Combining Philosophers

All the ideas for Dennis Whitcomb, Gerhard Gentzen and Hermann von Helmholtz

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

9 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
19695 The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb]
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]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
20646 Helmholtz used 'energy' to mathematically link heat, light, electricity and magnetism [Helmholtz, by Watson]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
20973 All forces conserve the sum of kinetic and potential energy [Helmholtz, by Papineau]