The East frees us from Thomism?

[Hastrman]

As indicated above, I see mathematics primarily as a system of formal logic. Of course, in the light of Godel’s Incompleteness Theorem, that means that there must be some propositions in mathematics which are neither true nor false, given my way of looking at things.

You think that’s what Goedel Incompleteness means, and you call yourself a mathematician?

Goedel Incompleteness states that any consistent group of axioms will contain axioms that cannot be proven within that group of axioms–proving them will require reference to other information. That does not mean that those axioms are neither true nor false–it *might *, sometimes, mean they’re not provable, but that’s not the same thing at all.

Basically you’ve commited this all-too-common fallacy:

Not provable=neither true nor false

And with arguments of this caliber does it ask me to deny my God?

 

[mathematician]

You think that’s what Goedel Incompleteness means, and you call yourself a mathematician?

Goedel Incompleteness states that any consistent group of axioms will contain axioms that cannot be proven within that group of axioms–proving them will require reference to other information. That does not mean that those axioms are neither true nor false–it *might *, sometimes, mean they’re not provable, but that’s not the same thing at all.

Basically you’ve commited this all-too-common fallacy:

And with arguments of this caliber does it ask me to deny my God?

Whether or not it means that they are neither true nor false depends upon whatever other presuppositions you bring to the table doesn’t it? If I were a Platonist, and I thought that there was some kind of mathematical universe existing independently of the minds which percieve it, then proposition P could have a truth value which was independent of my ability to establish that value. If you believe in no such platonic realm, however, P can only be true or false if its truth value can be deduced from the axioms.

 

[Hastrman]

Whether or not it means that they are neither true nor false depends upon whatever other presuppositions you bring to the table doesn’t it? If I were a Platonist, and I thought that there was some kind of mathematical universe existing independently of the minds which percieve it, then proposition P could have a truth value which was independent of my ability to establish that value. If you believe in no such platonic realm, however, P can only be true or false if its truth value can be deduced from the axioms.

No, obviously if anything has a truth value, it has that value independently of whether or not you happen to be able to prove it. You’d know that if you knew what truth meant (hint: not “provable,” otherwise you’re just begging the question).

But please don’t let’s get into a sidebar on “what is truth”; the point is that you were woefully misrepresenting Goedel Incompleteness. Nobody but nobody has ever interpreted it to mean “some things are neither true nor false” unless they were being willfully, disingenuously tendentious.

 

[mathematician]

No, obviously if anything has a truth value, it has that value independently of whether or not you happen to be able to prove it. You’d know that if you knew what truth meant (hint: not “provable,” otherwise you’re just begging the question).

But please don’t let’s get into a sidebar on “what is truth”; the point is that you were woefully misrepresenting Goedel Incompleteness. Nobody but nobody has ever interpreted it to mean “some things are neither true nor false” unless they were being willfully, disingenuously tendentious.

I wasn’t misrepresenting anything. In a formal system something has a truth value if and only if that value can be deduced from the axioms. How else do you propose to find a truth value without going outside of ZFC (say)?

Nobody but nobody has ever interpreted it to mean “some things are neither true nor false” unless they were being willfully, disingenuously tendentious.

You haven’t done very much reading on the subject have you? If they are not platonists they are merely being logically consistent. The facetious question has been asked about whether God is a mathematician, but so far as I know nobody has ventured to answer it in the affirmative. Perhaps the Pope is going to in his next infallible pronouncement?

 

[Hastrman]

Your puerile little sneers about what you think (wrongly–and laughably so) is the doctrine of infallibility, are essentially about as impressive, to me at least, as a “Your Mom” comeback.

It’s cute, though, the way you cover a thoroughly half-educated understanding of mathematical realism (Platonism! Ha!) with those little religious slurs. Bertrand Russell, Wittgenstein, Penrose, Lucas, and Goedel himself would have been quite peeved if you’d called any of them (except maybe Penrose) a Platonist.

 

[mathematician]

Your puerile little sneers about what you think (wrongly–and laughably so) is the doctrine of infallibility, are essentially about as impressive, to me at least, as a “Your Mom” comeback.

It’s cute, though, the way you cover a thoroughly half-educated understanding of mathematical realism (Platonism! Ha!) with those little religious slurs. Bertrand Russell, Wittgenstein, Penrose, Lucas, and Goedel himself would have been quite peeved if you’d called any of them (except maybe Penrose) a Platonist.

You still haven’t explained to me how something which can supposedly have a pre-existing truth value, but not provable within an axiom schema (the Axiom of Choice say) can simply be defined as true (or false) and then become part of the axiom schema.

 

[Hastrman]

You still haven’t explained to me how something which can supposedly have a pre-existing truth value, but not provable within an axiom schema (the Axiom of Choice say) can simply be defined as true (or false) and then become part of the axiom schema.

Um…because the Axiom of Choice is an abstraction from actual experience?

Wait, wait, I think I’ve met that before! Is it…Aristotelianism?

By Jove, whaddya know, it is.

 

[mathematician]

Um…because the Axiom of Choice is an abstraction from actual experience?

Wait, wait, I think I’ve met that before! Is it…Aristotelianism?

By Jove, whaddya know, it is.

I wouldn’t know. It isn’t part of my every day experience to make choices from amongst an infinite number of sets.

 

[Hastrman]

Aristotelianism, being a philosophy for those with mature intellects, allows one to apply principles abstracted from lived, actual experiences–and in theory, from experiments–to hypothetical situations one will never experience.

You know, not like quantum physics or relativity or anything like that, all of which we’ve directly observed in our everyday lives.

 

[mathematician]

Aristotelianism, being a philosophy for those with mature intellects, allows one to apply principles abstracted from lived, actual experiences–and in theory, from experiments–to hypothetical situations one will never experience.

It’s as well that you never had to do a degree in mathematics, otherwise you would know that that would never wash. All sorts of things can be “obviously” true, but still false.

 

[Aramis]

Nothing to replace Aristotlean physics with? Ever heard of Newton, Einstein, Bohr, Dirac…?

All of whom built on to the accumulation of knowledge which truly starts with Aristotle.

Most working scientists would not say “replace” but “correct”, “expand,” or “fill in the gaps”…

 

[Hastrman]

It’s as well that you never had to do a degree in mathematics, otherwise you would know that that would never wash. All sorts of things can be “obviously” true, but still false.

Did I say anything about things that are “obviously” true? No, I do believe I did not. Here’s a hint: I say exactly what I mean, nearly always. If you reply to something that is not contained in the literal text of what I said, you are reading it wrong. Understand?

Well I don’t care if you do. Or rather, that you don’t.

I think I’m going to add you to my ignore list (the most wonderful invention in the world); I cannot convince you (the only cure for what you’ve got is rather permanent, at least according to the Japanese proverb), and I’d as soon not have to read your nonsensical gurglings.

 

[mathematician]

Considering that this argument started with you questioning my application of Godel’s theroem to my understanding of mathematics, I would say that quantum physics is getting a bit off the point anyway.

The point being that if you have an axiom schema A on the basis of which proposition P can neither be proved nor disproved, then you can derive schema A1 by appending P to A, but you can also derive schema A2 by appending not-P to A, and both A1 and A2 will be self consistent, which is a bit odd given that, in your understanding, either A1 or A2 would have to contain a proposition which was false.

 

[mathematician]

All of whom built on to the accumulation of knowledge which truly starts with Aristotle.

Most working scientists would not say “replace” but “correct”, “expand,” or “fill in the gaps”…

The equations describing Newtonian Mechanics and those describing Relativity or Quantum theory, to say the least don’t bear a whole lot of similarity to one another. That fact alone justifies the word “replaced”. It is not as though there was a little gentle tweaking of the odd term here or there.

 

[mschrank]

This is why I did not bite, see, it’s the same argument… ad nauseam.

Thomists: Aristotle was never superceded!
Materialists: Nuh uh! He was! Look at technology, and science, and stuff!
Thomists: Ah yes but the basic metaphysics is the same!
Materialists: Science has no metaphysic! Atoms bond to other atoms and create chemical reactions! No need for a soul or other tosh!
Thomists: No! What are you then, a Democritian?!
Materialists: No! Troglodyte! We’re way past that!
Thomists: You don’t get it, do you!
Materialists: I get it, you don’t!
Thomists: I get it, you don’t!

… repeat as needed

 

[mathematician]

This is why I did not bite, see, it’s the same argument… ad nauseam.

Thomists: Aristotle was never superceded!
Materialists: Nuh uh! He was! Look at technology, and science, and stuff!
Thomists: Ah yes but the basic metaphysics is the same!
Materialists: Science has no metaphysic! Atoms bond to other atoms and create chemical reactions! No need for a soul or other tosh!
Thomists: No! What are you then, a Democritian?!
Materialists: No! Troglodyte! We’re way past that!
Thomists: You don’t get it, do you!
Materialists: I get it, you don’t!
Thomists: I get it, you don’t!

… repeat as needed

Two things I’m not:

1.) A Thomist
2.) A materialist

Both are untenable, for different reasons.

 

[Jean_Anthony]

This thread is closed. Please remember to post with charity, everyone. Thank you.