Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Chris Daly and Gerhard Gentzen

expand these ideas     |    start again     |     specify just one area for these philosophers

10 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]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
8526 We might treat both tropes and substances as fundamental, so we can't presume it is just tropes [Daly]
8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes
8527 More than one trope (even identical ones!) can occupy the same location [Daly]
8528 If tropes are linked by the existence of concurrence, a special relation is needed to link them all [Daly]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]