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April 08, 2003

PoMo nonesense (yes, the second goes without saying)

Reading Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science. Give this book to any young person who is considering majoring in any subject that might require PoMo. Check it out:
page 19:

This diagram [the Mobius strip] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much further than you may think at first, because you can search for the sort of surface able to receive such inscriptions. You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface, are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresonds to the neurotic subject, and on a cross-cut surface to another sort of mental disease [Lacan 1970, pp. 192-193]

Can you imagine a computer program writing this? A primitive one yes-it certainly wouldn't pass a Turing Test.

HARRY WOOLF: May I ask if this fundamental arithmetic and this topology are not in themselves a myth or merely at best an anology for an explanation of the life of the mind?

JACQUES LACAN: Analogy to what? "S" designates some-thing which can be written exactly as this S. As I have said that the "S" which designates the subject is instrument, matter, to symbolize a loss. A loss that you experience as a subject (and myself also). In other words, this gap between one-thing which has marked meanings and this other thing which is my actual discourse that I try to put in a place you are, you as not another subject but as people that are able to understand me. Where is the analogon? Either this loss exists or it doesn't exist. If it exists it is only possible to designate the loss by a system of symbols. In any case the loss does not exist before this symbolization indicates its place. It is not an analogy. It is really in some part of the realities, this sort of torus. This torus really exists and it is exactly the structure of the neurotic. It is not an analogon; it is not even an abstraction, becasue an abstraction in some sort of diminution of reality, and I think it is reality itself. (Lacan 1970, pp. 175-196)

Who said the soothsayers and raving oracles of the pagan age are no longer with us? This sort of stream-of-consciousness bullshit requires either great brilliance on the part of the bullshitter or extreme stupidity and unlawfull intellectual lazines on the part of the audience.

Posted by razib at 06:22 AM

I'm an English major and if I had to do it again I would study philosophy instead. I'm so sick of these PoMo losers with their paranoid fantasies and their hysterical projections onto innocent novels. I'm encouraging my 17 y/o brother to major in philosophy instead of English, or look DAMN hard for a non-PoMo English Dept.

Posted by: duende at April 8, 2003 11:28 AM

I haven't studied post-modernism in any depth but I recal the Sokal (sp?) scandal and I saw evidence of postmodernists latching on to math and science terminology as if they were fully aware of the weakness of their own philosophical foundation.

Anyone with a glimmer of knowledge of higher mathematics can appreciate how splendid it is. It is like some beautiful crystaline structure with an infinity of marvelous twists and turns.

Some postmodernists probably hate the idea that reality isn't subject to their egos. Some hate western civilisation and (possibly subconciously) are using postmodernism as a destructive meme. Some postmodernists may be stupid people who can't understand difficult ideas and resent people who can. I think that postermodernism is due to an interplay of these forces.

Posted by: Sporon at April 8, 2003 12:54 PM

I would not condemn post-modernism simply on the basis of a few passages that are truly unintelligible on first view. For example, I remember browsing through _Being and Time_ for the first time and thinking "what the !#4? is he talking about". Many post-modernists make idiomatic use of terminology or use familiar words in new ways.

I'm sure that there are intelligent and interesting writers (like Heidegger) whose writings are not penetrable on first view. I'm also sure that there are lots of people who write !#4? and try to pass it off as wisdom. And, I'm sure that most people, including most intelligent people can't distinguish between the two based on small passages.

I'm also a big supporter of experimenting with language. The trick is to distinguish between experimentation for its own sake and the kind that is the product of a mind that is trying to communicate ideas that are just too difficult to express in "plain words".

If we look at our own terminology and expressions, we soon realize how absurd many of them seem. I wonder how absurd "under-stand" first seemed to those who heard it for the first time. To see why this is the case, consider also expressions in foreign languages that appear to be nonsensical, and surprised you when you first heard about them.

Posted by: Dienekes at April 8, 2003 05:25 PM

i oppose PoMo as it is. i have been told its initial claims were modest and rational. and these passages deal with science specifically...they can say all they want about literature, i don't care, that's for the lit-crits to worry about.

Posted by: razib at April 8, 2003 07:20 PM

Dienekes wrote:

"I'm also a big supporter of experimenting with language. The trick is to distinguish between experimentation for its own sake and the kind that is the product of a mind that is trying to communicate ideas that are just too difficult to express in "plain words"."

The idea of inexpressable ideas has probably existed in most civilisations (I do not refer to permanently uncivilised places in which philosophy was never developped).

On one hand because of my love of logic I admit that I inately want to reject the idea of inexpressable truths, but I don't. However postmodernists don't say that there are inexpressible truths. What they instead say is that there are truths that can only be expressed with language like this:

"If you take the set of all elements wich are not members of themselves

x ![ x

[Note: I'm using the symbol "![" for the "does not belong to" operator.]

the set that you constitute wich such elements leads you to a paradox, which as you know leads to a contradiction. In simple terms this only means that in a universe of discourse nothing contains everything, and here you find again the gap that constitutes the subject."

[Note: I saw this in an online excerpt from Sokal's book at amazon.com.]

Lacan is refering to what is known as Russel's Paradox. Lacan did not denote the set properly. The (hypothetical ) set should be denoted as

{ x | x ![ x }

as opposed to

x ![ x,

which denotes a proposition.

Before the 20th century mathematicians were using something called "naive" set theory which was axiomised such that, for every first order property P the set {x | P(x)} existed.

In the universe of naive set theory Russel's set exists, and its existance does indeed result in a contradiction.

Because of Russel's paradox, set theory had to be axiomised to prevent sets like Russel's set from existing, so ZFC was developped. In ZFC, there are axioms to build sets from other sets with with like the Union and pairing axiom, axioms guaranteeing the existance of certain sets, like the axiom of the empty set and the axiom of infinity, and axioms by which sets can be generated from others like the comprehension axiom which states that for any set S and any first order property P the subset of S such that all elements have property P exists. (Please recognise that what I have written is very informal.). The axiom of comprehension in ZFC is far weaker than the axiom of naive set theory that allowed you to just build any set you wanted from any property, so Russel's paradox does not occur in ZFC.

Lacan describes Russel's paradox but it seems that he then jumps to Cantor's paradox, without explicitly saying so. In naive set theory, apart from Russel's set, the Universal set (set of all sets) exists. This also results in its own contradiction. That there can be no universal set has anything to do with Lacan's idea that "nothing contains everything". Sure some Buddhists consider consider that ultimate reality is some sort of metaphysical nothing or "void", but set theory has got nothing to do with *that*. Next he says "and here you find the gap that consitutes the subject". Pardon me but wtf is that supposed to mean. Could words like that ever mean *anything*?

So what we have here is a man who pretends to understand mathematical concepts but doesn't (and i hope its Lacan and not me that i'm talking about), so the idea that he is having a hard time expressing difficult concepts seems unlikely to me since he has failed to master some very concrete and unambiguous concepts that he explicity refers to.

Posted by: Sporon at April 9, 2003 09:45 PM

The Naive Set Theory book I read (Halmos) ended something like "Nothing contains everything, or to put it more dramatically, there is no universe". Maybe it's obsolete and there is a universe now. It's a fun topic to Google.

Posted by: zizka at April 10, 2003 02:50 PM

I wrote:
That there can be no universal set has anything to do with Lacan's idea that "nothing contains everything".

I admit that I had misread Lacan when he said that. I thought he was talking about some metaphysical *nothing*. I thought he was saying something like "everything is contained in some great nothing". It would have been far clearer had he said "no *thing* contains everything" but I did concur that there could no universal set (set of all sets). I realised that I had misread it later on but on this blog there is no edit feature so it was too late. I figured I would just explain later on if someone called me to account.

Well in ZFC it is easy to prove that the set
U={x | x=x}
(i.e. the set of all sets) cannot exist which can be translated as "nothing contains everything." There are three proofs that I know of. One of them is based on constructing the powerset of the universe , noting that it must be a subset of itself and then observing that Cantor's famous result that there can be no *onto* map from a set to its powerset contradicts the fact that for every subset there is always an onto map from the set to that subset.

Another proof which I thought of myself (but I assume that its standard) but I haven't seen anywhere (I've never actually read a set theory book) involves showing that russel's set is necessarily a subset of the Universe set. I haven't gone through it formally line by line so I'm not 100% sure of it this instant but i'm pretty sure that it or something like it works. I like this idea a bit better. This captures the notion of Russel's set being "too big".

The third proof involves simply noting that the axiom of foundation gets violated as U will contain istelf. This proof is slightly inferior to the first two proofs because it relies on an axiom which need not be relied upon for the theorem to hold.

NGB has universe of sets but not a universe of all individuals. (In NGB not all indivuduals are sets). Its also my understanding that some alternative set theories *do* have a universe of all individuals. Check out
I have not idea what it's really about but I understand that some sort of hierarchal scheme like what is used in type theory.

Set theory doesn't prove methapysically that "no thing contains everything". It could be pointing at some great metaphysical truth or it could just be an artifact of logic.

Anyway even though I misinterpreted that sentence all my other objections about Lacan's writing stand. He still confused cantor's paradox with russel's paradox. He still specified Russel's set incorrectly (where he attempted to write it out formally), and his babble about "the gap that constitutes the subject" is still babble. If you read the excerpt of Sokal's book at Amazon.com you can read many many howlers.

What I am saying is that many people claim that thir language is obscure because their ideas are *deep*. It is of course possible, *but* it often turns out that when these people refer to concrete unambiguous concepts, these people don't know what they are talking about, which indicates to me that they don't know what they are talking about at *all*.

Posted by: Sporon at April 10, 2003 05:48 PM

I agree about Lacan. I just lost an old old friend in part because he takes Lacan seriously.

Posted by: zizka at April 10, 2003 07:54 PM