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October 11, 2004

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My favorite line, by the way, is:

"Things are not made for the sake of words, but words for things."

Someone onced referred to Derrida as presenting "nihilism with a happy ending". That's about right to me though I also think happy endings are generally a construct of storytellers.

On another item mentioned in your post:

Moe also has great affection for Tacitus and your description of Derrida, "a too clever pain in the ass" seems to fit him as well.

"Moe also has great affection for Tacitus and your description of Derrida, "a too clever pain in the ass" seems to fit him as well."

As attempts at troublemaking go, it's weak, and that awkward pronoun confusion isn't helping matters any.

(After editing last comment) Ah, kharma.

In all seriousness, von, since I am apparently just immune to Derrida, I have never really been able to understand what's so novel about the thought that words don't have fully determinate meanings, and/or that authors sometimes undercut their own points. Not that he wasn't fun and all.

"As attempts at troublemaking go, it's weak..."

Thank god.

"In all seriousness, von, since I am apparently just immune to Derrida, I have never really been able to understand what's so novel about the thought that words don't have fully determinate meanings, and/or that authors sometimes undercut their own points."

I couldn't agree more, and the distinction between a lack of perfect precision in meaning and a lack of meaning at all is often lost on his students.

Sebastian
I see you as more of a Walker Percy fan. Not a bad crew to hang with.

Moe
Kind of ironic that in a thread about a deconsructionist, you're pointing out "awkward pronoun confusion".

As a linguist, I wasn't able to get past Derrida's alternately simplistic and nonsensical assertions about language, speech, and writing. His attempt to reverse the speech-writing hierarchy depended on a complete redefinition of those two terms, to the extent that they were hardly recognizable. As far as I could tell, his argument was roughly equivalent to, "you linguists think that white is lighter than black, but if we redefine black so that it's even whiter than white, this shows that you're all wrong!"

At least that was my impression from a very brief foray into his writing. I didn't have the patience to fight through and see if there were any genuinely good and novel ideas amid all the noise.

In all seriousness, von, since I am apparently just immune to Derrida, I have never really been able to understand what's so novel about the thought that words don't have fully determinate meanings, and/or that authors sometimes undercut their own points.

Well, yeah. There's that. Still, one has to be impressed that what took you a single sintence to express, Derrida required hundreds of thousands of words. It's a talent. Of sorts.

Thinking about words and meaning reminds me of my high school philosophy lessons. Plato's sort of ideal of a thing that in reality is never really the ideal and then a word similarly fixed used to describe it.

von: I once had a colleague who did, completely off the cuff, a hilarious shtick about his grandmother, whose folky aphorisms (according to him) anticipated most of Derrida. If memory serves, he began by saying, in a quavery grandmotherly voice, "You can't always believe everything you read, young man..." and by the end of a minute or two, there Derrida's main ideas were.

They are symbols of meaning. But unlike mathematical symbols, the phrasing of a document, especially a complicated enactment, seldom attains more than approximate precision.

And how. Just got back from an incredibly frustrating review session with my students having tried to teach them epsilon-delta calculus. It's not their fault they're not getting it -- no-one does -- but part of the problem when learning math is that mathematics does, insofar as it's possible, have absolute precision. It's just brutally, brutally hard for most people to strip away the imprecision with which they usually face the world and pare themselves down to the level of rigor required. In that, at least, Derrida et al. were completely correct.

It's just brutally, brutally hard for most people to strip away the imprecision with which they usually face the world and pare themselves down to the level of rigor required.

The law strives for the same precision -- that's why lawyers get so hung up on particularities. As evident from the Frankfurter quote and the AutoGiro case, however, it's never quite achieved due to the limitatiosn of language.

Mathematics has its own inadequacies. How about we think of mathematics as a sort of Olympic timed event, while language is more like ice dancing?

Ice, because it's slippery out there.

Mathematics has its own inadequacies.

And god bless it for doing so, because otherwise I'd be out of a job.

[Have I mentioned that I'm a logician?]

If so, I missed it. What exactly does a logician do, Anarch?

I'm pink, therefore I'm Spam.

- Decarte's pesky kid brother

Thank you, kenB, for your comment. As someone who was once trained (in the mists of the distant past) as a linguist I've had precisely the same reactions.

If you're saying Wittgenstein is a 10, I'd agree. And would prefer to talk 'bout him.

If we can't talk we could always point...

Dave,

Ne za chto. And thank you, too. Surely we can't both be wrong.

von,

however, it's never quite achieved due to the limitations of language.

Oh, sure, blame it on language. Certainly can't be the lawyers' fault, can it? :-)

Oh, sure, blame it on language. Certainly can't be the lawyers' fault, can it? :-)

Well, if it's not the language, it's probably the client. Or perhaps those "activist judges."

If you're saying Wittgenstein is a 10, I'd agree. And would prefer to talk 'bout him.

"Whereof one cannot speak, thereof one must be silent."

If so, I missed it. What exactly does a logician do, Anarch?

Well *this* logician fritters far too much time away surfing the blogosphere, so I'll have to cast my net a little wider and speak from impersonal experience... ;)

The short answer is that we look at the limits of truth and provability. Godel's First Incompleteness Theorem (which is what you linked, IIRC) begins the subject: for any "sufficiently powerful", "sufficiently well-defined" set of axioms T, there will be a sentence of (ordinary) arithmetic that is true but not provable from T. This inevitably leads itself to a bunch of different questions:

  1. What does it mean to be "true"? What does it mean to be "provable"?
  2. What is "sufficiently powerful"? What is "sufficiently well-defined"?
  3. What does this "true but not provable sentence" look like?
  4. What, in general, are the limits of axiomatization? What can be axiomatized and what can't? Given a particular set of axioms, what can you conclude about the structures which model them?

Answering these questions lead you to the three main branches of mathematical logic:

  1. Computability Theory (formerly Recursion Theory until Bob Soare, I believe, single-handedly forced everyone to change it), which deals with questions of effectiveness, of what could be computed on an (ideal) comptuer, and of relative complexities.
  2. Model Theory (which has a number of different hoppin' subbranches, including Stability Theory and Simplicity Theory), which asks what one can conclude about structures which model a particular set of axioms.
  3. Set Theory (my field), which studies the axioms that generate the "mathematical universe" itself. It (sort of) splits into two subfields: (infinitary) combinatorics, which studies the way that "very large" infinite sets can be split apart and put back together; and consistency theory, which studies what happens if you add (or subtract) axioms to the standard ZFC universe, usually with Paul Cohen's method of forcing.

In addition, there are the lesser-studied branches of

  • Differently-valued Logics -- what happens if we allow more truth-values than just "true" and "false" (including continuous logics, Boolean-valued logics, and intuitionist/Heyting-valued logics)
  • Infinitary logics -- what if we allow "infinitely long" sentences? How does this change our notions of true (easy) and provable (not so much)?
  • Non-standard Models -- a subfield of model theory, this takes the standard structures of the natural or real numbers and asks what happens if we allow "infinitely large" (and, over the hyperreals, "infinitely small") numbers. Non-standard analysis turns out to be a really useful way of formalizing our intuitive notions about limits, continuity and differentiability (e.g. the Leibniz notation dy/dx is literally how the non-standard derivative is defined) and allows much easier proofs of certain theorems.

Being mathematics, all of these branches are intimately related with one another. For example, my current research involves set theory, consistency proofs, forcing, large cardinals & combinatorics, infinitary logics and infinitary/non-standard model theory.

Gotta run -- student in need! *dundun!*

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