Combining Texts

All the ideas for 'What is so bad about Contradictions?', 'Theory of Knowledge (2nd edn)' and 'works'

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8 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy

2945	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

2946	You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]

2. Reason / B. Laws of Thought / 3. Non-Contradiction

9123	Someone standing in a doorway seems to be both in and not-in the room [Priest,G, by Sorensen]

5. Theory of Logic / A. Overview of Logic / 2. History of Logic

11022

Gentzen introduced a natural deduction calculus (NK) in 1934 [Gentzen, by Read]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11065

The inferential role of a logical constant constitutes its meaning [Gentzen, by Hanna]

11023

The logical connectives are 'defined' by their introduction rules [Gentzen]

11213

Each logical symbol has an 'introduction' rule to define it, and hence an 'elimination' rule [Gentzen]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

10067

Gentzen proved the consistency of arithmetic from assumptions beyond arithmetic [Gentzen, by Musgrave]