Combining Philosophers

All the ideas for Einstein,A/Infeld,L, Nicholas Rescher and Giuseppe Peano

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11 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
3338 Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
5897 0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / B. Change in Existence / 2. Processes
22626 Process philosophy insists that processes are not inferior in being to substances [Rescher]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
10650 In the military, persons are parts of parts of large units, but not parts of those large units [Rescher]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
20365 We only see points in motion, and thereby infer movement [Rescher]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
18202 The concept of a field gradually replaced the substances in explaining relations between charges [Einstein/Infeld]