Combining Philosophers

All the ideas for Timon, Sphaerus and Gerhard Gentzen

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8 ideas

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]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

13832

Natural deduction shows the heart of reasoning (and sequent calculus is just a tool) [Gentzen, by Hacking]

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]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

20769

Sphaerus he was not assenting to the presence of pomegranates, but that it was 'reasonable' [Sphaerus, by Diog. Laertius]

13. Knowledge Criteria / E. Relativism / 3. Subjectivism

2975	That honey is sweet I do not affirm, but I agree that it appears so [Timon]