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

The PDF of our notes about Kant and Euclidean Geometry

Cantor

The PDF of our clarification about the diagonal argument

Frege and Logicism

Hilbert

The PDF of our notes about Formalism, Intuitionism, and the relevant implications of some of Hilbert's Problems

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