Originally posted by lee_merrill
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A review of the Craig v. Malpass discussion
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"[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by lee_merrill View PostThere is an actual infinity of points in every finite interval! Thus Achilles can catch the tortoise, in Zeno's paradox, by traversing an actual infinity of intervals. You only travers actual infinites of points in time in the human mind, and not in nature.
Blessings,
Lee
The closest thing in science is the smallist theoretical measure of time 'planck time,' and the smallest measure used is the Chronon. Again . . . these are human attempts to measure time.Last edited by shunyadragon; 05-08-2020, 07:35 PM.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
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Originally posted by Boxing Pythagoras View PostThat still doesn't make sense to me.
Imagine, for a moment, that I had not clarified that Benardete believed the precise opposite of Dr. Craig regarding the metaphysics of infinity. Which part of Craig's statement would indicate that Benardete says something with which Craig disagrees? It's certainly not the acknowledgment that actual infinites are not logically inconsistent, as Craig himself believes that. It's not in his characterization of actual infinites as "monstrosities" or in the direct claim that they are metaphysically impossible. It is nowhere in his discussion of the infinite book. At no point does Dr. Craig make any indication that he is citing someone who believes the exact opposite of what he is saying.
And I do think he gives ample indication using tone of voice, facial expression and head gestures to indicate disagreement with Benardete, so even if he doesn't explicitly state that Benardete thinks actual infinities are possible, but that he himself disagrees with that notion, I think he still implies it with all of the previous mannerism I mentioned. Assuming I'm correct that all of the above indicates disagreement, given that he clearly agrees with Benardete that actual infinities are not logically impossible, his disagreement would be with something not directly stated, which would reasonably be the position that actual infinites are metaphysically possible. If I'm correct that Craig is expressing disagreement in the part that I bolded, then it's also reasonable to infer that Benardete's position is the opposite of Craig's. IOW, Craig doesn't have to explicitly state what Benardete's position is on the issue, because by stating his own opinion in a way that expresses disagreement with Benardete, the implication is that Benardete holds to the opposing position.
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Originally posted by Boxing Pythagoras View PostI honestly don't notice any such shift in tone; however, Benardete never even refers to actual infinites as "monstrosities," even if the second half of the sentence is meant to be Dr. Craig's own thoughts. It certainly seems like Dr. Craig is attempting to cite Benardete as supporting his position-- otherwise, why reference Benardete at all? There's no need to cite another scholar simply to acknowledge that he's not claiming actual infinites are logically inconsistent.
I assume, without having read Benardete's book myself, that Benardete is saying that a physical infinite is possible, and he bases that on the fact that there's no logical contradiction and does not address the metaphysical aspect.Curiosity never hurt anyone. It was stupidity that killed the cat.
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Originally posted by QuantaFille View PostI'm going to add my 2˘. I take Dr Craig to be saying, "look, here's this guy who agrees with me that there is no logical contradiction here, and I'd like to add that there is a contradiction I see and it's a metaphysical one".
I assume, without having read Benardete's book myself, that Benardete is saying that a physical infinite is possible, and he bases that on the fact that there's no logical contradiction and does not address the metaphysical aspect."[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Incidentally, I just had my wife listen to the section in question, completely without context, and she agrees with Chrawnus and QuantaFille that it does not seem like Dr. Craig is citing someone who agrees with him; so I'll certainly concede that I'm likely the one misunderstanding his intention here.
That said, what do we think about his actual argument? I'm still not clear on how Dr. Craig moves from "these things are strange" to "these things are metaphysically impossible.""[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by QuantaFille View PostI'm going to add my 2˘. I take Dr Craig to be saying, "look, here's this guy who agrees with me that there is no logical contradiction here, and I'd like to add that there is a contradiction I see and it's a metaphysical one".
I assume, without having read Benardete's book myself, that Benardete is saying that a physical infinite is possible, and he bases that on the fact that there's no logical contradiction and does not address the metaphysical aspect.
Personally my approach to the problem from a matter of fact of the limits of descriptive math when applied to metaphysical (?) assertions. Further, clarification is needed what is considered to be the metaphysical aspect as opposed the math of actual versus potential infinites as applied to our physical existence. Actual infinities are defined as 'closed' sets of infinities, and potential infinities are' open' sets without any defined limit. The usefulness of Math is defined as the ability to be descriptive of our physical existence. The only way an actual infinity can be applied to the past is to define a closed infinity with a beginning point, which cannot be done, nor can it be a closed set in the present.
Again . . . please explain What is the 'metaphysical aspect' where the math of infinities can be applied when they are asserted to be descriptive of the nature of our physical existence. This is as slippery as trying to nail a ten pound block of Jello to the wall.Last edited by shunyadragon; 05-09-2020, 09:07 AM.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
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Originally posted by shunyadragon View PostFirst, I am not satisfied with Benardete's argument.
Actual infinities are defined as 'closed' sets of infinities, and potential infinities are' open' sets without any defined limit.
A potential infinite, on the other hand, describes a process and not a set. A potential infinite refers to a process which can be iterated indefinitely. Here, the classic example is simple counting. This is a step-by-step process which can (at least theoretically) continue indefinitely, since every number counted has a successor which can be counted in the next step.
The usefulness of Math is defined as the ability to be descriptive of our physical existence.
The only way an actual infinity can be applied to the past is to define a closed infinity with a beginning point, which cannot be done
nor can it be a closed set in the present.
Again . . . please explain What is the 'metaphysical aspect' where the math of infinities can be applied when they are asserted to be descriptive of the nature of our physical existence. This is as slippery as trying to nail a ten pound block of Jello to the wall."[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by Boxing Pythagoras View PostDo you mean Dr. Craig's argument? We haven't actually discussed any of Benardete's arguments, other than to say that he thinks actual infinites ARE metaphysically possible.
This isn't quite correct. An actual infinite is any set which can form a bijection with a proper subset of itself. The classic example is the Natural numbers which can be placed in one-to-one correspondence with, for example, the Even numbers. Since the Evens are a proper subset of the Naturals, this implies that the Naturals form an actually infinite set.
A potential infinite, on the other hand, describes a process and not a set. A potential infinite refers to a process which can be iterated indefinitely. Here, the classic example is simple counting. This is a step-by-step process which can (at least theoretically) continue indefinitely, since every number counted has a successor which can be counted in the next step.
Neither of these points is actually correct. It's fairly trivial to imagine an infinite past without a beginning point. And even if we suppose that time is finitely bounded in the past direction, it's not difficult to define a scenario in which the number of past moments is still actually infinite.
Not sure what you mean, here.
I'm not sure what you are getting at, here, either. There's quite a number of metaphysical questions as regards mathematics, in general, and actual infinities, in particular.Last edited by shunyadragon; 05-09-2020, 12:56 PM.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
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Originally posted by Boxing Pythagoras View PostIncidentally, I just had my wife listen to the section in question, completely without context, and she agrees with Chrawnus and QuantaFille that it does not seem like Dr. Craig is citing someone who agrees with him; so I'll certainly concede that I'm likely the one misunderstanding his intention here.
That said, what do we think about his actual argument? I'm still not clear on how Dr. Craig moves from "these things are strange" to "these things are metaphysically impossible."Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
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Originally posted by shunyadragon View PostBoth arguments are flawed. I do not believe actual infinities are metaphysically meaningfully possible.
I disagree, as far as an infinite set of either even or odd numbers represent potential infinities as you describe below.
Agree with your description of a potential infinity, I disagree. In math infinities are also defined in terms of sets.
I am not sure what you are getting at. Philosophers try to apply math to metaphysical question, but I consider it fruitless effort.
Applying math to this apologetic argument needs too many metaphysical assumptions.
No explanation is forthcoming how these assertions of metaphysical claims can be justified by math.
The question still stands what are the metaphysical aspects involved here?"[Mathematics] is the revealer of every genuine truth, for it knows every hidden secret, and bears the key to every subtlety of letters; whoever, then, has the effrontery to pursue physics while neglecting mathematics should know from the start he will never make his entry through the portals of wisdom."
--Thomas Bradwardine, De Continuo (c. 1325)
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Originally posted by Boxing Pythagoras View PostWhy not? They seem to me to be just as meaningful for metaphysics as any other aspect of mathematics.
No, they don't. We can meaningfully talk about the whole set of Even numbers without having to enumerate them in a step-wise fashion. And it's rather simple to show that the Even numbers form a bijection with proper subsets of the Even numbers (for example, the multiples of 4). This is precisely what mathematicians have meant by an actually infinite set for centuries, now.
Actual infinities refer to sets, in math. Potentially infinite refer to processes.
Why do you consider it fruitless? Quite the contrary, mathematics seems very fruitful for metaphysics. After all, if something is mathematically impossible most people would agree that such a thing is metaphysically impossible.
What metaphysical assumptions would those be?
What assertions are you talking about?
The concepts of number, magnitude, and quantification.
Still waiting for what are the metaphysical aspects I asked about. There is no explanation forthcoming.Last edited by shunyadragon; 05-09-2020, 03:57 PM.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
Comment
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Originally posted by shunyadragon View PostTime and space do not have any intervals attached. Even WLC's reference to moments are a human concept of viewing time. Again . . in nature time is not divided into 'moments.'
The closest thing in science is the smallist theoretical measure of time 'planck time,' and the smallest measure used is the Chronon. Again . . . these are human attempts to measure time.
Blessings,
Lee"What I pray of you is, to keep your eye upon Him, for that is everything. Do you say, 'How am I to keep my eye on Him?' I reply, keep your eye off everything else, and you will soon see Him. All depends on the eye of faith being kept on Him. How simple it is!" (J.B. Stoney)
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Originally posted by lee_merrill View PostNo, but we can divide time and space into intervals.
And just because there is a smallest measure of time that we can theoretically measure does not mean we cannot consider intervals of time (and space) that are arbitrarily small.
Actually science is not all that concerned whether our physical existence is fine nor infinite, because it cannot be falsified either way. In fact in math has been demonstrated in physics to work very well even without the symbol of infinity.
Metaphysics makes claims based philosophy and beliefs, which are premises in their arguments to justify their beliefs. Science does not make claims that cannot be falsified by scientific methods.Last edited by shunyadragon; 05-09-2020, 07:05 PM.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
Comment
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Originally posted by Boxing Pythagoras View PostQuite the contrary. The title of the book is Infinity: An Essay In Metaphysics. The entire goal of the book is to defend the notion of infinity against both metaphysical and mathematical finitists.Curiosity never hurt anyone. It was stupidity that killed the cat.
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