TIRESIAS: fathering the set, mothering the theory

I’m having dinner with a friend, who is just about the most erudite person I’ve known. I praise my luck. Every time I see him. Our discussion spans from bizarre academic practices at universities across Denmark to spelling Geismar the wrong way. We talk about knowledge, ignorance, subjects presuming to know, and Sophocles’s Oedipus. I’m surprised to hear that he even knows, as a matter of course, as he insists by pointing out, that Tiresias, and not Cantor, is considered the father of set theory. Indeed.

I’m reminded of one of Lacan’s sentences in one of his unpublished seminars, also quoted by Shoshana Felman in an article about teaching “terminable and interminable” analytical tasks (here in relation to Socrates and Freuds’s convictions that teaching itself is ultimately impossible). Taking her cue from Lacan who said that the unconscious is “knowledge that can’t tolerate one’s knowing that one knows” (Seminar, Feb. 19, 1974), Felman makes the interesting inference that the unconscious must be some kind of “unmeant knowledge” (28). As Tiresias had just served me for inspiration in connection with some writing, Lacan’s idea that where signs are concerned we always mobilize many more of them than we know, I think of numbers – also metaphorically here – that we play on others, or that others play on us.

Says Felman: “For knowledge to be spoken, linguistically articulated, it would constitutively have to be supported by the ignorance carried by language, the ignorance of the excess of signs that of necessity its language, its articulation – “mobilizes”. Thus human knowledge is by definition that which is untotalizable, that which rules out any possibility of totalizing what it knows, or of eradicating its own ignorance”. (29)

Says Cantor: “the set of all sets in a universe does not constitute a set.”

Says Teiresias in an exchange with Oedipus:

Teiresias: …You are the land’s pollution.
Oedipus: How shamelessly you started up this taunt! How do you think you will escape?
Teiresias: … I have escaped. The truth is what I cherish and that’s my strength.
Oedipus: And who has taught you truth? Not your profession surely!
Teiresias: You have taught me, for you have made me speak against my will.
Oedipus: Speak what? Tell me again that I may learn it better!
Teiresias: Did you not understand before or would you provoke me into speaking?
Oedipus: I did not grasp it, not so to call it known. Say it again.
Teiresias: I say you are the murderer of the king whose murderer you seek.

I tell my friend: “If psychoanalysts will come up with solutions to some of the most famous mathematical unsolved puzzles and conjectures formulated this and the past century, I won’t be surprised”. He concurs. And tells me that it will take the Other – the woman speaking, with whom the knowledge that is already there is always there – to articulate a proof.

And so says Felman: “From a philosophical perspective knowledge is mastery – that which is mastery of its own meaning. Unlike Hegelian philosophy, which believes it knows all that there is to know; unlike Socratic (or contemporary post-Nietzschean) philosophy, which believes it knows it does not know – literature, for its part, knows it knows but does not know the meaning of its knowledge – does not know what it knows.” (41)

What we learn better, I’d like to tell Oedipus, is that any proof must first be a style, and any knowledge must first be poetic.

Cited work:

Shoshana Felman: "Psychoanalysis and Education: Teaching Terminable and Interminable". Yale French Studies, No. 63, The Pedagogical Imperative: Teaching as a Literary Genre (1982), pp. 21-44


Anonymous said…
My God, Camelia, I would never discuss set theory with a lady at the restaurant. Only if the wine was bad :))
Camelia said…
Horia, as a good mathematician interested in quantum transport, you should know about narratorial vehicles. Besides, with this lady in question, you would talk about everything, and I mean just that. Because this 'everything' is like a superconducting ring: it comes out of nothing, goes through a good laugh, and out it goes into nothing raised at the 10th power, or so. We should get together soon.
Anonymous said…
Hi Camelia. Thanks for a very delectable entry. I couldn't help being reminded of one of my favourite New Yorkers, flâneurs and pedestrian poets who knew that the (hu)man body is nothing but a means of transport - both literally and metaphorically, and, most importantly, knew how to count - especially his metaphorical blessings. Let these poetic steps and numbers by Frank O'Hara prompt your body to carry you to the rest of his wonderful poem "In Memory of My Feelings" (1956) (pp. 252-257 in The Collected Poems), incidentally dedicated to his then female friend Grace Hartigan:

My quietness has a man in it, he is transparent
and he carries me quietly, like a gondola, through the streets.
He has several likenesses, like stars and years, like numerals.

My quietness has a number of naked selves,
so many pistols I have borrowed to protect myselves
from creatures who too readily recognize my weapons
and have murder in their heart!
though in winter
they are warm as roses, in the desert
taste of chilled anisette.
Bent said…
In "The Purloined Letter" Dupin is lecturing his sidekick about logic, poetry and math:

"'This functionary [the Prefect of Police], however, has been thoroughly mystified; and the remote source of his defeat lies in the supposition that the Minister is a fool, because he has acquired renown as a poet. All fools are poets; this the Prefect feels; and he is merely guilty of a non distributio medii in thence inferring that all poets are fools.'

'But is this really the poet?' I asked. 'There are two brothers, I know; and both have attained reputation in letters. The Minister I believe has written learnedly on the Differential Calculus. He is a mathematician, and no poet.'

'You are mistaken; I know him well; he is both. As poet and mathematician, he would reason well; as mere mathematician, he could not have reasoned at all, and thus would have been at the mercy of the Prefect.'"

In other words all mathematicians are on their way to jail, unless they possess a little poetical skill to keep them out. Most poets are also fools (which however is not necessarily a crime), and thus no match for the logician. It's when we get the combo of poet and mathematician that things get interesting - and the criminals get arrogant. However, they can still get caught by an even better poet, such as Dupin - the super poetico-logico-math-master...

But then you know all that, as you yourself are the supremo master of the - if not undistributed, then - excluded middle!


1. All poets are mathematicians.
2. My father is a mathematician.
3. Therefore, my father is a poet.
(undistributed middle 'logic')


1. All poets are mathematicians.
3. Therefore, my father is a poet.
(excluded middle, or Camelia, 'logic')

See also The Fallacy Files
Anonymous said…
Well, I'm no match for you in putting words together. I try to replace my abstract symbols with beautiful orgies of feelings, without any success. This makes me angry, and very unstable. I get out in the street totally frustrated and enraged, and start calling everybody a damn poet. The chief of police is passing by: "Grab this mathematician!" he says. "Don't let him leave until he's writing a poem!"

QED. :)
Camelia said…
Søren, Horia, Bent, and (Charles in the wings) thanks for the really great fun on this. Who would have thought that Tiresias and all that psycho thought could have sparked such wit! Well, obviously a poet and a mathematician would...

Bent, as always you hit the mark right on the spot. I do tend to leave the middle out, but that's because I'm more interested in listening to/reading about peoples' inferences. This greatly amuses me, especially when the inferences are wrong. On the other hand it's also exciting not to ever know what conclusion the missing middle might elicit. So there.

But then Poe himself was not such a great logician after all, unless he was a poet who thence intended his imprecision on purpose. As others have observed: "The argument that Poe cites is indeed fallacious, but it is not an instance of undistributed middle, rather it's an example of illicit conversion. In fact, the argument from 'All fools are poets' to 'All poets are fools' doesn't even have a middle term, since it is an immediate inference. The middle term is, by definition, the term shared by both premises in a categorical syllogism, but an immediate inference has only one premise." (Fallacy Files)

You want to know about my father. As he died when I was 8 I have few memories. If asked, my mother would say he was only a mathematician and no poet. She would also say that she was the better logician. Mana and I can at least confirm that she was better than the rest - by inference of probability then also better than my father. As she insisted that our own logic be impeccable, especially when we would go the poetic way in a foolish way, when we got it wrong, however, it was like being in Alexander Pope's universe: "Sir I admit your general rule, that every poet is a fool; but you yourself may serve to show it; that every fool is not a poet."

Horia, I'm tempted to say that your making a scene with the Prefect wouldn't help much - I doubt that he would have the spirit of presence to ask you, the frustrated mathematician, to write a poem - and it is very improbable that he would identify a poem performed as you just did. QED.

Prefects often commit a favorite fallacy of mine: "the masked man fallacy". Cf. formal logic: "If someone were to say, 'I do not know the masked man,' it implies, 'If I do know the masked man, I do not know that he is the masked man.' The Masked Man fallacy omits the implication."

Consider this:

I know who my father is.
I don't know who the poet is.
Therefore my father is not the poet.


I know who Horia is.
I don't know who the Prefect is.
Therefore Horia is not the Prefect.

So Horia, next time you feel frustrated, take out your guns, shoot something and then walk like O'Hara's poet, instead of waiting to be apprehended like the mathematician who already starts counting his time in jail.
Anonymous said…
the sheriff is shot
how lucky I got!
the deputy escaped,
but beware! cause I'm beeeeed :)

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