General

Re: philosophy help.

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Re: philosophy help.

Clayton — Sat, 20 Oct 2012 04:17:07 GMT

Oh, you mean Umberto Eco's book - Eco comes down squarely against the possibility of any universal language and that is, in fact, the whole point of his book. I haven't read it (where am I supposed to find the time to read all these books!) but it comes highly recommended.

Clayton -

Re: philosophy help.

Aristophanes — Sat, 20 Oct 2012 04:07:18 GMT

"the lanugage of babel"

Genesis 11:5, 6, 7, 8, & 9

"And the Lord came down to see the city and the tower, which the children of men builded."

"And the Lord said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do."

"Go to, let us go down, and there confound their language, that they may not understand one another's speech."

"So the Lord scattered them abroad from thence upon the face of all the earth: and they left off to build the city."

"Therefore is the name of it called Babel; because the Lord did there confound the language of all the earth: and from thence did the Lord scatter them abroad upon the face of all the earth."

Referring to the book that you cited earlier involving the quest of unviersal language. The lanugage of Babel looked to be the myth that they are referring to not that of a philosophical language.

Re: philosophy help.

Clayton — Sat, 20 Oct 2012 03:09:26 GMT

Aristophanes:
you keep telling people to look for Babel as the 'universal language'

Can you please explain this statement? I've never said anything even remotely like this so I don't understand what prompted you to say this.

Clayton -

Re: philosophy help.

Fephisto — Thu, 11 Oct 2012 15:06:31 GMT

Maynard, if you're going to try to put this thread back on track, so will I:

http://www.youtube.com/user/flame0430/videos?view=0

Flame0430's channel. All of the Bryan Magee interviews. ALL OF THEM.

Re: philosophy help.

Maynard — Thu, 11 Oct 2012 06:20:00 GMT

To the OP, I'm just going to put these here:

(Please visit the site to view this media)

Re: philosophy help.

Clayton — Tue, 09 Oct 2012 22:00:37 GMT

Universal by contrast to what?
Is logic universal?

This is tiring. Universal by contrast to what??

Logic is a category of human knowledge - language, in particular. So, what is "universal" about it?

2) Mathematics is no better than any other domain of human language (I meant no closer to Absolute truth)

Uh, you mean knowledge? "...is no better than any domain of human knowledge"?

No, I mean what I said. Mathematics is a language. It originates in the intuitive theory of physics Steven Pinker discusses here. Specifically, mathematics is the intuitive theory sans the physics.

So, if you are claiming 1 to be false, please specify the aspect of mathematics that is not human.

The very nature of it.

WTF??

Sure, mathematics (the expression of it) is a human invention, but so is logic...what is being expressed is universal. Is mathematics going to be different past the Hubble zone?

Neither mathematics nor logic are human inventions. Both originate in the human brain which is of Nature's devising. Even the specific conventions and notations of logic and mathematics are not of human invention (design), they are merely the byproducts of human action. This is the case for all human language (of which mathematics and logic are but one department).

If you are claiming 2 to be false, please specify how mathematics reveals any portion of Absolute truth, even one iota.

Absolute truth as contrasted to what?

As contrasted to relative, uncertain. Absolute truth is truth that is certainly true. Everything else is uncertain. But no human knowledge is certain. Hence, the intersection of human knowledge and Absolute truth is nought.

Which article did you go through? He makes a pretty good case for the formalization of language into logical form. Russell only expounded what Frege dealt with. Didn't you vehemently deny this as a useful avenue of philosophy?

Frege was blind-sided by the Russell paradox. To construct the paradox, Russell used the very form of a diagonal argument which Cantor had earlier used to define powersets. Godel's argument can be understood as an extension of this technique to provability (rather than truth).

It is well-established that human language cannot be formalized. Hilbert had set the vision of formalizing mathematical proof, a project which has succeeded in one sense (general-purpose computers, automated proof-checkers) but failed in its most ambitious sense... to render the mathematician obsolete. We have proved that the mathematician is ineradicable and that human language simply cannot be completely formalized (at least, not by humans). If you want to understand why this is, please read anything by Gregory Chaitin or watch any of his lectures.

The only reference to universal language that you are willing to entertain is Babel (which is a strawman).

What is Babel? When have I ever mentioned Babel? I haven't the first clue what you're talking about.

If mathematics isn't universal what would be the point in doing things like this and this? (to which you replied "WTF?")

Because we can see that the laws of physics hold within the local environment where we shot the Pioneer probes into... if there is an intelligent alien species out there, they will have evolved subject to the same laws of physics that we are subject to. How does anything "universal" or "absolute" fall out from that??

Clayton -

Re: philosophy help.

Aristophanes — Tue, 09 Oct 2012 06:42:08 GMT

Universal by contrast to what?

Is logic universal? Is it analytic?

Frege tries to demonstrate that arithmetic is analytic and on par with logic (that they are in essence the same thing). Logical objects (like thoughts) exist in nature and whatever the logical object is it can be known to us simply through our intellects. It is Universal unto itself due to logic (since logic is true in an analytic sense).

The point he makes aboutlanguage is that the Sinn is a logical object. All langauge emanates this. Formalization avoids ambiguity (this stuff is a given for further extrapolations).

2) Mathematics is no better than any other domain of human language (I meant no closer to Absolute truth)

Uh, you mean knowledge? "...is no better than any domain of human knowledge"?

So, if you are claiming 1 to be false, please specify the aspect of mathematics that is not human.

The very nature of it. Sure, mathematics (the expression of it) is a human invention, but so is logic...what is being expressed is universal. Is mathematics going to be different past the Hubble zone?

If you are claiming 2 to be false, please specify how mathematics reveals any portion of Absolute truth, even one iota.

Absolute truth as contrasted to what? Truth is truth. 2+2=4. Truth. I would dare say that that is a portion of truth. It was true 1000 years ago and will be true in another 1000 years. What about geometry? I envoke Frege due to his insistance that geometrical objects are graspable by our intellect and will not change from human perception, time, or place. In Sinn und Bedeutung he demonstrates this.

I have no idea what you're even on about... how the hell could I possibly be denying anything?? I scanned the Frege article and I see nothing I disagree with. What next?

Which article did you go through? He makes a pretty good case for the formalization of language into logical form. Russell only expounded what Frege dealt with. Didn't you vehemently deny this as a useful avenue of philosophy? The only reference to universal language that you are willing to entertain is Babel (which is a strawman). Your first point about elucidation is a demonstration of the problems of natural language that a logical language can do away with (particularly with geometry).

I'm exactly like a fat girl

I knew it. You can shit and it won't stink. Amazing.

If mathematics isn't universal what would be the point in doing things like this and this? (to which you replied "WTF?")

Re: philosophy help.

Clayton — Tue, 09 Oct 2012 06:12:18 GMT

@Smiling Dave:

I see where the confusion is arising and it is my mistake. I wrote: "no matter how carefully you choose words and grammar - even if you choose as carefully as mathematicians choose them ... the possibility of deriving a contradiction... is ever-present." As stated, this is false. However, I meant this in the context of a regression argument, as Malachi has hinted at. If we formalize the system in which Cohen proved the consistency of the axioms of set theory (call it A), then we have a new formal system A', whose consistency is unproven and, hence, uncertain. Ad nauseum.

Apologies for the confusion.

Clayton -

Re: philosophy help.

Clayton — Tue, 09 Oct 2012 06:06:11 GMT

I'm not about to "sum up" Frege's arguments

*shrug - OK

Based on scanning the article, I don't think I have any issues with Frege's ideas here except that I think there might be better ways to elucidate the problem nowadays than were available to him when he wrote (namely, it was not known that the brain is a neural-net computing device and so it makes sense to speak of information present or not present in the brain).

It is no such thing. Mathematics is a wholly human language and is no better or worse than any other domain of human language.

Bullshit. Expression of mathematics vary, but the conclusions (truths) of those expressions are universal.

Universal by contrast to what? Do you know what lies beyond the Hubble sphere?

The claims in my sentence were:

1) Mathematics is a wholly human language

2) Mathematics is no better than any other domain of human language (I meant no closer to Absolute truth)

So, if you are claiming 1 to be false, please specify the aspect of mathematics that is not human.

If you are claiming 2 to be false, please specify how mathematics reveals any portion of Absolute truth, even one iota.

they will inform you to a world that you unreasonably deny.

I have no idea what you're even on about... how the hell could I possibly be denying anything?? I scanned the Frege article and I see nothing I disagree with. What next?

You're like a fat girl

You got me, I'm exactly like a fat girl. Everything I've ever written hereby comes crashing to the ground.

*crash*

No, you seem to percieve a difference here...

I was using the words as synonyms. In every other field besides philosophy, modern and contemporary are synonyms.

Clayton -

Re: philosophy help.

Clayton — Tue, 09 Oct 2012 05:47:16 GMT

I figured that is where your mistake lies.

What mistake??

You see, there is more than one way to skin a cat. You may try using F to prove itself consistent, or you may try something else. Godel proved that a rich enough system may not be able to prove itself consistent, but that does not slam the door on every possible proof there is.

Of course. I've never once stated otherwise. Godel's Incompleteness Theorems are not woe upon humanity... they are woe upon the project of The Perfect Language - a project that a large number of people still think has a chance of success.

The modern understanding is that we are human beings. We think using common sense, as sharpened by millenia of geniuses such as Aristotle at al. We then study a system F. We are certainly not inside the system F. We are people, not symbols on a page. We can then prove that, although F cannot prove itself consistent, we can prove F is consistent using our common sense, if we are clever enough.

But why are people reliable, I think is the unanswered question. The whole point of formalizing in the first place is because of the reliability problems of natural language. When it turns out that you cannot bootstrap a formal language from itself, then how does it help with the original goal of working around unreliable natural language by resorting back to (presumably unreliable) human common sense? I think that if you are the sort of person who is nervous about using natural language, you are also going to be nervous about relying on common sense.

An example is Paul Cohen, who proved that the axioms of set theory, the axiom of choice, and the continuum hypothesis, all of them together, are consistent. You will never find that they contradict each other. Again, they cannot prove themselves consistent [meaning the set of all valid conclusions of those axioms does not contain the statement that they are consistent], but Paul Cohen can, and did.

Yes, because "proof" generally is not restricted to any particular formalism. But even Paul Cohen cannot prove that the axioms of set theory are consistent from those very same axioms. Godel proved that.

Clayton -

Re: philosophy help.

Malachi — Tue, 09 Oct 2012 04:17:19 GMT

Smiling Dave:

Your argument is that I am wrong because cohen disproved godel.

No. That Cohen disproved Clayton.

My move is to point you here: http://mises.org/community/forums/p/31831/495702.aspx#495702

Then obviously you dont understand either Clayton, or Cohen, or both. Which is no surprise to anyone.

Re: philosophy help.

Malachi — Tue, 09 Oct 2012 04:15:19 GMT

Smiling Dave:

Dont think I would want to waste a real mathematician's time with your sophistry, since Its easily debunkable here.

Oh, I know you personally will never go to someone who might teach you something. My intention was to hint to other readers that if they want to know the truth, they have an easy way to find out.

Consistent with Godel, Cohen went outside of the system F by introducing a new technique, ramified forcing .That still doesnt violate Godel's theorems...

Thank you for admitting I am right. You have just stated very clearly that one can prove a system consistent.

...which is probably why you felt the need to go back and embellish your post with more nonsense.

Yes, I understand that my posts are at times incomprehensible to you, to the point of seeming nonsensical. i can live with that.

Are you the only person who thinks that Cohen disproved Godel...

You need a scorecard to remind you who the players are. Clayton is the one who claimed all systems might contain hidden contradictions that we will never know about. This is false, and reveals a deep ignorance fo mathematics. In particular, Paul Cohen's theorem is an instance, one of many , of mathematicians proving a certain system F contains no hidden contradictions.

So I was asserting, correctly, that Cohen disproves Clayton.

You, on the other hand, claimed that Malachi disproves Paul Cohen. You did not grasp that you are saying that, so I pointed it out to you. You are welcome.

You strawmanned both Clayton and myself, likely because you know youre wrong. Clayton asserted that a system cant prove itself. You sidestepped and said that Cohen disproves Clayton. He doesnt, and you have misrepresented Cohen as well.

Paul Cohen's theorem is an instance, one of many , of mathematicians proving a certain system F contains no hidden contradictions.

given that system G is consistent, yes. But we already knew that. This is consistent with Godel.

Re: philosophy help.

Smiling Dave — Tue, 09 Oct 2012 04:09:29 GMT

Your argument is that I am wrong because cohen disproved godel.

No. That Cohen disproved Clayton.

My move is to point you here: http://mises.org/community/forums/p/31831/495702.aspx#495702

Re: philosophy help.

Smiling Dave — Tue, 09 Oct 2012 04:02:39 GMT

Dont think I would want to waste a real mathematician's time with your sophistry, since Its easily debunkable here.

Oh, I know you personally will never go to someone who might teach you something. My intention was to hint to other readers that if they want to know the truth, they have an easy way to find out.

Consistent with Godel, Cohen went outside of the system F by introducing a new technique, ramified forcing .That still doesnt violate Godel's theorems...

Thank you for admitting I am right. You have just stated very clearly that one can prove a system consistent.

...which is probably why you felt the need to go back and embellish your post with more nonsense.

Yes, I understand that my posts are at times incomprehensible to you, to the point of seeming nonsensical. i can live with that.

Are you the only person who thinks that Cohen disproved Godel...

You need a scorecard to remind you who the players are. Clayton is the one who claimed all systems might contain hidden contradictions that we will never know about. This is false, and reveals a deep ignorance fo mathematics. In particular, Paul Cohen's theorem is an instance, one of many , of mathematicians proving a certain system F contains no hidden contradictions.

So I was asserting, correctly, that Cohen disproves Clayton.

You, on the other hand, claimed that Malachi disproves Paul Cohen. You did not grasp that you are saying that, so I pointed it out to you. You are welcome.