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GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH [6.8.05] - A Talk with Rebecca Goldstein
Edge ^ | June 8, 2005

Posted on 06/08/2005 7:40:56 PM PDT by snarks_when_bored

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To: snarks_when_bored
One doesn't have to be a platonist to hold a quite similar worldview.

Wittgenstein seemed to be saying the latter; that there are aspects of reality that exceed our ability to express them.

Much the same as Godel's Incompleteness. When this discussion deals with the border between knowledge - reason and beyond reason - it of course speaks from one side, logic/reason about the existence of the other side, transcendence.

And here, leaving philosophy, we enter the sphere of religion, and the experiments (experientialism/mystics) agree:

"Tao which can be spoken of is not the true Tao. The name which can be named is not the true name… If it could be talked about, everybody would have told their brother."

And so on, with extemely similar teaching in hinduism, christianity, buddism, islam (sufism), judaism...

What's fascinating in the article is the edge - in this case I mean the physicists and mathmaticians looking across the border.

thanks for the post.. Are you familiar with "Quantum Questions" edited by Ken Wilber?

21 posted on 06/08/2005 9:51:29 PM PDT by D-fendr
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To: snarks_when_bored

My view is that we have modern science only because men such as Galileo were platonists. Simplistic to call modern philosophy nominalist, but it certainly shrinks from encounters with hard questions.


22 posted on 06/08/2005 9:53:30 PM PDT by RobbyS (chirho)
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To: D-fendr
I'm not sure what you mean when you write, "One doesn't have to be a platonist to hold a quite similar worldview." Do you mean a worldview that regards truth as objective rather than constructed?

I haven't seen the Wilber collection that you reference, but I'll confess to feeling a bit of concern about Wilber's own work after glancing at his website. But that's a topic for another day, perhaps...

23 posted on 06/08/2005 10:12:03 PM PDT by snarks_when_bored
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To: RobbyS
My view is that we have modern science only because men such as Galileo were platonists.

Well, Galileo did his best to combat the pervasive, suffocating influence of Aristotelian physics (as filtered through Thomas Aquinas and Catholic doctrine). The degree to which Galileo was influenced by Renaissance neo-Platonism is not clear. Here's an interesting link:

"Renaissance Neo-Platonism" by Richard Hooker

Galileo is mentioned in the last couple of paragraphs.

24 posted on 06/08/2005 10:22:45 PM PDT by snarks_when_bored
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To: snarks_when_bored
But, either way, I don't know why you'd be displeased with Platonists.

Where did I say that I was displeased with Platonists? I am rather fond of Plato and the Neo-platonists (Plutarch, Proclus, Plotinus, Porphyry) as well. Now who can explain and arrive at objective truth why all these great Platonists have names that begin with 'P'?

What I said was that the humanities are not a science, whether your science is positivist or realist. And unfortunately out of envy of the sciences, pseudo-scientific methodology has overtaken the humanities, much to its harm.

So no wishy-washy subjectivism for Platonists, no world in which reality is 'constructed by social groups', that sort of stuff. This doesn't sit well with you?

It's exactly that wishy-washy reality constructed by social groups that I am arguing against. That's what I referred to in post #6. That wishy-washy reality is also called multiculturalism, and it came about from the humanities trying to do anthropology, all the while denying that they were trying to be scientific or even expressing anti-scientific attitudes.

This doesn't comport with the little that I know about recent and current schools of literary criticism.

There are myriads of theories of literary criticism. There is probably a new one being created right now in a PhD thesis as I type this. I didn't attempt to list all of them--but only one that is rather Platonic in its approach.

The Freudian critics, the Marxist critics, the 'structuralist' critics, the Derrida-ist critics—those sorts are much closer to being nominalists than Platonists, and most wouldn't be averse to arguing that there is no objective truth

You won't get any argument from me about what you said because I agree. But what all of these critical schools have in common is that they have adopted some method to explain the text or work of art, as if it is a problem that must be worked out and solved like a problem in calculus is solved by applying a method--some set of steps to arrive at the answer.

I am arguing that there can't be any method in the humanites because it is an on-going conversation with others and an inner meditation with oneself about the human condition. And its purpose is to derive pleasure in ordering your thoughts and feelings. As Pascal said, this is the realm of the intuitive mind, not the geometric.

25 posted on 06/08/2005 11:30:38 PM PDT by stripes1776
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To: stripes1776
We seem to be arguing past one another. We're probably pretty much in agreement about whether there's objective truth or not. My only point in reaction to your original post was that I think you've mis-identified Professor Goldstein. She's not your standard humanities multi-culturalist whackjob. As far as I've been able to determine, she's level-headed and understands the difference between finding something out and making something up.

Best regards...

26 posted on 06/08/2005 11:45:28 PM PDT by snarks_when_bored
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To: snarks_when_bored
Yeah, Ken's gone hollywood. It's a shame. I'll tell more about the book later.

About the worldview. There's two basic ways of looking at reality. The stereotypical scientific, or materialistic view, is that the big is derived from the lesser: for example, life derived from matter; human intelligence and consciousness derived from brain matter and structure, and so on. (the bigger did not exist until it emerged from the lesser - no intelligence/consciousness before man)

In this worldview the bigger CANNOT be more than the accretion of the lesser. In other words, the sum of all math is all the math there is, the sum of all that can be conceptualized is all that exists...

The traditional - Plato, et. al - is the inverse: the lesser is derived from the greater. The transcendent ("spirit" or "absolute/unbound" among its many references), is the greater. Matter, life, intelligence, all finite reality is derived from this. (the bigger DID exist before it emerged in the lesser - intelligence/consciousness existed before man)

I hope I haven't obscured the point to where you cannot recognize Plato yet.

So in the traditional worldview, the finite, conceptual (certainly logic/reason) are subsets of reality - yes an objective reality. As such they share attributes and since they are finite, changing, they are not "perfect" which by definition is infinite and unchanging.

I hope I've circled back to plato somewhere about here.

Plato's worldview was "traditional." The basic worldview up until the enlightenment was all traditional. And this worldview was, and is, shared by all major religions (and most pre-post modern philosophers - Kant, for example).

Another overlap: Christian theology was heavily influenced by greek philosophy, you can particularly see it in Plotinus who was, of course, a neo-Platonist. The primary theological synoptic is John: "In the beginning was the Word, and the Word was with God, and the Word was God… and the Word became flesh and dwelt among us..." And Jesus says, "the Kingdom of God is within you."

Christianity, and the other major religions teach that God is immanent and transcendent; again the lesser is derived from the greater. This holds for every major religion and darn near every minor one as well. You can see where the positivist took quite the other track, followed on by post-modernism and the whole area discussed in the article.

In Buddism, the transcendent is observable - provided you stop naming (talking to yourself and narrating reality) and simply observe reality. This observance of reality, Truth transcending concepts, incapable of expression in words - seeing/realizing the transcendent immanent in/reflected/shadowed in the finite forms/types is common to all religions in their experiential cores and teaching: it's not unique to Plato, though it'd be hard to separate platonic influence. It's at the core of hinduism, judaism, taoism, buddhism...

Enough on that except to say, rather than "regards truth as objective rather than constructed," I prefer two points: acknowledges the existence of an absolute truth transcending mind/intellect/reason-logic.

If your worldview only consists of the "constructed," in other words the sum of the lesser, then there IS nothing transcending it. You cannot see it. Hence the blank stares of pure materialists and small-scale empiricists.

The author talks about "beauty," and so does Einstein and many other giants in science. The divine attributes are often listed as Truth, Goodness, and Beauty. Yet none of these have quantity or simple location. They are completely impossible to measure or "prove" by science or logic.

Have a mathmatician or physicist define beauty and you will discover their worldview. Some will, like Godel, Einstein, Heisenberg and Planck, describe it in the traditional worldview; however, in addition to Platonists they may be more akin to hinduism, taoism or, even Christianity.

Finally, putting this in the box of philosophy is a mis-categorization. Philosophy is still in the sphere of reason-logic, and you'll get a lot of streams and major variations. Put it in the realm of religion and the discussion is more at home - and on the fundamentals you'll find agreement.

27 posted on 06/09/2005 12:16:45 AM PDT by D-fendr
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To: snarks_when_bored
We seem to be arguing past one another...My only point in reaction to your original post was that I think you've mis-identified Professor Goldstein. She's not your standard humanities multi-culturalist whackjob.

Another pupose of the humanities is to bring clarity of thought to the conversation. If we are arguing past one another, then let's try to talk more directly to one another instead. This doesn't mean that we will agree, but at least we will be clear about the disagreement.

I did not say that Goldstein was a multi-culturalist whackjob. I called her a Platonist, a rather distinguished name for any philosopher to carry. My main point is that the humanities is not a science, and that trying to "solve" it by methods does great damage to it.

Perhaps if Gödel had understood that philosophy was also one of the humanities before it tried to become a science, he may have turned outward in conversation with someone rather turn in on himself in isolation.

Any please understand that I am not anti-science or anti-mathematics. I am very fond of calculus, particularly vector calculus, determining if a triple variable vector field is conservative or not, and then successively integrating and differentiating to work back to its potential funtion. This is how I relax.

I tend to agree with Goldstein, although it may not be the only place: "Mathematics seems to be the one place where you don't have to choose, where truth and beauty are always united."

28 posted on 06/09/2005 1:02:39 AM PDT by stripes1776
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To: VadeRetro; Junior; longshadow; RadioAstronomer; Doctor Stochastic; js1138; Shryke; RightWhale; ...
SciencePing
An elite subset of the Evolution list.
See the list's description at my freeper homepage.
Then FReepmail to be added or dropped.

29 posted on 06/09/2005 3:58:07 AM PDT by PatrickHenry (Felix, qui potuit rerum cognoscere causas. The List-O-Links is at my homepage.)
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To: longshadow

In one sense, Gödel's theorems do point out that there are many (uncountably, of course) mathematical realities. We get to choose which one we want. The Continuum Hypothesis is neither true nor false; we can go either way. A Platonist is thus forced to admit the existence of many mathematical systems; not that there is anything wrong with that.


30 posted on 06/09/2005 6:34:28 AM PDT by Doctor Stochastic (Vegetabilisch = chaotisch is der Charakter der Modernen. - Friedrich Schlegel)
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To: stripes1776
exactly. forgive me everyone for dumping on this gal, but is just another feeble attempt to rescue one of the philosophical underpinnings of Marxism, scientific socialism. how quaint.

the giveaway is her invoking Einstein (a religious icon to scientific socialists), in the first sentence, as in well, our philosophy is in line with Albert Einstein's, so if you don't agree with it you are stupid or ignorant

i think godel actually blew away mathematics as containing any 'self evident truth' unless we can agree that the 'truth' of mathematics is that a mathematician willed into existence a certain set of (clearly self referential) equations and relations to create a self consistent (equation) world, which gains its "status" by being able to predict physical phenomena. the dirty little secret of mathematics (& physics) is that as soon as you stray from *very* simple phenomena, things get very messy in a hurry. compare differential equations (very neat and tidy) with partial differential equations (more heuristic than formulaic) to get a sense of what i am talking about...

godel is to mathematics what heisenberg is to quantum mechanics, and in a way einstein is to newtonian mechanics, showing what the LIMITS to human analysis of our world, rather than postulating some absolute reality about it...

31 posted on 06/09/2005 6:58:03 AM PDT by chilepepper (The map is not the territory -- Alfred Korzybski)
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To: snarks_when_bored

It's an interesting book. The relation of Wittgenstein to the Vienna Circle was clarified, and Goedel is presented along with an attempt to explain his Incompleteness theorem, but it will take study of his actual papers and a deep comprehension of math to bring it into clear focus. His papers should be public domain because of their importance, but they are not. You have to sign up.


32 posted on 06/09/2005 8:05:32 AM PDT by RightWhale
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To: snarks_when_bored

You overestimate the influence of Thomism. As for Catholic doctrine, the only point in dispute there was the right of Galileo to interpret scripture. He was like many Catholics today who insist on instructing the pope on matters that are above their pay grade. He was so convinced of the truth of his system that he behaved like a bull in a china shop and put himself in the hands of his enemies.


33 posted on 06/09/2005 9:11:31 AM PDT by RobbyS (chirho)
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To: chilepepper

Of course there are limits, but the question is still do we discover or do we invent reality?. And we shouldn't take Kant as the final word on this.


34 posted on 06/09/2005 9:16:29 AM PDT by RobbyS (chirho)
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To: RobbyS

kant of course with his categorical imperative would say humans will *always* try to breech the noumena: that is our nature...


35 posted on 06/09/2005 9:23:46 AM PDT by chilepepper (The map is not the territory -- Alfred Korzybski)
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To: chilepepper

But these are, after all, words, and Kant's words, his personal way out of the dilemma (paradox)that Hume presented to him. IAC, we have at all costs to avoid a skepticism which denies to reason any efficacy at all. To this outsider, it seems that the approach of most matheraticians is to stick to their last and not think about things they do not think about. There is a huge range for them to work in and so they try to stay away from the edginess of someone like Goedel. I mean, did Babe Ruth worrry about the physics of baseball?


36 posted on 06/09/2005 9:34:10 AM PDT by RobbyS (chirho)
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To: chilepepper
exactly. forgive me everyone for dumping on this gal, but is just another feeble attempt to rescue one of the philosophical underpinnings of Marxism, scientific socialism. how quaint.

You are riding an invisible hobby horse here. I cannot find anything in this article that seems like "an attempt to rescue...the philosophical underpinnings of Marxism".

As far as I can tell, from what is written here, The lady comes across as a slingshootin' champion of objective reality, like a heroine in an Ayn Rand novel.

37 posted on 06/09/2005 9:50:32 AM PDT by donh
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To: donh
Science-based thinking among enlightened humanities scholars is now part of public culture and Goldstein is one of the writers leading the way

errrr, well, lets see now: i'd say "enlightened humanities scholars" is a typical buzzword for a scholar who is actually socialist and, among the "more enlightened" group, downright Marxist. When you make an "enlightened humanities scholar" more scientific, you are basically makeing them a more "scientific socialist". just what we need more of...

please, by all means believe if you so desire that this lady is actually a randian.

i for one do not...

38 posted on 06/09/2005 9:59:58 AM PDT by chilepepper (The map is not the territory -- Alfred Korzybski)
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To: chilepepper
"enlightened humanities scholars"

So...what did you do, read up until you found this phrase and stop? I've got news for you, Ayn Rand was an "enlightened humanities scholar". And what most of the rest of this thread was about, was celebrating the abandonment of relativistic philosophies by "enlightened humanities scholars".

You'd make sounder critical comments if you read what you were commenting on.

39 posted on 06/09/2005 10:05:22 AM PDT by donh
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To: snarks_when_bored

Sincere apologies for such a long post last night.

'Quantum Questions" is a collection of writings of major quantum physicist - and Einstein - on their philosophical or religious underpinnings for their view of science.


40 posted on 06/09/2005 11:37:20 AM PDT by D-fendr
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