Ralph Dumain: "The Autodidact Project": Dialogue: Logic vs Mathematics, Category Theory, Irony, Self-Reference, Performative Meaning, Theodor W. Adorno

Logic vs Mathematics, Category Theory, Irony, Self-Reference,
Performative Meaning, Theodor W. Adorno

Dialogues between chatGPT & Ralph Dumain

6 May 2025

—> DOCX FILE <—

9 May 2025, revised 16 May 2025

Key sections:

Logic & Mathematics . . . & Category Theory: Subsumption, Merger, or Divergence?
Dialogue on the Foundations of Mathematics: Category Theory and Logic
Historical Roles of Logic & Mathematics
- Historical Roots of the Division
- Where They Differ in Purpose Today
- PART 1: Essay Outline: Mathematics and Logic: Divergent Aims Beneath Formal Unity
- PART 2: Has Category Theory Progressed to Deal with Semantics?
- Philosophical Reading List: Logic, Mathematics, and Category Theory
Irony & Logic
- Many-Valued Logic and Paraconsistent Logic
- Supporting Readings: Logic, Irony, and Modeling
Self-reference, Pragmatics, & Raymond Smullyan
- Self-Reference and Speech Acts: A Tight Connection
- Why This Matters
The Analytic/Continental Divide
Theodor W. Adorno: Negative Dialectic vs Logic
Outlines, Summaries, Fragments, & Bibliographies for a Proposed Essay on Adorno & the Formal Sciences
Intersections of Mathematics, Formal Logic, Category Theory, and Adorno’s Philosophy: Annotated Bibliography

The first two sessions of dialogue occurred on 6 May 2025. They have been roughly concatenated here, omitting some initial questions on Einstein viz. philosophical interpretation of relativity, and on Louis Althusser’s relation to Gaston Bachelard.

In the attached document we begin where I launched into inquires concerning the relation between logic and mathematics, with consideration of category theory, then proceeding on to the other topics. There is some confusion in my record later on where chatGPT tries out various outlines for an essay combining all these topics and proceeds to write proposed sections, concluding with an annotated bibliography. The content in any case is very rich.

II compiled the texts of these first two dialogues as a prologue to engaging the third. This is how the third dialogue began:

ChatGPT: Yes — I remember that detailed comparison: we explored how logic and mathematics are formally unified (through systems like set theory or categorical foundations), yet diverge philosophically and practically in their goals, methods, and conceptual flexibility. Logic often prioritizes proof, consistency, and truth-preserving formality; mathematics, especially in its modern incarnations, embraces constructive structures, abstraction, and even conceptual ambiguity (e.g., in geometry, topology, category theory). That divergence becomes especially meaningful when viewed through your critical-theoretical lens.

The third dialogue, titled “Logic, Mathematics, Category Theory, Irony, Models, Historical Development, Theodor W. Adorno, Evald Ilyenkov,” has been reproduced separately. See also the chatGPT summary essay: