Combining Philosophers

All the ideas for Augustin-Louis Cauchy, Keith Lehrer and George Boole

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11 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin]
Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend]
5. Theory of Logic / H. Proof Systems / 2. Axiomatic Proof
Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals
Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
Justification is coherence with a background system; if irrefutable, it is knowledge [Lehrer]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
Generalization seems to be more fundamental to minds than spotting similarities [Lehrer]
16. Persons / C. Self-Awareness / 1. Introspection
All conscious states can be immediately known when attention is directed to them [Lehrer]