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Lecture outlines for Language, Logic, and Thought

Craig DeLancey, PHL 309

**I. A Historical Random Walk along the Limits of Reason**

Leibniz and The Characteristica Universalis

Galileo Introduction

Galileo on Infinity

Cantor

The PDF of our clarification about the diagonal argument

The PDF of our notes about Kant and Euclidean Geometry

Frege and Logicism

Hilbert

Brouwer

Logicism Continued: Russell

A note about theories

**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