Combining Philosophers

All the ideas for Speussipus, Peter Singer and Giuseppe Peano

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25 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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
594 Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
20289 Ethics is universalisable - it must involve an impartial and universal view of things [Singer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
20286 Following an inner voice for morality is irresponsible in a rational agent [Singer]
22. Metaethics / B. Value / 2. Values / c. Life
20282 The sanctity of a human life depends either on being of our species, or on being a person [Singer]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
20278 'Marginal utility' says something is more useful if it is in short supply [Singer]
23. Ethics / B. Contract Ethics / 1. Contractarianism
20281 Why should I do anything for posterity? What has posterity ever done for me? [Singer]
23. Ethics / D. Deontological Ethics / 1. Deontology
20276 Conflict of rules might be avoided by greater complexity, or by a hierarchy of rules [Singer]
23. Ethics / F. Existentialism / 4. Boredom
20290 Psychopaths may just be bored, because they cannot participate in normal emotional life [Singer]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
20288 You can't condemn violent revolution without assessing the evils it prevents [Singer]
21997 In Marxism the state will be superseded [Singer]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
20287 If 49% of the population can be wrong, so can 51% [Singer]
24. Political Theory / D. Ideologies / 9. Communism
21993 Materialist history says we are subject to incomprehensible forces [Singer]
25. Social Practice / B. Equalities / 1. Grounds of equality
20277 Equality of interests is a minimal principle, not implying equal treatment [Singer]
25. Social Practice / B. Equalities / 4. Economic equality
20279 Equality of opportunity unfairly rewards those lucky enough to have great ability [Singer]
25. Social Practice / C. Rights / 1. Basis of Rights
20285 If a right entails having the relevant desire, many creatures might have no right to life [Singer]
25. Social Practice / F. Life Issues / 3. Abortion
20284 Why should a potential person have the rights of an actual person? [Singer]
25. Social Practice / F. Life Issues / 6. Animal Rights
20283 Killing a chimp is worse than killing a human too defective to be a person [Singer]
28. God / C. Attitudes to God / 5. Atheism
2632 Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]