Combining Philosophers

All the ideas for Paul Bernays, Robert B. Brandom and Gerhard Gentzen

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11 ideas

3. Truth / C. Correspondence Truth / 2. Correspondence to Facts

10355

Facts can't make claims true, because they are true claims [Brandom, by Kusch]

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory

10304

Very few things in set theory remain valid in intuitionist mathematics [Bernays]

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]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

10303

Restricted Platonism is just an ideal projection of a domain of thought [Bernays]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

10306

Mathematical abstraction just goes in a different direction from logic [Bernays]

19. Language / A. Nature of Meaning / 6. Meaning as Use

7765	The use of a sentence is its commitments and entitlements [Brandom, by Lycan]