The Immanence of Truths is the final volume of Badiou’s Being & Event trilogy and the most important work of mathematical ontology to appear in this century. While there are many angles from which to approach the text, my focus, in the short time we have together, will be on Badiou’s stunning introduction of large cardinal theory—the rational thought of the higher infinite—into continental philosophy. In the understated idiom typical of mathematicians, ‘large’ cardinals are infinities which, if they are not contradictory (and therefore can exist at all) are too immense for their existence to be established in standard set theory (ZFC), which Badiou identified with ontology in Being & Event. This extended ontology pivots on the interpretation of four instances of large cardinals: strongly inaccessible, weakly compact, measurable, and large large cardinals. Roughly, these are taken typify the infinite considered from below, from the outside, from the inside, and from above. The ultimate goal of this seminar is for each participant to work toward eidetic intuitions of some or all of these large cardinals—that is, having a vision of the things themselves—guided by Badiou’s trailblazing interpretation. It is intended for ambitious, though not necessarily experienced, participants, and I’ll encourage you to use chat liberally outside of meeting hours to work through issues with me.
Session 1. January 10, 2023
- Text: General Introduction, Prologue, C3.4 and C9-S10 of Section II: The Modernity of Finitude: Covering-Over.
- Recommended reading: Section I: The Classic Forms of Finitude, rest of Section II: The Moder- nity of Finitude: Covering-Over.
- Forms: Axioms of standard (ZFC) set theory, ‘Russell’s Paradox,’ Cantor’s Theorem, the Cu- mulative Hierarchy of sets V , the Constructible Universe L, the Axiom of Choice.
Session 2. January 17, 2023
- Text: Section III: The Supremacy of Infinity
- Forms: Inaccessible cardinals, models of ZFC, [worldly cardinals], compactness, weakly compact cardinals
Session 3. January 24, 2023
- Text: Section IV: Approaching the Absolute
- Forms: Measurable (‘complete’) cardinals, filters and ultrafilters, proper classes, elementary em- beddings, ultraproducts and ultrapowers, the fundamental theorem
Session 4. January 31, 2023
- Text: Section V: Conditions for Defeating Covering-Over
- Forms: Scott’s Theorem, 0#, Silver’s Theorem, Jensen’s Theorem.
Session 5. February 7, 2023
- Text: Section VI: Parmenides’ Revenge, Section VII: The General Theory of Works-in-Truth, General Conclusion.
- Recommended reading: Section VIII: Works Based on the Object: Art, Science, Section IX: Works Based on Becoming: Love, Politics.
- Forms: Reflection principles, consistency strength, the large cardinal hierarchy as a non-whole, su- percompact cardinals, huge cardinals, n-huge cardinals, Kunen’s Theorem, proper classes again.
Please read the texts prior to each meeting, if at all possible. The presentations may include some summaries, for purposes of reminding, but will not be designed primarily for that purpose.