GÖDEL AND THE NATURE OF MATHEMATICAL TRUTH [6.8.05] - A Talk with Rebecca Goldstein

Edge ^ | June 8, 2005

[snarks_when_bored]

BOILERPLATE: I've been otherwise occupied for the last 24 hours or so, so I'm just catching up on the thread.

chilepepper, you wrote this:

"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"

It looks to me as if you've placed a template over Ms. Goldstein that doesn't seem to fit; at least, it doesn't follow from the interview and the other things I've read by and about her.

[snarks_when_bored]

BOILERPLATE: I've been otherwise occupied for the last 24 hours or so, so I'm just catching up on the thread.

Hey, glad to hear that you've read and enjoyed the book. I've still not read it (I decided to amble through Penrose's The Road to Reality first). Goldstein's book is next.

[Lancey Howard]

I hear the Democrats are looking for language experts who can teach them how to lie.

[snarks_when_bored]

BOILERPLATE: I've been otherwise occupied for the last 24 hours or so, so I'm just catching up on the thread.

Hey, RobbyS, I wouldn't say that mentioning Thomas Aquinas convicts me of overestimating the influence of Thomism! (smile)

As for Galileo, he was an arrogant man, but he had the intellect and the discoveries to back his arrogance up. What he did not have was control of his own personal destiny, although he thought that he did.

[D-fendr]

it's hard to deny that the large… definitely arises out of the small…

Here's the odd thing, and frustrating thing, about worldviews: they are impossible to prove. You either see it this way (large derived from small) or you don't. The large and small are the same either way.

The best anyone can do is try to spark the same realization, the same way of looking at it if you will.

An attempt, hopefully not too lame, at a thought experiment:

Imagine compeletely empty space, theoretically now, a thought experiment. Completely absolutely devoid of anything, merely space.

Now introduce into this space a gram of molecules. Would these molecules follow the laws of chemistry/physics?

I think you would answer, "yes."

Did the molecules (the small) carry the laws into the space with them? Do the laws arise out of the molecules (each and every time)?

Or do the laws (the big) exist even in the empty space, even without the presence of the small?

[snarks_when_bored]

BOILERPLATE: I've been otherwise occupied for the last 24 hours or so, so I'm just catching up on the thread.

Hello, g_w, glad to hear from you!

As for Freudianism and Marxism and such -ism's, perhaps there's some truth in them—it would after all be pretty amazing if there were nothing sound in them—but it's not clear to me that it's worth the effort to muck through all of that mud in search of a small cubic zirconium crystal.

BTW, what novel have you quoted from? I don't recognize the passage.

[snarks_when_bored]

Isn't one of them the current head of the Democratic party?

[snarks_when_bored]

I tend to the view that there was never a time when there wasn't something physical (even though it's not at all clear that a global time in the multiverse makes sense). So if the multiverse always was, the large was always there, with small bits of it bubbling up and expanding all of the time throughout its extent.

As for the 'laws' of physics that you mention in your thought experiment, some physicists are coming around to the view that perhaps (perhaps) the laws that we observe are just the laws of our local bubble, and that elsewhere, there are different laws, indeed, an infinite variety in an infinite number of elsewheres (which is the 'worst case scenario', I guess).

But this is all still rank speculation, and we shouldn't allow ourselves to be deceived into believing it the way some folks believe articles of faith. These are possibilities, not certainties.

I recall seeing an interview with Richard Feynman in which he said that, unlike many people, he was able to live with not being certain about the ways things are, that he was not happy about not knowing everything, but was able to deal with it. I like that attitude.

[D-fendr]

'twas a thought experiment.

Oh well.

I really really really really appreciate your posting this article and I read the others listed too. This area of metaphysics, er, I mean meta-science, is fascinating.

Thanks very much; I hope you continue.

thanks,

D-

[snarks_when_bored]

Thanks to you for contributing your thoughts to the thread. I keep my eye out for stuff which interests me, and sometimes I post it with the idea that maybe it will interest others.

Best regards...

[grey_whiskers]

I recall seeing an interview with Richard Feynman in which he said that, unlike many people, he was able to live with not being certain about the ways things are, that he was not happy about not knowing everything, but was able to deal with it. I like that attitude.

Oh, you mean humility as opposed to intellectual pride.

Kinda rare in someone so intellectually accomplished.

PS The quote from the earlier posting of mine was from
Dorothy L. Sayers, Gaudy Night.

Cheers!

[grey_whiskers]

Snarks' BOILERPLATE goes for me too, kind of...:-)

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.

For more on this, try reading the essay "Problem Picture" by Dorothy Sayers--you can find the essay in a reprinted partial anthology entitled The Whimsical Christian. The main point is that the artistic world (unlike scientific endeavor) is full of messy, ill-defined problems, where there is no "optimal" answer because there are multiple trade-offs, and people are not in agreement as to which aspects of life are the most important.

Full Disclosure: Sayers is (was? she is now deceased) a British mystery writer, famous for her Lord Peter Wimsey novels (e.g. Murder Must Advertise). She kept a pretty decent grip on science as well--one of her novels revolved around a man poisoned, ostensibly by Amanita muscaria (fly agaric). The murderer was caught because he had used synthetic muscarine to do the poisoning--and hence a racemic mixture.

Not much to sneeze at today, but that novel was written in the 1930's when organic chemistry didn't have the theory of stereoisomers down pat yet. . .

Cheers!

[grey_whiskers]

employed to relieve the puzzlement generated by philosophers' misuse of ordinary language.

This is another interesting behavioural tidbit--I suspect that the philosophers' misuse of ordinary language partly results out of attempting to attempt mathematical precision with words, and about qualitative or (to coin a phrase--see how easy it is ?) essential qualities.

And as a consequence, since the philosophers, like ordinary scientists, use the same base of words as ordinary folks, but with (for the philosophers) distinct and specialized meanings, the philosophers may be tempted to believe "Hey! We're scientific! (and therefore enlightened)."

Cheers!

Full Disclosure: recall Feynman's discussion of cargo cults and his comparison of them to psychologists in particular, I believe in Surely You're Joking, Mr. Feynman.

[grey_whiskers]

The problem with Freudianism and Marxism is that they attempt to make cohesive, all-encompassing systems out of observations which are only applicable to some people / groups, some of the time.

Full Disclosure: ...and at least by reputation, many of their adherents seem to be rather, well, virulently anti-theistic. Thereby making their own behaviour instances of their own categories stated vices (atheism is the opiate of the Marxist)--recall St. Paul said "if for this life only we have hoped in Christ, we are of all men most to be pitied" which is not much of an escape, is it?)

Cheers!

[bvw]

You are both right. Certs -- two mints in one.

[bvw]

So Albert was keeping Kurt sane ... those walks home.

[bvw]

"never a time when there wasn't something physical"

That makes sense. Time and physicality are intertwined.

[donh]

ah, lets see... so you are claiming that Goldberg, as an "objectivist" will 'rescue' the average "enlightened humanist" socialist college professor from the clutches of their marxist mindset and turn them into "enlightened humanist" randians? what a laugh.

No, I didn't make that claim, but this level attention to what you read is certainly consistent behavior.

believe what you will but to me "enlightened humanist" is invariantly equivalent to "tenured socialist humanities professor", and sadly, goldberg's hope is not to turn them from socialism ........... ......... ...........

There is absolutely nothing in this article, nor in any of her cites here, that would lend one any insight whatsoever as to her broad political convictions.

Since you seem to prefer philosophical blovation to reading, perhaps I can help you out. Here is a quote from the text.

I like to think that the shallower aspects of the intellectual scene of the last century have played themselves out. I mean in particular the assaults on objectivity and rationality, which often take the form of attacks on science. There's nothing less exhilarating than reducing everything to social constructs.

As to Whitehead vs. Russell..."objectivism is a trap"--a' la Popper: the world is not an illusion--someone has fed you bad drugs. The fact that we exist in separate subjective bags of flesh is a poor excuse for believing that a stable, objective reality isn't impinging on us all mutually, and that, therefore, the main game in science and reasoning is not to "construct" reality, but to fathom it.

[beavus]

Gödel's Incompleteness Theroems have virually no impact upon what ordinary mathematicians do

The impact comes if the ordinary mathematician begins to wonder if his work is simply true, rather than true given stipulations. That affects how he values his product, and that in turn can greatly affect his motivation.

The article says that physics is always contingent upon observation, and that there is never a guarantee that some future observation won't change whatever conclusions you've made from current observations. But, that is precisely why empirical sciences are prima facie objective. The question is, does a similar objectivity exist for the purely abstract sciences, where it is ultimatly founded upon a reality beyond the creations of consciousness? Godel's theorems permit that possibility by showing the impossibility of the converse.

[beavus]

First there were the knee-jerk liberals. Then came the knee-jerk "they-are-all-a-bunch-of-worthless-liberals" conservatives.

Thanks for the very interesting article. She obviously is not the stereotype other posters claim.