The [Philosophical] Foundations Of Arithmetic – Gottlob Frege
In this episode of Canonball we discuss "The Foundations Of Arithmetic," which was written by Gottlob Frege and published in 1884.
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00:00 Frege's Life
01:29 General Notes On Frege's View – Platonism, Nominalism, Psychologism, Formalism, And Logicism
07:59 Frege's Begriffsschrift, or Concept Writing, As A Predecessor To The Work Of Bertrand Russell, Alfred North Whitehead, And Kurt Gödel
10:43 Frege's High Standard For Certainty
11:34 The Foundations Of Arithmetic: The Linguistic Turn; The Concept-Object Distinction; The Context Principle
14:20 Note On The Harper And Brothers'Edition
16:09 Analytic, Synthetic, A Priori, And Posteriori
17:37 Frege's Examination Of The Work Of Other Thinkers
21:22 The Problem With Units
23:31 Statements Of Number Are Statements Of Fact Explained By The Objectivity Of Concepts
25:57 Frege's Main Disagreement With Kant
26:11 Beginning Of Passages From "The Foundations Of Arithmetic" – Presenting The Question
33:15 His Reason For Exploring Other Thinkers' Positions
34:49 The Origin Of An Idea Is Not Its Definition; Against Psychologism; Rigor And His Three Principles
40:03 The Rewards Of Rigor And The Search For Exhaustive Proof
42:53 More On Analytic, Synthetic, A Priori, And Posteriori Justifications For Judgments
47:12 Whether Arithmetical Formulas Are Provable; The Basis Of Arithmetic
49:58 Number, The North Sea, And Astronomy
51:49 Frege's Conclusion