Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Edmund O. Wilson and Giuseppe Peano

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22 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 / C. Structure of Existence / 3. Levels of Reality
5311 If observation goes up a level, we expect the laws of the lower level to remain in force [Wilson,EO]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
5312 A child first sees objects as distinct, and later as members of groups [Wilson,EO]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
5309 Beliefs are really enabling mechanisms for survival [Wilson,EO]
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]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
5310 Philosophers study the consequences of ethics instead of its origins [Wilson,EO]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
22187 Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
5313 The rules of human decision-making converge and overlap in a 'human nature' [Wilson,EO]
22. Metaethics / B. Value / 2. Values / f. Altruism
5316 We undermine altruism by rewarding it, but we reward it to encourage it [Wilson,EO]
5318 Pure hard-core altruism based on kin selection is the enemy of civilisation [Wilson,EO]
23. Ethics / B. Contract Ethics / 1. Contractarianism
5317 The actor is most convincing who believes that his performance is real [Wilson,EO]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
20662 The biology of societies: kin selection, parenting, mating; status, territory, contracts [Wilson,EO]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
5308 The only human purpose is that created by our genetic history [Wilson,EO]
27. Natural Reality / G. Biology / 3. Evolution
5314 Cultural evolution is Lamarckian and fast, biological evolution is Darwinian and slow [Wilson,EO]
5315 Over 99 percent of human evolution has been in the hunter-gatherer phase [Wilson,EO]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
5320 It is estimated that mankind has produced 100,000 religions [Wilson,EO]