Juliette Kennedy

On the philosophical development of Kurt Gödel

Godel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. Based on research in Godel’s archive, from which a number of unpublished items are presented, we argue that (1) Godel turned to Husserl in search of a means to make Leibniz’ monadology scientific and systematic, and (2) This explains Godel’s specific turn to Husserl’s transcendental idealism as opposed to the realism of the earlier Logical Investigations. We then give three examples of concrete influence from Husserl on Godel’s writings.

Interpreting Gödel : critical essays

1. Introduction: Godel and analytic philosophy: how did we get here? Juliette Kennedy Part I. Godel on Intuition: 2. Intuitions of three kinds in Godels views on the continuum John Burgess 3. Godel on how to have your mathematics and know it too Janet Folina Part II. The Completeness Theorem: 4. Completeness and the ends of axiomatization Michael Detlefsen 5. Logical completeness, form, and content: an archaeology Curtis Franks Part III. Computability and Analyticity: 6. Godels 1946 Princeton bicentennial lecture: an appreciation Juliette Kennedy 7. Analyticity for realists Charles Parsons Part IV. The Set-theoretic Multiverse: 8. Godels program John Steel 9. Multiverse set theory and absolutely undecidable propositions Jouko Vaananen Part V. The Legacy: 10. Undecidable problems: a sampler Bjorn Poonen 11. Reflecting on logical dreams Saharon Shelah.

Turing, Gödel and the “Bright Abyss”

We consider the development of computability in the 1930s from what we have called the formalism free point of view. We employ a dual conceptual framework: confluence together with grounding.

“Gödel’s Modernism: On Set-Theoretic Incompleteness,” Revisited

On Friday, November 15, 1940, Kurt Godel gave a talk on set theory at Brown University. The topic was his recent proof of the consistency of Cantor’s Continuum Hypothesis, henceforth CH, with the axiomatic system for set theory ZFC. His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness:

Aesthetics and the Dream of Objectivity: Notes from Set Theory

In this paper, we consider various ways in which aesthetic value bears on, if not serves as evidence for, the truth of independent statements in set theory. ... the aesthetic issue, which in practice will also for me be the decisive factor—John von Neumann, letter to Carnap, 1931 For me, it is the aesthetics which may very well be the final arbiter—P. J. Cohen, 2002

Gödel’s Reception of Turing’s Model of Computability: The “Shift of Perception” in 1934

The emergence of the mathematical concept of computability in the 1930 s was marked by an interesting shift of perspective, from viewing the intuitive concept, “human calculability following a fixed routine” in terms of calculability in a logic, to viewing the concept as more adequately expressed by Turing’s model.

Kant, Co-Production, Actuality, and Pedestrian Space: Remarks on the Philosophical Writings of Fred Sandback

My mom told me about this Charlie Chaplin film…said she enjoyed a clip of Charlie Chaplin eating an artichoke. Finding himself befuddled at a fancy dinner, he took one leaf off, looked at it, and threw it over his shoulder. And so on through the meal until he got to the lovely heart, he looked at it, and regarded it a little longer and threw it over his shoulder. And at that age when mom told it to me it was still already a potent image of moving on beyond Immanuel Kant and the thing itself and leaving that borderline with Platonism behind in the dust somehow. All right, so much for that.