A couple of paragraphs from Aristotle - his thinking about Zeno.  Relation between motion, mind, and time.  Motion without time.  Time slices, four dimensional stasis.  The moment of transition.  Is space real?  Is nothingness spatial?

Axioms and self-evidence.  Euclid's fifth postulate.  Non-Euclidean geometry and the difference between infinite and unbounded space.  Anaximander and Parmenides, and the principle of sufficient reason.

More on the difference between extension and intension. Intension as similar to the category of the interesting, and paradoxes of interestingness.  Interestingness of 6210001000 and 1729.  Zeno's paradoxes.  Galileo's paradox.

Mainly about the idea of one-to-one correspondence, after some review of the infinity of primes, and then of some controversies in set theory, especially over whether intensional or extensional ways of referring to sets are more basic.  Counting as coming after one-to-one correspondence.  One-to-one correspondence and infinite sets.

How it could be that we could think of God as a circle whose center is everywhere and circumference nowhere (to use the formula Borges is so fond of).  A little bit about infinite sets.  Seeing the Aleph (or another Aleph) in the Aleph.  The relation of such sight to the Library of Babel: could there be an accurate (multi-volume) catalogue in the Library of Babel which listed every catalogue that didn't list itself?  Leonardo on focal points and their relation to the Aleph.  By occasion, mention of the Kabbalistic idea of the Aleph uttered only once in history, by God at Mt. Sinai.

We mainly discuss Borges's "Library of Babel" and its implications, but this leads us a little to discussions of black holes, the sphericality of the universe, the nature of codes, meaning, OuLiPo, Quine, and infinitesimals.

THINKING ABOUT INFINITY

“The definitive clarification of the nature of the infinite, instead of pertaining just to the sphere of specialized scientific interests, is needed for the dignity of the human intellect itself.” –David Hilbert

Syllabus:

W 5 SeptIntroduction: Dickinson

M10 SeptBorges: “Library of Babel"

“The Aleph"

Leonardo da Vinci (in class distribution)

W12 SeptHilbert: “On the Infinite,” (Latte) Borges, Early Greek Philosophers

[EGP], Chapter 3

M17 SeptNO CLASS (Rosh Hashanah)

W19 Sept Russell: “Introduction to Mathematical Philosophy” (Latte) EGP, 9-11

Th20 SeptEGP, 9-11 (Brandeis Monday)

M24 Sept Aristotle (Latte), Poincaré: “On the Nature of Mathematical

Reasoning” (Latte)

W26 Sept NO CLASS (Yom Kippur)

M 1 OctNO CLASS (Sukkot)

W 3 OctAristotle, Augustine, Confessions Books: 1-4

M 8 OctNO CLASS (Shmini Atzeret)

T 9 OctAugustine, Confessions, Book: 11

W10 OctShakespeare: Macbeth

M15 OctMacbeth, Tennyson: “Tithonus”

W17 OctPascal: Pensées, nos. 47, 68, 113, 131, 147-66, 198-201, 220, 271, 373, 418, 420, 427, 564, 597-99, 653, 682, 688, 721-23, 919

M22 OctPascal

W24 OctTucker: “Prisoner’s Dilemma” (Latte) FIRST PAPER DUE

M29 OctJoyce: Portrait of the Artist as a Young Man

W31 OctPortrait

M 5 NovDescartes: Meditations

W 7 NovDescartes, Lem “Non Serviam” (Latte)

M12 NovWilliam Gibson: Neuromancer

W14 NovGibson

M19 NovKant on space and time

W21 NovNO CLASS (Thanksgiving)

Th22 NovNO CLASS

M26 NovKant

W28 NovShelley: Mt. Blanc

M 3 DecShelley

W 5 DecEGP 5-6, Smolin “Atoms of Space and Time”

M10 DecAaronson: “Who Can Name the Bigger Number?”

W 12 DecReview of CantorSECOND PAPER DUE

The Brain -- is wider than the Sky --

For -- put them side by side --

The one the other will contain

With ease -- and You -- beside

The Brain is deeper than the sea --

For -- hold them -- Blue to Blue --

The one the other will absorb --

As Sponges -- Buckets -- do --

The Brain is just the weight of God --

For -- Heft them -- Pound for Pound --

And they will differ -- if they do --

As Syllable from Sound --

--Emily Dickinson

[Renaissance poetry: last class] Two sonnets of Milton's: Milton's dream compared with Adam's; Adam before the fall; Eve after the fall.

[close reading] Last class: a last class, on Merrill's Book of Ephraim; La Tempesta, on the surface nothing less than earthly life in all its mystery; holding still, being held still; photography; burning the box (Children while you can...).

[renaissance poetry] Last official class, a short one, on Marvell and his self-involved imagery: the flowers that stand under their own colors in "Upon Appleton House," the drop of dew that looks like its own tear, the self-sustaining images of "The Garden," and "Damon the Mower."