on Nietzsche

[Kuciwalker]

Thank you. I wasn't sure if that was a typo either.

[Agathon]

Originally posted by Kuciwalker
Thank you. I wasn't sure if that was a typo either.

It's wholly my fault.

[McCrea]

Originally posted by Kuciwalker

Originally posted by McCrea
I was confirming that nothing can be proven.

Then you'd be wrong. Sorry, kid. Every single math professor on the planet disagrees with you.

Fine, you win. (I hope I didn't confuse anyone yet. "Fine" is a euphemism meaning "I surrender", not "please charge a fee.")

Here's what I read on Wikipedia, the most accredited source in Macedonia, mere minutes ago, and have since based my anti-terrorism funding upon.

Gooney Goo Goo, Kid

If only some "math professor" had an ounce of wisdom.

This whole message has been fabricated at my expense, and is not to be understood.

[Kuciwalker]

Hint: Godel's incompleteness theorem demonstrates that some true propositions can't be proven, not that no true propositions can be proven.

Unlike you, I've actually studied formal logic...

Incidentally, Godel's incompleteness theorem is one of those things that can be proven. So you've provided another counterexample to your own argument.

[McCrea]

Originally posted by Kuciwalker
Incidentally, Godel's incompleteness theorem is one of those things that can be proven.

I concur.

[Agathon]

Originally posted by Kuciwalker
Hint: Godel's incompleteness theorem demonstrates that some true propositions can't be proven, not that no true propositions can be proven.

Unlike you, I've actually studied formal logic...

It's a long time since I did that, but isn't Gödel's Theorem rather like the Liar Paradox? I seem to remember it being the same sort of trick.

[Kuciwalker]

Godel's theorem is essentially a proof that any sufficiently powerful* logical system must have something like a liar's paradox. Specifically, it must have a proposition which is true but unprovable.

* roughly, powerful enough to express basic arithmetic and number theory. First-order logic counts, propositional calculus doesn't.

[Agathon]

Originally posted by Kuciwalker
Godel's theorem is essentially a proof that any sufficiently powerful* logical system must have a liar's paradox.

* roughly, powerful enough to express basic arithmetic and number theory

Then ordinary language (under certain assumptions about it) would be a member of this set. I wonder if Gödel had the paradox in mind when he formulated his theorem (I just googled, but I couldn't find anything).

I remember someone on Apolyton saying that only morons would be interested in the liar paradox and related statements about self reference and so on. "Stupid bull****" was the phrase used, or some cognate.

You ever hear of Graham Priest, Kuci? I went to a talk about his dialethic logic once. It's all a bit modern and trendy for me.

[Kuciwalker]

Then ordinary language (under certain assumptions about it) would be a member of this set.

Yes.

I wonder if Gödel had the paradox in mind when he formulated his theorem (I just googled, but I couldn't find anything).

As I recall, the incompleteness theorem ultimately arose out of the desire to prove the opposite. There were a number of open problems in mathematics at the time that essentially asked "how would you build a machine that can mechanically prove or disprove mathematical statements". Godel's theorem, which shows that this isn't possible, came as a rather strong shock to the mathematical community.

You ever hear of Graham Priest, Kuci? I went to a talk about his dialethic logic once. It's all a bit modern and trendy for me.

The name is familiar, but I don't know anything about him.

[Agathon]

Originally posted by Kuciwalker

Then ordinary language (under certain assumptions about it) would be a member of this set.

Yes.

I wonder if Gödel had the paradox in mind when he formulated his theorem (I just googled, but I couldn't find anything).

As I recall, the incompleteness theorem ultimately arose out of the desire to prove the opposite. There were a number of open problems in mathematics at the time that essentially asked "how would you build a machine that can mechanically prove or disprove mathematical statements". Godel's theorem, which shows that this isn't possible, came as a rather strong shock to the mathematical community.

You ever hear of Graham Priest, Kuci? I went to a talk about his dialethic logic once. It's all a bit modern and trendy for me.

The name is familiar, but I don't know anything about him.

BTW Gödel was a platonist IIRC. Any idea on the connection?

nm. I found this

http://www.nytimes.com/2005/05/01/books/review/01SCHULMA.html?_r=1&oref=slogin&pagewanted=print&position=

Plato himself would say that Gödel's problem was thinking dianoetically. What he needed to do was stop screwing and thinking about food, drink and girls, in order that his mind would be free from his body and he could noetically cognize the Forms. Weird ancient beliefs FTW.

[Kuciwalker]

TBH, I don't think any philosophy of mathematics really matters. If a given philosophy makes math give different answers, then it is obviously wrong; if it makes math give the same answers, then it's unnecessary.

Notably, anyone who's ever used a philosophy of mathematics to argue against some new discovery has been swept aside by history. Stuff like imaginary numbers, Cantor's infinite sets, etc. were initially opposed by a lot of people, but since they work they got used anyway.

[Jon Miller]

According to Wiki, Godel was a realist.

My classes, and Wiki, say that Godel came up with his proof as after working with Russells attempts to formalize all of mathematics in logic.

JM

[Kuciwalker]

Originally posted by Jon Miller
According to Wiki, Godel was a realist.

My classes, and Wiki, say that Godel came up with his proof as after working with Russells attempts to formalize all of mathematics in logic.

JM

Yeah, wiki says he was working on Hilbert's 2nd problem (proof that arithmetic is consistent), which is pretty fundamentally connected to the Entscheidungsproblem, which is what I was talking about earlier.

[Agathon]

Originally posted by Kuciwalker
TBH, I don't think any philosophy of mathematics really matters. If a given philosophy makes math give different answers, then it is obviously wrong; if it makes math give the same answers, then it's unnecessary.

From the point of view of a mathematician, yes. The general rule of contemporary analytical philosophy is to "leave everything as it is". Whether or not the incompleteness theorem makes platonism more plausible is an interesting question for all sorts of reasons, none of which may bother mathematicians per se, but seem to have bothered Gödel a great deal. One obvious issue being that it would render physicalism false. If physicalism is false, then it follows that physics cannot contain everything there is to say about reality, and that would be pretty interesting.

[Kuciwalker]

What is physicalism?

edit: it looks like materialism or reductionism. Is there some subtle difference here?