Lecture outlines for Language, Logic, and Thought

Craig DeLancey, PHL 309

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I. A Historical Random Walk along the Limits of Reason

Leibniz and The Characteristica Universalis

Galileo Introduction

Galileo on Infinity

Cantor

Frege and Logicism

A note about theories

Hilbert

Brouwer

Logicism Continued: Russell

II. An Aside: Conventionalism and Radical Skepticism

Conventionalism: Kripkenstein

III. Results and Implications

Godel's Incompleteness Theorems

Turing, Turing machines, UTMs, and the Halting Problem

Kolmogorov Complexity, 1

Kolmogorov Complexity, 2

Practical Constraints on Reason

Speculations on Effects of the Limits of Reason