Combining Philosophers

All the ideas for Xenophon, Gerhard Gentzen and Lord Kelvin (Wm Thomson)

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]
14. Science / B. Scientific Theories / 1. Scientific Theory
22363 You have only begun to do real science when you can express it in numbers [Kelvin]
22. Metaethics / B. Value / 2. Values / h. Fine deeds
5845 Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]
25. Social Practice / E. Policies / 5. Education / b. Education principles
5833 Education is the greatest of human goods [Xenophon]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / a. Energy
20644 Energy has progressed from a mere formula, to a principle pervading all nature [Kelvin]