Atheism and rationality

[ZackMartin]

Hello Juice

“many paraconsistent logics validate the Law of Non-Contradiciton.”

Of course, the choice of "many" rather than "all" implies "some paraconsistent logics deny or lack the Law of Non-Contradiction" - and those are the forms of paraconsistent logic that I am most interested in here.

My understanding of Paraconsistent logic is that it attempts to address inconsistent information in a meaningful way.

That is one motivation, but not the only motivation. Another motivation is to try to "solve" difficult mathematical paradoxes (like Russell's paradox in set theory) and linguistic paradoxes (like the liar sentence), with the innovative declaration that the paradox requires no solution and can be accepted as is. If you look at the history of dialetheism in Indian logic (Hindu, Buddhist and Jain), my understanding is that in that case it has theological motivations also. "Orthodoxy" varies from culture to culture - what is unorthodox in Western logic is orthodox in Indian logic.

I'd also reiterate my prior mention of intuitionistic logic and its rejection of the law of the excluded middle - even if everything you have said about the law of non-contradiction is right, you still have to contend with the argument over that.

But you seem to be making the mistake of thinking that because there are new systems emerging that deal with inconsistent data and challenge orthodoxy that this means logic is subjective and disputes over which system is superior is as unsolvable as disputes over the morality of abortion.

To be honest, the "challenge" to orthodoxy is very old. In the days in which Aristotle was proposing the law of non-contradiction and the law of the excluded middle, there were people disagreeing with him (as he notes in his works). In India, we have an entire logical tradition largely rejecting these two laws.

I don't believe logic is ultimately subjective - I believe that both logic and ethics are objective. However, I do believe, that disputes in both are very difficult, at times impossible, to resolve - and that is one of the indications of subjectivity which opponents of objective ethics use to argue for its subjectivity. But, my argument is, if that indication of subjectivity is present in ethics, it is equally present in logic. To be consistent, if you use that indication of subjectivity in ethics as an argument for ethical subjectivity, then you must use the same indication in logic as an argument for rational subjectivity.

Further, there is some irony here because you have employed logic yourself in your OP to demonstrate the validity of your beliefs. Which tells me you must believe your beliefs can be objectively shown to be rational via logic.

As I said, personally I believe in the objectivity of logic. But note the following parallel between ethics and logic: in ethics, there is vast areas of radical disagreement over what is ethical; but at the same time, in many concrete cases, there is near universal agreement. People have irreconcilable differences about the morality of abortion, but the same people will agree completely that if someone decides to go on a shooting spree in a public place as a way of letting off steam, that's gravely evil. In the same way, the existence of irreconcilable differences in logic does not exclude the existence of areas of near universal agreement. So we can still use logic in our discourse, so long as neither of us relies on a logical principle which the other rejects; a good way forward is to start on a presumption of agreement, and then deal with disagreements if and when we bump into them.

You attempted modens ponens

- there is a distinction between "modus ponens" on the one hand, and the laws of non-contradiction and the excluded middle on the other. The former, I am not aware of any logician or logical system which denies it; whereas the later two are controversial. (Of course, I can't say for sure no one denies "modus ponens", maybe someone does.) Given that, I feel on much safer ground using "modus ponens" than using the laws of non-contradiction and of the excluded middle. This is analogous to the relationship between the immorality of shooting sprees and the immorality of abortion. If I was trying to construct an ethical argument to convince as many people as possible, then the immorality of shooting sprees is a much better choice of premise than the immorality of abortion, since the former has near universal acceptance while the later doesn't. In the same way, if I'm trying to construct a logical argument to convince as many people as possible, then modus ponens is a much better choice of inference rule to choose than one which relies on the law of the excluded middle or the law of non-contradiciton.

If ethics is purely subjective, then rationality is purely subjective also Which by the way appears to be a non-sequitur.

On the contrary, my point is that when you take two entities X and Y, and then someone claims some property P is true for X but false for Y, then the degree of similarity between X and Y is a relevant consideration in determining the plausibility of their claim. If X and Y have little in common, their claim is much more plausible, than if numerous similarities and analogies are shown to exist between them.

So, the irony of course is that if logic is subjective as you assert you have no way of demonstrating objectively that your arguments are rational.

I don't claim logic is subjective. I claim that both logic and ethics are objective. I also claim that, arguments for the subjectivity of ethics work also as arguments for the subjectivity of logic - I see ethics and logic as a package deal, whose objectivity stands and falls together. I don't think it makes sense to accept the objectivity of one while denying it for the other.

But you are missing the salient point which is, logically speaking, rationality/irrationality is objectively demonstrable. Ethics are not.

I don't agree with that. There is a lot more to rationality than just logic. For example, people argue about what is the rational burden of proof (does the person who claims God exists bear the burden of proving his existence?) - and yet I don't know of any logical system which deals with burdens of proof. And the basic principles of logic cannot be demonstrated, one has to just accept them - once you agree on the basic principles, you can seek to apply them, and those applications involve demonstrations. But in the same way, once you agree with someone on basic ethical principles, then you can demonstrate various conclusions as an application of those principles. I don't think the immorality of abortion is demonstrable starting from the bare minimum of those ethical principles which all humans agree on, but if you agree on more (e.g. the basic principles of Catholic moral theology), then you have shared principles from which you can demonstrate that conclusion.

But you seem to like employing modus ponens, a rule of inference to show your belief is rational. From this I infer you agree that it is a correct rule. Or do I infer incorrectly?

I agree that it is correct - but it is impossible to demonstrate its correctness, it is just something that must be accepted without proof or reason. Much in the same way that it is impossible to demonstrate the correctness of ethical principles - "It is wrong to kill and maim innocent people for the sheer pleasure of it" - that is an ethical principle I'm sure we all agree on, but there is no way to prove or demonstrate its correctness, it is just something that must be accepted without proof or reason.

[nickcopernicus]

Hi

My name is Zack. I am a theist - I believe in a deity of some shape, form or description - but I am not what this site would consider to be a Christian. I'm new to this particular site, but I have spent much time before arguing about God's existence, etc., on the Internet and elsewhere.

Nick:
Hey Zack,

Zack:
I find very many atheists, agnostics, etc., subscribe to the belief that religious belief is not rational. At the weakest, they hold that it is not rational for them personally to believe in God, given the evidence and arguments available to them. At the strongest, they hold that it is not rational for anyone else to believe in God either.

Nick:
My personal opinion is that first, I’m more concerned about people arriving at their beliefs rationally and less about what they believe. I think there are plenty of rational theists around just as there are plenty of irrational atheists/agnostics. This brings me to my second point. It appears that I encounter more rational atheists than I do theists (in this sense, when I say ‘rational theist/atheist’ I mean they arrived at their religious beliefs (or lack thereof) rationally).

Zack:
But, how do we know what is and isn't rational? I think we can all come up with belief-situations where everyone would agree on the rationality or irrationality of the belief. Yet, despite the wide areas of agreement, I think there are also areas without this universal agreement, and when two people disagree about what is rational, there is no clear way forward in resolving these disagreements.

Nick:
I would say the most common reason people disagree, in my experience, about what is rational and what is not, is from colloquial use of the word. Used loosely, ‘rational’ can mean a lot of things. When we use the textbook definition of the word, it’s easier for us to nail down what is ‘rational.’
By textbook definition, I mean for a belief to be rational, it must have been obtained using REASON. Reason is using known facts to arrive at new facts.
A tool of reason, Logic, is the study of valid inference. So if our ‘reasoning’ is logical (consistent), then we can be sure of our conclusions. I suspect there will be less disagreement when we talk about rationality this way.

Zack:
I think rationality has many parallels or analogies with ethics/morality. We see in both cases the same phenomena of significant areas of universal agreement yet also areas of vast disagreement. Everyone agrees that helping an old person to cross the road is a good deed, and that if instead one was to push them under an oncoming bus that would be an evil deed (just to be clear, let's assume they are completely innocent, killing them won't save any lives or have any other positive benefits, etc.) But, while there is a lot of universal moral agreement, on cases like these (agreement so obvious most people don't see it), there are also the obvious moral disagreements (abortion, homosexuality, pre-marital sex, divorce, prostitution, pornography, masturbation, war, capital punishment, euthanasia, etc.) When we hit these areas of disagreement, it can be very hard, or impossible to prove one side right and the other wrong. But the same can be true of rationality - if you and I adopt different standards of evidence, how can we prove one right and the other wrong?

Nick:
Your juxtaposition or analogy of ethics and rationality unravel when the word ‘rational’ is used more vigorously.

Zack:
Many atheists/agnostics deny that there is any objective reality to ethics. And yet, given the analogies between rationality and ethics, if ethics is purely subjective, why isn't rationality purely subjective also? Alternatively, if rationality can be objective, why can't ethics be objective also?

Nick:
To answer your two questions: It's because ethics and rationality are not logically connected. To be rational, one must use reason to make ethical evacuations; however it’s possible to make ethical evaluations without reason. One can argue ethics by emotional outrage, after all. There is no such comparison when it comes to reason.

Zack:
Personally, my primary reason for believing in a deity is faith. There are a lot of arguments against faith, but I believe they can be answered. The main argument I see in favour of faith (admittedly more of a suggestive argument than a conclusive one), is that the many analogies between rationality and ethics, suggests that they are part of one coherent whole. If that is true, then it can be rational to believe something if one feels it would be ethically superior for one to do so, and there is no evidence against it, and there is no likelihood that any such evidence will emerge in the future. That is what I understand as faith.

Nick:
I am not sure how you concluded that ‘faith’ is the part of one ‘coherent whole.’ It feels like ‘coherent whole’ is an adjective without a referent. IOW, a coherent whole…..what?
Let’s start by you explaining exactly what you mean by ‘faith.’ The word ‘faith’ can mean a lot of different things to a lot of different people.

Zack:
I should note my faith is not in the Bible, in the particular doctrines of Christianity or any other religion. My faith is simply in root principles like "The good always wins in the end". I think the most straightforward way for these root principles to be true is if God, an afterlife, etc., exists. People talk about all the evils people have done in the name of faith, but that was faith in specific scriptures or doctrines or prophets or so on, not faith in root principles like the one I just espoused. I'm not aware of any evil done due to this kind of more abstract faith, and if there ever was, I would say it was a consequence of faulty reasoning based on those principles, rather than an inescapable consequence of those principles themselves.

Regards
Zack

Nick:
What kind of god do you believe in, exactly?

Cheers,

Nick

[ZackMartin]

Hi Nick

I would say the most common reason people disagree, in my experience, about what is rational and what is not, is from colloquial use of the word. Used loosely, ‘rational’ can mean a lot of things. When we use the textbook definition of the word, it’s easier for us to nail down what is ‘rational.’

I think people have real disputes about what is rational, which aren't simply based on misunderstandings of what the word means. For example, Is it rational to believe something on the basis of faith? Some people will say that it can be rational, at least in some cases, to believe something on the basis of faith; other people will say that faith is never rational.

By textbook definition, I mean for a belief to be rational, it must have been obtained using REASON. Reason is using known facts to arrive at new facts. A tool of reason, Logic, is the study of valid inference. So if our ‘reasoning’ is logical (consistent), then we can be sure of our conclusions. I suspect there will be less disagreement when we talk about rationality this way.

I think inference is part of rationality, but it is not the whole of rationality. Consider the belief "The sky is blue (right here, right now)" - is that belief rational? Well, the rationality of a belief depends on my reasons for believing it - are they good reasons or not? One reason for believing that, might be, I look up at the sky, and see that it is blue. In those circumstances, my belief is rational, but I don't see any process of inference involved - it is direct experience. So I don't agree with your "textbook definition", I think it is too narrow. Once we've identified that rationality has multiple components - sense experience, memory, deductive reasoning, inductive reasoning, etc. - it's a fair question to ask, whether we've exhaustively identified it's components, or if there are more to be discovered. Could faith be a component of rationality?

Your juxtaposition or analogy of ethics and rationality unravel when the word ‘rational’ is used more vigorously.

I don't agree - as I said, I think your "more vigorous" definition is actually an overly narrow definition.

To answer your two questions: It's because ethics and rationality are not logically connected.

I think they have many similarities - they are both systems of positive/negative valuation (good vs. evil, rational vs. irrational); they are both systems of obligation and prohibition (to be ethical, you must do this and must not do that; to be rational, you must believe this and must not believe that); they both have significant areas of near universal agreement (e.g. serial killing is wrong; believing that "1+1=2" is rational) juxtaposed with significant areas of major disagreement (e.g. is abortion wrong? can it be rational to believe on the basis of faith?); for both it is disputed whether they are objective or subjective.

To be rational, one must use reason to make ethical evacuations; however it’s possible to make ethical evaluations without reason. One can argue ethics by emotional outrage, after all. There is no such comparison when it comes to reason.

One can be rational without using inference. I have a headache, so I believe I have a headache. No inferences involved in justifying my belief; my belief is justified by my immediate experience. And "One can argue ethics by emotional outrage" seems mistaken, because most people would agree that mere presence of emotional outrage doesn't mean the ethical beliefs justified by that outrage are correct. Suppose a man walks in on his wife having an affair; his emotional outrage at the situation convinces him that murdering them would be morally acceptable. But surely, while that's an "argument" for murder being moral, it's not a good argument, because the conclusion is false.

I am not sure how you concluded that ‘faith’ is the part of one ‘coherent whole.’ It feels like ‘coherent whole’ is an adjective without a referent. IOW, a coherent whole…..what?

The coherent whole composed of rationality and ethics (and I would add aesthetics to it as well). Since they have so much in common, I believe that rationality and ethics are two parts of a larger whole, which I would label axiology, rather than being two completely separate and unrelated things. So, how is faith part of that coherent whole? Hopefully that will be clear in a moment.

Let’s start by you explaining exactly what you mean by ‘faith.’ The word ‘faith’ can mean a lot of different things to a lot of different people.

To me, faith is believing something because one is morally obliged to believe it. So, consider the proposition "The good always triumphs in the end", or the proposition "Every evil which occurs is necessary for some greater good". I believe that proposition by faith, because I believe that I am morally obliged to believe it. Now, you might not agree with me on that - you might not feel any moral obligation to believe that proposition. But I think we can divide the issue into several parts (1) whether, in principle, one could be morally obliged to believe one thing rather than another? (2) if so, how do those moral obligations interact with ones rational obligations? (3) if so, what specifically are one's moral obligations in regards to belief? I'd like to focus on (1) and (2), and we can leave (3) for another day - (1) and (2) determine whether my concept of faith is legitimate in the abstract, (3) is more about what specifically we should have faith in.

So the question is, can it be rational to believe in a proposition, simply because one is morally obliged to believe it? I say yes. This is where the "coherent whole" argument comes in. If ethics and rationality are unrelated, we have no reason to expect rational and ethical obligations to coincide; one might be ethically obliged to believe one thing, and rationally obliged to believe another. On the other hand, if they are closely related, and two parts of one coherent whole, then we should expect our ethical and rational obligations to be harmonious.

To me, faith in its highest form has three key ingredients:
(1) if we believe X, we will be ethically superior than if we didn't
(2) there is a lack of other evidence against X
(3) this lack of evidence against X is unlikely to ever change

Considering "The good always triumphs in the end", it meets the three criteria:
(1) I think believing "The good always triumphs in the end" makes me ethically a better person than if I didn't think that
(2) There is no evidence against it. Obviously it doesn't always hold in this life - but with an afterlife it could easily hold always, and there is no evidence against an afterlife
(3) That situation is unlikely to ever change - there is never going to be any evidence against an afterlife - by its nature, it will always remain impossible to disprove

What kind of god do you believe in, exactly?

I believe in a God who created the universe, and who loves us, and loves all that is good and true and beautiful. Although God created all that is evil, God only did so for the sake of the far greater goods those evils achieve, even if what those goods are, and how they are achieved, is presently obscure to us. I believe that everyone comes out of unity with God - God chose to empty himself/herself of divinity, and divide himself/herself into many, in order to become us - and eventually (not immediately after death, but some time later), we will all return to unity and identity with God and with one another. I suppose the later belief might be described as panentheism, although I'm not sure that's a completely accurate label (not that we need to go into that right now).

Regards, Zack

[Juice]

Hi again Zack,

Of course, the choice of "many" rather than "all" implies "some paraconsistent logics deny or lack the Law of Non-Contradiction" - and those are the forms of paraconsistent logic that I am most interested in here.

No, not necessarily. It simply means that many paraconsistent logics validate the LNC. If you can negate the LNC using paraconsistent logic I would be interested in seeing that. You need to spend a little time trying to grasp what paraconsistent logic is. By definition, any logic that is not explosive is paraconsistent. This does not mean it negates the LNC.

That is one motivation, but not the only motivation. Another motivation is to try to "solve" difficult mathematical paradoxes (like Russell's paradox in set theory) and linguistic paradoxes (like the liar sentence), with the innovative declaration that the paradox requires no solution and can be accepted as is. If you look at the history of dialetheism in Indian logic (Hindu, Buddhist and Jain), my understanding is that in that case it has theological motivations also. "Orthodoxy" varies from culture to culture - what is unorthodox in Western logic is orthodox in Indian logic

Whatever the motivations may be it remains that paraconsistent logic does not negate the LNC.

I'd also reiterate my prior mention of intuitionistic logic and its rejection of the law of the excluded middle - even if everything you have said about the law of non-contradiction is right, you still have to contend with the argument over that.

An oversight on my part. As with your claim that paraconsitent logic denies the LNC, this claim regarding intuitionistic logic is similarly not accurate either. Intuitionisitc logic does not formally deny the law of the excluded middle per se. Intuitionistic logic simply does not assume the law of the excluded middle as an axiom. There is a meaningful difference.

To be honest, the "challenge" to orthodoxy is very old. In the days in which Aristotle was proposing the law of non-contradiction and the law of the excluded middle, there were people disagreeing with him (as he notes in his works). In India, we have an entire logical tradition largely rejecting these two laws.

The laws of thought are simply axioms assumed to be true as they are self evident. Though it is conceivable to construct a system that does not assume one of these laws, it’s important to note that as far as I am aware these laws have not been formally negated.

I don't believe logic is ultimately subjective - I believe that both logic and ethics are objective. However, I do believe, that disputes in both are very difficult, at times impossible, to resolve - and that is one of the indications of subjectivity which opponents of objective ethics use to argue for its subjectivity. But, my argument is, if that indication of subjectivity is present in ethics, it is equally present in logic. To be consistent, if you use that indication of subjectivity in ethics as an argument for ethical subjectivity, then you must use the same indication in logic as an argument for rational subjectivity.

I think we agree that logic and ethics are objective. But your argument is contradictory. You are arguing logic is subjective because there exists disagreement over systems in an attempt to argue that both logic (or that which is rational) and ethics are also conversely objective. Surely you can see this fundamental flaw in your reasoning, which ironically makes it irrational. There are much more rational ways at arriving at the conclusion that ethics and reason are objective.

- there is a distinction between "modus ponens" on the one hand, and the laws of non-contradiction and the excluded middle on the other. The former, I am not aware of any logician or logical system which denies it; whereas the later two are controversial. (Of course, I can't say for sure no one denies "modus ponens", maybe someone does.) Given that, I feel on much safer ground using "modus ponens" than using the laws of non-contradiction and of the excluded middle. This is analogous to the relationship between the immorality of shooting sprees and the immorality of abortion. If I was trying to construct an ethical argument to convince as many people as possible, then the immorality of shooting sprees is a much better choice of premise than the immorality of abortion, since the former has near universal acceptance while the later doesn't. In the same way, if I'm trying to construct a logical argument to convince as many people as possible, then modus ponens is a much better choice of inference rule to choose than one which relies on the law of the excluded middle or the law of non-contradiciton.

The reason you feel safe using modus ponens (I’m not convinced you were even aware you were even employing modus ponens at the time) is that it is logical and verifiably so, unlike ethics. An ethical argument, though it can certainly be logical, cannot be verifiable in the same way a rule of inference can. In fact, your ethical argument would only hold water if it was logical. The rationality of your ethical argument is contingent upon the argument itself being logical.

On the contrary, my point is that when you take two entities X and Y, and then someone claims some property P is true for X but false for Y, then the degree of similarity between X and Y is a relevant consideration in determining the plausibility of their claim. If X and Y have little in common, their claim is much more plausible, than if numerous similarities and analogies are shown to exist between them

We can always consider similarities between X and Y but must be careful not commit the False Analogy fallacy., which it appears you have done.

I don't claim logic is subjective. I claim that both logic and ethics are objective. I also claim that, arguments for the subjectivity of ethics work also as arguments for the subjectivity of logic - I see ethics and logic as a package deal, whose objectivity stands and falls together. I don't think it makes sense to accept the objectivity of one while denying it for the other.

It is true that you have not directly claimed logic is subjective but you have certainly implied it. You wrote in your earlier post #9 – ”So, this is part of why I think that logic has much more of a subjective flavour than many people think it does.”

I don't agree with that. There is a lot more to rationality than just logic. For example, people argue about what is the rational burden of proof (does the person who claims God exists bear the burden of proving his existence?) - and yet I don't know of any logical system which deals with burdens of proof. And the basic principles of logic cannot be demonstrated, one has to just accept them - once you agree on the basic principles, you can seek to apply them, and those applications involve demonstrations. But in the same way, once you agree with someone on basic ethical principles, then you can demonstrate various conclusions as an application of those principles. I don't think the immorality of abortion is demonstrable starting from the bare minimum of those ethical principles which all humans agree on, but if you agree on more (e.g. the basic principles of Catholic moral theology), then you have shared principles from which you can demonstrate that conclusion.

I agree that it is correct - but it is impossible to demonstrate its correctness, it is just something that must be accepted without proof or reason. Much in the same way that it is impossible to demonstrate the correctness of ethical principles - "It is wrong to kill and maim innocent people for the sheer pleasure of it" - that is an ethical principle I'm sure we all agree on, but there is no way to prove or demonstrate its correctness, it is just something that must be accepted without proof or reason.

I’m sorry Zack, but this simply is not correct. It is very possible to demonstrate the correctness of a rule of inference such modus ponens. See here. And this is where your argument fundamentally breaks down.

Zack, you didn’t answer my question (or maybe you did and I missed it). How do you determine what is and is not rational? What mechanism(s) do you use if not logic?

Cheers.

[Juice]

Hi Nick, I agree with most of your post which is why I gave it an "amen." But, of course, notwithstanding the author of this thread, I would dispute what the following claim implies

This brings me to my second point. It appears that I encounter more rational atheists than I do theists (in this sense, when I say ‘rational theist/atheist’ I mean they arrived at their religious beliefs (or lack thereof) rationally).

Further, this statment above does not make sense unless you are arguing atheism itself is in fact a religious belief.

[bertatberts]

Further, this statment above does not make sense unless you are arguing atheism itself is in fact a religious belief.

Lets not forget the atheist's who have studied religions and religious beliefs and found them wanting. Atheist only means to be without god, nothing else, atheist's do not have to accept any dogma or tenets to study a thing.

[ZackMartin]

any logic that is not explosive is paraconsistent. This does not mean it negates the LNC.

Let's consider a specific paraconsistent logic, a simple propositional one, LP. Wikipedia provides a brief relational presentation here; personally, I find the presentation based on three-valued logic easier to follow. LP has three truth values: true, false, both. The truth tables:

p	~p
F	T
T	F
B	B

p	q	p|q	p&q
F	F	F	F
F	T	T	F
F	B	B	F
T	F	T	F
T	T	T	T
T	B	B	B
B	F	B	F
B	T	T	B
B	B	B	B

Now, let's apply this to the law of non-contradiction, ~(p & ~p):

p	~p	p&~p	~(p&~p)
F	T	F	T
T	F	F	T
B	B	B	B

So you can see, in LP, the law of non-contradiction is always true, but sometimes it is also false (depending on the truth values of the propositional variables). It may still be a "law" in the sense of being always true, but it's no longer a "law" in the sense of being never false - so in a very real sense it is no longer a law, more of a "half-law". You said "paraconsistent logic does not negate the LNC" - well, LP does negate LNC, for some propositions, but not for all.

An oversight on my part. As with your claim that paraconsitent logic denies the LNC, this claim regarding intuitionistic logic is similarly not accurate either. Intuitionisitc logic does not formally deny the law of the excluded middle per se. Intuitionistic logic simply does not assume the law of the excluded middle as an axiom. There is a meaningful difference.

The law of the excluded middle is (p|~p). Let's check what that evaluates to in LP:

p	~p	p|~p
F	T	T
T	F	T
B	B	B

So, same story as with the law of non-contradiction - the law of the excluded middle is not a law in LP. Yes, it is always true; but sometimes it is also false.

Asking does LP "negate" LNC or LEM is ambiguous. Does "negate" mean always evaluate as false? If that is what is meant, then it doesn't. Or does "negate" mean sometimes evaluate as false? If that is what is meant, then it does. Both, given the right propositions, are both true and false simultaneously, and that which is both true and false simultaneously is indeed false, albeit not only false.

The laws of thought are simply axioms assumed to be true as they are self evident. Though it is conceivable to construct a system that does not assume one of these laws, it’s important to note that as far as I am aware these laws have not been formally negated.

But not everyone agrees that they are self-evident - adherents to the constructivist position in the philosophy of mathematics do not agree that the law of the excluded middle is self-evident, at least as applied to all cases. Although I've never met the guy personally, from reading one of his books, I don't get the impression that Prof. Graham Priest (arguably the world's leading authority on paraconsistent logic) considers LNC to be self-evident. LNC and LEM aren't self-evident to me either - while I don't definitively adhere to dialetheism, it seems to me to be a definite possibility. And as I've pointed out, your asking for the laws to be "formally negated" is ambiguous.

I think we agree that logic and ethics are objective. But your argument is contradictory. You are arguing logic is subjective because there exists disagreement over systems in an attempt to argue that both logic (or that which is rational) and ethics are also conversely objective. Surely you can see this fundamental flaw in your reasoning, which ironically makes it irrational. There are much more rational ways at arriving at the conclusion that ethics and reason are objective.

Consider someone who believes that rationality is objective and ethics is subjective. I ask, why treat one as objective and the other as subjective? They both seem the same to me. They respond, How can you believe ethics is subjective? There is so much disagreement about it, and the disagreement seems impossible to ever resolve. Says I: Ah, but there is just as much disagreement about rationality/logic, and the disagreement seems impossible to ever resolve. (Well, in absolute terms, there is much more disagreement about ethics, since ethics is an intensely practical subject, while logic and rationality are the abstract domain of philosophers and mathematicians - but among those who think seriously and deeply about logic, I believe there is an equivalent degree of disagreement, proportionally speaking.) So, if your argument works to show that ethics is subjective, it also works to show that rationality/logic are also subjective. And my hope is they jump from here to the both objective position, rather than the both subjective position.

Then, there is another aspect of the argument: Those who agree that both rationality and ethics are objective, but think they are largely unrelated things, as opposed to my position that they are two parts of a larger unified whole. Pointing to this similarity between ethics and rationality, is evidence in favour of my position - since the more similarities between the two I can point to, the more evidence for that I have. I called this similarity the "flavour of subjectivity" (existence of apparently insoluble radical disagreements), not because I ultimately believe that it is subjective, or that this "flavour" is convincing evidence of subjectivity, but because it is something that subjectivists use to argue for their position.

The reason you feel safe using modus ponens (I’m not convinced you were even aware you were even employing modus ponens at the time) is that it is logical and verifiably so, unlike ethics. An ethical argument, though it can certainly be logical, cannot be verifiable in the same way a rule of inference can. In fact, your ethical argument would only hold water if it was logical. The rationality of your ethical argument is contingent upon the argument itself being logical.

I'm not sure about the claim that modus ponens is always "logical and verifiably" so. Modus ponens is actually ambiguous. MP states "P -> Q, P, therefore Q". But what is "->"? Is it material implication, strict implication (and if so, which modal logic?), or relevant implication (and if so, which relevance logic?). I suppose the structure is the same in every case, but really MP is not a single inference rule, but numerous rules.

The paradoxes of material implication ("If I'm a donkey, two plus two is four") are a good example of how people disagree on logic. We have a choice here: one the one hand, material implication is easy to formalise, yet violates common sense; on the other hand, relevant implication obeys common sense much better (at least for some test cases), yet is far more complicated. Some people say that the simplicity of material implication is worth a few affronts to common sense, others will say that the affront to common sense is worse than the complexity of relevance logic. Who is right?

We can always consider similarities between X and Y but must be careful not commit the False Analogy fallacy., which it appears you have done.

How is my analogy a false one?

It is true that you have not directly claimed logic is subjective but you have certainly implied it. You wrote in your earlier post #9 – ”So, this is part of why I think that logic has much more of a subjective flavour than many people think it does.”

I think my above comments about what I mean by "flavour of subjectivity", and my purpose in invoking it, have hopefully cleared this up.

It is very possible to demonstrate the correctness of a rule of inference such modus ponens. See here. And this is where your argument fundamentally breaks down.

I don't see any proof of the correctness of modus ponens on that page - I see a bunch of truth tables. I gave truth tables for LP above, but I didn't demonstrate LP was correct, in the sense of being the logical system we should use. In fact, LP is undoubtedly wrong, because it is way too simple (it is only propositional calculus; it has very weak inference rules).

Zack, you didn’t answer my question (or maybe you did and I missed it). How do you determine what is and is not rational? What mechanism(s) do you use if not logic?

Neither rationality nor ethics can be reduced to a simple formula. The formula is complex, and we don't fully know what it is. We know bits of it; we can consider generalising from those bits, but we should be a bit cautious unless we overgeneralize. As we stumble around in the dark of what we do not know, we remain hopeful that we will find some light, but we can't say for sure what that light will look like until we've seen it.

We don't always need mechanisms. I know that "1+1=2", I know that "killing innocent people for the sheer pleasure of it is wrong", I know that "I exist". By what mechanism do I know these things? I don't believe I know them by any mechanism, I just know them. I don't know them on the basis of logical inference - I can prove "1+1=2" in Peano arithmetic, but I knew that "1+1=2" is true long before I knew what the axioms of Peano arithmetic were, or even what a proof was.

Regards, Zack

[OtherCheek]

ZackMartin:

A philosophical belief, must be a belief and not an opinion, it can't be a viewpoint either, it must be based on the information available, it must also be able to attain a level of seriousness, cohesion, importance and cogency, and be worthy of respect.

Two examples of philosophical belief are atheism and humanism, faith does not even enter the equation.

I prefer this one philosophical dictionary http://www.philosophy-dictionary.org...tionary/BELIEF

"Belief, is a form of judging something to be true, intermediate between mere opinion and certain knowledge. To believe something in this sense is to judge that it is true by virtue of "a ground that is objectively insufficient but subjectively sufficient" in mere opinion neither are sufficient, in knowledge both conditions are met.

So could you tell me how faith/belief meets both?
Thus it cannot be justified true, no matter how you play it.

Can't the belief in a certain proposition or principle be tested? Which experiment (and the results) can then lead to knowledge of that thing?

[Soyeong]

Lets not forget the atheist's who have studied religions and religious beliefs and found them wanting. Atheist only means to be without god, nothing else, atheist's do not have to accept any dogma or tenets to study a thing.

Are you sure that's not one of your tenets right there?

[ZackMartin]

Can't the belief in a certain proposition or principle be tested? Which experiment (and the results) can then lead to knowledge of that thing?

Hi OtherCheek,

Some propositions or principles can be easily tested; others are difficult or impossible to test.

The proposition "Killing people just for fun is immoral" - clearly that's true, everyone agrees on it (excluding a small minority of very disturbed people, like serial killers - and even many of those agree that what they do is wrong.) But how can we test it? I'm not aware of any way to test this proposition. Either you accept it, or you don't. You could try to demonstrate it based on some broader principles - you could start with e.g. Jeremy Bentham's greatest happiness principle "good is whatever causes the greatest happiness for the greatest number of people", or a principle like "the Bible is a reliable source of moral truth", and then prove "Killing people just for fun is immoral" based on that assumption. But I think in a way you've gone backwards, because you are proving something which is near universally accepted, using premises which are far from being universally accepted.

An example of a proposition we can test is "There is a life after death". The test involves dying. If you die, and find yourself in another place (heaven, hell, purgatory, reincarnation) - you have proof of the existence of an afterlife, and the test succeeded. If you cease to exist, then you have no such proof, and the test failed. (Of course, I'd strongly discourage anyone from dying prematurely for experimental reasons; but it is a valid experiment nonetheless.)

The bare claim "God exists", can't be tested. But the claim "God exists, and he will judge you after death" - that can be tested through death - if you die and cease to exist, or if you find yourself in a very different afterlife (e.g. being reincarnated as a rat), both would be evidence that "God exists, and he will judge you after death" is incorrect, while seeing God standing there in judgement after death, that would be evidence that "God exists, and he will judge you after death" is correct

Regards, Zack

[Juice]

Hi Zack,

So you can see, in LP, the law of non-contradiction is always true, but sometimes it is also false (depending on the truth values of the propositional variables). It may still be a "law" in the sense of being always true, but it's no longer a "law" in the sense of being never false - so in a very real sense it is no longer a law, more of a "half-law". You said "paraconsistent logic does not negate the LNC" - well, LP does negate LNC, for some propositions, but not for all.

According to the link you provided to wiki (who in turn cites B.H. Slater), - “ Others, such as David Lewis, have objected to paraconsistent logic on the ground that it is simply impossible for a statement and its negation to be jointly true. A related objection is that “negation” in paraconsistent logic is not really negation; it is merely a subcontrary-forming operator.”

Asking does LP "negate" LNC or LEM is ambiguous. Does "negate" mean always evaluate as false? If that is what is meant, then it doesn't. Or does "negate" mean sometimes evaluate as false? If that is what is meant, then it does. Both, given the right propositions, are both true and false simultaneously, and that which is both true and false simultaneously is indeed false, albeit not only false.

Under a system where a proposition can be both true and false simultaneously can that proposition ever fully be declared to be false (or true for that matter)?

But not everyone agrees that they are self-evident - adherents to the constructivist position in the philosophy of mathematics do not agree that the law of the excluded middle is self-evident, at least as applied to all cases. Although I've never met the guy personally, from reading one of his books, I don't get the impression that Prof. Graham Priest (arguably the world's leading authority on paraconsistent logic) considers LNC to be self-evident. LNC and LEM aren't self-evident to me either - while I don't definitively adhere to dialetheism, it seems to me to be a definite possibility. And as I've pointed out, your asking for the laws to be "formally negated" is ambiguous.

My point was not that it is necessary for everyone to agree that they are self evident.

Consider someone who believes that rationality is objective and ethics is subjective. I ask, why treat one as objective and the other as subjective? They both seem the same to me. They respond, How can you believe ethics is subjective? There is so much disagreement about it, and the disagreement seems impossible to ever resolve. Says I: Ah, but there is just as much disagreement about rationality/logic, and the disagreement seems impossible to ever resolve. (Well, in absolute terms, there is much more disagreement about ethics, since ethics is an intensely practical subject, while logic and rationality are the abstract domain of philosophers and mathematicians - but among those who think seriously and deeply about logic, I believe there is an equivalent degree of disagreement, proportionally speaking.) So, if your argument works to show that ethics is subjective, it also works to show that rationality/logic are also subjective. And my hope is they jump from here to the both objective position, rather than the both subjective position.

But on what rational grounds should they make that “jump” to objectivity? This is where your argument gets fuzzy and I am not at all clear. All your argument would succeed in accomplishing is to show that both logic and ethics are subjective to varying degrees. What those degrees are remains a mystery at this point. You’ll need to show that the degree to which there is subjectivity in logic is at least the same as the degree of subjectivity in ethics to make your argument even begin to work. Which you have conceded is in absolute terms not the case. You bear the burden here and have a tremendous hill to climb. It is not enough simply to establish that there is subjectivity in logic or merely assert the degree of disagreement in logic is equivalent to ethics.

Then, there is another aspect of the argument: Those who agree that both rationality and ethics are objective, but think they are largely unrelated things, as opposed to my position that they are two parts of a larger unified whole. Pointing to this similarity between ethics and rationality, is evidence in favour of my position - since the more similarities between the two I can point to, the more evidence for that I have. I called this similarity the "flavour of subjectivity" (existence of apparently insoluble radical disagreements), not because I ultimately believe that it is subjective, or that this "flavour" is convincing evidence of subjectivity, but because it is something that subjectivists use to argue for their position.

If you concede that the “flavour of subjectivity” (existence of apparently insoluble radical disagreements) is not convincing evidence of subjectivity why argue it and would I accept it? Further, this “unified whole” you speak of, what is it? Can you objectively establish its existence?

I'm not sure about the claim that modus ponens is always "logical and verifiably" so. Modus ponens is actually ambiguous. MP states "P -> Q, P, therefore Q". But what is "->"? Is it material implication, strict implication (and if so, which modal logic?), or relevant implication (and if so, which relevance logic?). I suppose the structure is the same in every case, but really MP is not a single inference rule, but numerous rules

The paradoxes of material implication ("If I'm a donkey, two plus two is four") are a good example of how people disagree on logic. We have a choice here: one the one hand, material implication is easy to formalise, yet violates common sense; on the other hand, relevant implication obeys common sense much better (at least for some test cases), yet is far more complicated. Some people say that the simplicity of material implication is worth a few affronts to common sense, others will say that the affront to common sense is worse than the complexity of relevance logic. Who is right? .

Despite your complaints about modus ponens and attempts to strengthen your argument by muddying the water, you were more than happy to use modus ponens earlier. Or did you not realize you were using it?

How is my analogy a false one?

The “False” in False Analogy is a bit of a misnomer. It isn’t so much “false” per se as it is weak. It is weak because there seem to be very few similarities between ethics and logic. And the one similarity you seem to have grasped onto (i.e. the existence of subjectivity evidenced by the existence of unsolvable disagreements) is disputed.

I think my above comments about what I mean by "flavour of subjectivity", and my purpose in invoking it, have hopefully cleared this up.

Your comments above appear to be disingenuous considering you have claimed that Logic is not subjective, but objective.

I don't see any proof of the correctness of modus ponens on that page - I see a bunch of truth tables. I gave truth tables for LP above, but I didn't demonstrate LP was correct, in the sense of being the logical system we should use. In fact, LP is undoubtedly wrong, because it is way too simple (it is only propositional calculus; it has very weak inference rules).

When you said “correct,” I understood you to mean valid. You do agree modus ponens is valid don’t you? You must, you used it.

Neither rationality nor ethics can be reduced to a simple formula. The formula is complex, and we don't fully know what it is. We know bits of it; we can consider generalising from those bits, but we should be a bit cautious unless we overgeneralize. As we stumble around in the dark of what we do not know, we remain hopeful that we will find some light, but we can't say for sure what that light will look like until we've seen it.

But you were happy to reduce that basis of your world view down into an argument built off a single rule of inference - modus ponens.

We don't always need mechanisms. I know that "1+1=2", I know that "killing innocent people for the sheer pleasure of it is wrong", I know that "I exist". By what mechanism do I know these things? I don't believe I know them by any mechanism, I just know them. I don't know them on the basis of logical inference - I can prove "1+1=2" in Peano arithmetic, but I knew that "1+1=2" is true long before I knew what the axioms of Peano arithmetic were, or even what a proof was.

You know these things because they are somewhat self evident (perhaps with exception of killing innocent people). But how do you handle things that aren’t so self evident? How do you know that which you think is rational is in fact rational when the rationality of that thing is not so self evident?

I would agree that there is no single mechanism that can answer every question. Logic alone doesn’t answer every question. And you are right, sometimes we don’t need even need a mechanism. But sometimes we do.

I’ll simply note that if your position truly is that we do not need a mechanism to establish that which is rational then I would assume you subscribe to no particular mechanism(s). (But we do know you at least subscribe to modus ponens? ). If you truly subscribe to no mechanism(s) for establishing that which is rational then you have no way of objectively demonstrating your beliefs rational. Consequently, you have no objective way to declare atheism to be irrational either. In short, if that truly is your position we have no real baseline from which to discourse and sadly you’ll offer nothing meaningful in the end.

Cheers.

[Chrawnus]

This is wear your argument gets fuzzy and I am not at all clear.

You might want to rewrite this particular sentence, because I don't think it's conveying the meaning you intended when you wrote it.









The Grammar Nazi strikes again!

[Juice]

You might want to rewrite this particular sentence, because I don't think it's conveying the meaning you intended when you wrote it.









The Grammar Nazi strikes again!

Ya vol. Done.



Damn you Grammar Nazi, damn you.

[Juice]

Lets not forget the atheist's who have studied religions and religious beliefs and found them wanting. Atheist only means to be without god, nothing else, atheist's do not have to accept any dogma or tenets to study a thing.

Which is fundamentally what I’m driving at. If the atheistic position is arrived at merely by withholding intellectual assent to the conclusion God exists, then atheism is not, strictly speaking, arrived at rationally, if we understand that which is arrived at rationally to mean that which is arrived at by the means of adhering to the principles of logic. In light of this, the only way an atheist can say he has arrived at his position rationally is to present a valid argument against the existence of God. Atheists would have more credibility making the claim their position is rational if they spent more time presenting positive arguments for their position rather than sitting back and sniping theistic arguments.



Cue the complaint, "bbbut it's hard to prove a negative"

[Psychic Missile]

Which is fundamentally what I’m driving at. If the atheistic position is arrived at merely by withholding intellectual assent to the conclusion God exists, then atheism is not, strictly speaking, arrived at rationally, if we understand that which is arrived at rationally to mean that which is arrived at by the means of adhering to the principles of logic. In light of this, the only way an atheist can say he has arrived at his position rationally is to present a valid argument against the existence of God. Atheists would have more credibility making the claim their position is rational if they spent more time presenting positive arguments for their position rather than sitting back and sniping theistic arguments.



Cue the complaint, "bbbut it's hard to prove a negative"

Would you agree that you have an irrational disbelief in fairies?