is mass-energy.

Also, apparently the law of conservation of linear momentum derives from the fact that in our universe the physical laws are position invariant. Because the laws of our universe do not change from point to point in space something must be conserved from point to point. That something is linear momentum.

If the laws of our universe were not time and space invariant then mass-energy and linear momentum might not be conserved. Perhaps the universe couldn't even exist under such conditions.

The law of causality is a logical condition for change. If there's change there should be a reason for that change, a cause for that. If the universe were unchanging then there would be no use for the law of causality.

NOMAD:
ok, so these assumptions are your basis for science. do you just accept these assumptions because your experience deems them reasonable, or is there something more than that?


POWELL:
My experience deems them reasonable. There may be theoretical reasons why our universe must be that way to even exist.

We observe in our part of the universe that the laws of nature do not appear to depend on time or location to within the errors of our measurements and we can't think of a good reason why our vantage point should be special, so we assume or conclude that the rest of the universe is the same way. We consider that our conclusion is validated when observations of distant objects appear, to within the errors of our measurements, to be what one would expect if the laws of nature were perfectly invariant to time and location.

NOMAD:
i'm curious, because to a christian, we believe God keeps the universe in order, so we even have a reason to believe in these assumptions. i'm mostly curious as to if there is some similar _base_ assumption that exists for you, or if you are just content to accept certain assumptions and leave it at that.


POWELL:
Modern science owes a debt to Christianity for giving this idea of an ordered universe.

As a believing Mormon, I imagined that the universe was ordered because every electron and proton was controlled by an intelligence which was obedient to God's commands. If God had chosen some intelligences that were disobedient then the universe would not have been so ordered. Our human spirits were some of these disobedient intelligences. However, that also meant we could become Gods ourselves, whereas most intelligences could not.

I no longer have the same assumptions, however. If there's order in the universe then it's not because God made it that way, but for some other reason. In fact, it's possible that the universe is a lot less ordered than we think it is. Our brains can create order in our idea of the universe where it does not really exist in the universe. One must test those ideas against specimens in the real universe to verify that our ideas are correct.

POWELL:
If you can't confirm his predictions, then why should you trust his theory? Testing morality might be like testing preferences. To each his own, maybe.

NOMAD:
it's not a theory, that's sort of the point. there ARE no predictions, just imperatives.

or maybe that is the root... i guess as Christian, it IS supported by a basic imperative - you do not obey what is inside the Christian moral order (that of salvation by faith to most Christians), you do not go to heaven. this is an untestable proposition, but actually i suppose you are right, without backing even an imperative 'lacks teeth'...


POWELL:
Right. When people like Houdini return to Earth like he promised that he would if such were possible (and if anyone could escape, you'd think he could) and bring back persuasive evidence that heaven and hell exist THEN you'll have some teeth. Dreams and hallucinations and traumatic near-death experiences and "heart-felt" testimonies and darkened parlor tricks and wishful thinking and such things aren't persuasive enough to modern skeptics.

NOMAD:
we can argue about which courses of action 'minimize pain' or 'maximize happiness', but these two (among a whole plethora of other choices) may lead to a different set of actions, and if we can't even agree on the goal, we're certainly not going to be able to agree on the methods.


POWELL:
I think this is a far more productive approach, however, than arguing about what our particular God might think is right. We can measure, to some degree, happiness. We only have the words of self-proclaimed spokesmen to "measure" God's views.

POWELL:
An atheist correspondent has argued that ex-members should sue their religions for past donations because the church obtained them under the unsubstantiated guarantee that donations would improve one's position with God now and in the afterlife when the religion has no provable ability to fulfil such a promise.

NOMAD:
so this would be like false advertising or something, a right to 'get your money back' so to speak? interesting... obviously i don't agree with it, but it's something i haven't seen before...


POWELL:
I had not seen it before he presented it to me.

Why don't you agree? Don't you think that the vast majority of churches (those that aren't your own) promise more than they can deliver? Isn't it only your church and those you approve of that actually can and do deliver what they advertise? Surely you believe the Mormon advertisement for things like "eternal marriages" and "future Godhood" are false, right?

John Powell

[nomad]

POWELL:

The symbolic statement &quot;x + x = xx&quot; can be considered a definition, but the idea of a thing in one hand joined with another thing in the same hand making &quot;two&quot; things in that hand is something that is experienced. If glock balls were to multiply such that every time you brought two similar-sized glock balls together a third would instantly appear then we might have the rule &quot;x + x = xxx&quot; when dealing with glock balls, at least. If nature were to behave quite differently then our math and our logic and our language might be quite different.


yes, i see what you are saying. we might have different concepts of what +, or =, or 1 and 2 mean. but still, the language 1 + 1 = 2 is so by definition, tribbles or no tribbles, because our definitions of +, =, 1, and 2 make them true (and of course, we define them based on what we see).

there is a lot in math that isn't definition, it is proven from inside the system (based on definitions but not defined itself), but the basics have to be.


POWELL:

My experience deems them reasonable. There may be theoretical reasons why our universe must be that way to even exist.


so, it is taken a priori - without proof.


We observe in our part of the universe that the laws of nature do not appear to depend on time or location to within the errors of our measurements and we can't think of a good reason why our vantage point should be special, so we assume or conclude that the rest of the universe is the same way. We consider that our conclusion is validated when observations of distant objects appear, to within the errors of our measurements, to be what one would expect if the laws of nature were perfectly invariant to time and location.


i must admit that i don't know as much about this as i would like to, but how do we really know that? since we haven't been to any distant space objects, our measurements of their distances are based on our own assumptions. if the assumptions were wrong, maybe we'd never know, if it all came up somewhat consistent...


If there's order in the universe then it's not because God made it that way, but for some other reason. In fact, it's possible that the universe is a lot less ordered than we think it is. Our brains can create order in our idea of the universe where it does not really exist in the universe. One must test those ideas against specimens in the real universe to verify that our ideas are correct.


why couldn't it be God? i can understand an assertion that it doesn't have to be a God, but that it isn't is a stronger statement.

point taken on humans making 'order from chaos' though, in the mind. interesting though... if i see order, does it really exist?

POWELL:

I think this is a far more productive approach, however, than arguing about what our particular God might think is right. We can measure, to some degree, happiness. We only have the words of self-proclaimed spokesmen to &quot;measure&quot; God's views.


well, a christian would say 'everybody knows the truth, but not everyone is willing to obey it'. cs lewis pointed to the incredible amount of commonality in moral codes all over the earth. yes, there are many variations, but a lot of similarities too.

beyond that, we are getting into philosophy ;)

POWELL:

Why don't you agree? Don't you think that the vast majority of churches (those that aren't your own) promise more than they can deliver? Isn't it only your church and those you approve of that actually can and do deliver what they advertise? Surely you believe the Mormon advertisement for things like &quot;eternal marriages&quot; and &quot;future Godhood&quot; are false, right?


actually, no, i don't. this won't happen in america, at least for a while, because of the current (and declining) respect for religion. but that will go away eventually. and it's not a justification.

however, there are two main problems with this, at least to the degree you state.

one is proving that the expected benefits weren't received. if you talk to a lot of christians, they will tell you that they would be worse off if they weren't christians; i'm sure we can find many stories. or they will tell you how God blessed them, or saved them from something. you may look at it and say 'no, it was just this strictly materialistic explanation', but often they are not mutually exclusive explanations, and in either case they may not have a way to prove it is God, but neither do you have a way to prove it is not. enough of these types experiences may prove God to some people, but not to you because, by definition, they can't be God because he doesn't exist.

each position assumes something, and the conclusion is valid with the assumptions used.

cs lewis once wrote in an essay that one 'anti-proof' of God is how Christians aren't always the nicest people. but then again, we really don't know if they would be worse if they weren't christians. all we have is their word. same idea here, you can say you weren't 'happier' or 'wealthier' or whatever, but i can easily assert that you would have been worse off if you hadn't; this judgment is valid or invalid depending on the assumptions given.

second is that there is still a debate out there (and a pretty big one, if what i am reading is right) between science and philosophy/religion over the relative truth claims. so, a defense might also include a claim that the philosophic and religious claims are superior to the science claims. i know where you stand on this, but i'm currently reading a CSPR summary, and this was a big thing there.

and if you say 'well, you only say that because you are a christian' :) i probably am biased a little, but only by my beliefs - i do believe God is real, and fall into the 'bad' camp in both of the above so to speak. but i would extend this to all religious beliefs as well.

now, there ARE some people who are shucksters and try to milk people out of their money. under orthodox christianity, you can't buy blessings anyways :) though some seem to claim it sometimes. the concept that a God that made the universe would be swayed by our feeble greenbacks is pretty ridiculous anyways. most churches i have been in really say 'if you obey God, God will take care of you, and this is just part of obedience' - and God is a person, not a legal contract or a bank account. so, the money simply 'buys' you obedience, not any sort of blessing directly. this also avoids the problem.

yeah, i did have to think about this :) maybe this should be a new thread.

[John Powell]

POWELL:
The symbolic statement "x + x = xx" can be considered a definition, but the idea of a thing in one hand joined with another thing in the same hand making "two" things in that hand is something that is experienced. If glock balls were to multiply such that every time you brought two similar-sized glock balls together a third would instantly appear then we might have the rule "x + x = xxx" when dealing with glock balls, at least. If nature were to behave quite differently then our math and our logic and our language might be quite different.

NOMAD:
yes, i see what you are saying. we might have different concepts of what +, or =, or 1 and 2 mean. but still, the language 1 + 1 = 2 is so by definition, tribbles or no tribbles, because our definitions of +, =, 1, and 2 make them true (and of course, we define them based on what we see).

there is a lot in math that isn't definition, it is proven from inside the system (based on definitions but not defined itself), but the basics have to be.

POWELL:
My experience deems them reasonable. There may be theoretical reasons why our universe must be that way to even exist.

NOMAD:
so, it is taken a priori - without proof.


POWELL:
Without "proof" as in a mathematical proof / philosophical deductive argument, yes, but not without good argument. Usually it is just assumed to be the case. However, theories based on it seem to work better than theories that assume something quite different. We try to use whatever works.

POWELL:
We observe in our part of the universe that the laws of nature do not appear to depend on time or location to within the errors of our measurements and we can't think of a good reason why our vantage point should be special, so we assume or conclude that the rest of the universe is the same way. We consider that our conclusion is validated when observations of distant objects appear, to within the errors of our measurements, to be what one would expect if the laws of nature were perfectly invariant to time and location.

NOMAD:
i must admit that i don't know as much about this as i would like to, but how do we really know that? since we haven't been to any distant space objects, our measurements of their distances are based on our own assumptions. if the assumptions were wrong, maybe we'd never know, if it all came up somewhat consistent...


POWELL:
Yes, that's why studying the specimens of nature is so important. Hopefully, if we're oversimplifying or misunderstanding then that will appear soon enough.

POWELL:
If there's order in the universe then it's not because God made it that way, but for some other reason. In fact, it's possible that the universe is a lot less ordered than we think it is. Our brains can create order in our idea of the universe where it does not really exist in the universe. One must test those ideas against specimens in the real universe to verify that our ideas are correct.

NOMAD:
why couldn't it be God? i can understand an assertion that it doesn't have to be a God, but that it isn't is a stronger statement.


POWELL:
It could be God. You're right. I should have made it more clear that this was my personal conclusion.

NOMAD:
point taken on humans making 'order from chaos' though, in the mind. interesting though... if i see order, does it really exist?


POWELL:
Not necessarily. In a subjective or personal sense perhaps, but not in an objective sense or from the point of view of the larger population.

POWELL:
I think this is a far more productive approach, however, than arguing about what our particular God might think is right. We can measure, to some degree, happiness. We only have the words of self-proclaimed spokesmen to "measure" God's views.

NOMAD:
well, a christian would say 'everybody knows the truth, but not everyone is willing to obey it'. cs lewis pointed to the incredible amount of commonality in moral codes all over the earth. yes, there are many variations, but a lot of similarities too.

beyond that, we are getting into philosophy ;)


POWELL:
Yes, Christians would say that, but then they don't agree on many important issues like abortion, euthanasia, homosexuality, slavery, women's rights, etc.

POWELL:
Why don't you agree? Don't you think that the vast majority of churches (those that aren't your own) promise more than they can deliver? Isn't it only your church and those you approve of that actually can and do deliver what they advertise? Surely you believe the Mormon advertisement for things like "eternal marriages" and "future Godhood" are false, right?

NOMAD:
actually, no, i don't. this won't happen in america, at least for a while, because of the current (and declining) respect for religion. but that will go away eventually. and it's not a justification.

however, there are two main problems with this, at least to the degree you state.

one is proving that the expected benefits weren't received. if you talk to a lot of christians, they will tell you that they would be worse off if they weren't christians; i'm sure we can find many stories. or they will tell you how God blessed them, or saved them from something. you may look at it and say 'no, it was just this strictly materialistic explanation', but often they are not mutually exclusive explanations, and in either case they may not have a way to prove it is God, but neither do you have a way to prove it is not. enough of these types experiences may prove God to some people, but not to you because, by definition, they can't be God because he doesn't exist.

each position assumes something, and the conclusion is valid with the assumptions used.

cs lewis once wrote in an essay that one 'anti-proof' of God is how Christians aren't always the nicest people. but then again, we really don't know if they would be worse if they weren't christians. all we have is their word. same idea here, you can say you weren't 'happier' or 'wealthier' or whatever, but i can easily assert that you would have been worse off if you hadn't; this judgment is valid or invalid depending on the assumptions given.

second is that there is still a debate out there (and a pretty big one, if what i am reading is right) between science and philosophy/religion over the relative truth claims. so, a defense might also include a claim that the philosophic and religious claims are superior to the science claims. i know where you stand on this, but i'm currently reading a CSPR summary, and this was a big thing there.

and if you say 'well, you only say that because you are a christian' :) i probably am biased a little, but only by my beliefs - i do believe God is real, and fall into the 'bad' camp in both of the above so to speak. but i would extend this to all religious beliefs as well.

now, there ARE some people who are shucksters and try to milk people out of their money. under orthodox christianity, you can't buy blessings anyways :) though some seem to claim it sometimes. the concept that a God that made the universe would be swayed by our feeble greenbacks is pretty ridiculous anyways. most churches i have been in really say 'if you obey God, God will take care of you, and this is just part of obedience' - and God is a person, not a legal contract or a bank account. so, the money simply 'buys' you obedience, not any sort of blessing directly. this also avoids the problem.

yeah, i did have to think about this :) maybe this should be a new thread.


POWELL:
Good points. It should be in its own thread, probably in Theology 101. I'll start it there.

John Powell