Combining Philosophers

All the ideas for Carneades, Giuseppe Peano and Pierre Duhem

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19 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
2666 Carneades' pinnacles of philosophy are the basis of knowledge (the criterion of truth) and the end of appetite (good) [Carneades, by Cicero]
3. Truth / B. Truthmakers / 10. Making Future Truths
21390 Future events are true if one day we will say 'this event is happening now' [Carneades]
21672 We say future things are true that will possess actuality at some following time [Carneades, by Cicero]
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 / F. Identity among Objects / 6. Identity between Objects
15825 Carneades denied the transitivity of identity [Carneades, by Chisholm]
10. Modality / A. Necessity / 3. Types of Necessity
21389 Carneades distinguished logical from causal necessity, when talking of future events [Long on Carneades]
14. Science / A. Basis of Science / 6. Falsification
22137 Observation can force rejection of some part of the initial set of claims [Duhem, by Boulter]
14. Science / B. Scientific Theories / 6. Theory Holism
18197 Experiments only test groups of hypotheses, and can't show which one is wrong [Duhem]
16. Persons / F. Free Will / 2. Sources of Free Will
21671 Voluntary motion is intrinsically within our power, and this power is its cause [Carneades, by Cicero]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
21391 Some actions are within our power; determinism needs prior causes for everything - so it is false [Carneades, by Cicero]
16. Persons / F. Free Will / 6. Determinism / b. Fate
21674 Even Apollo can only foretell the future when it is naturally necessary [Carneades, by Cicero]
22. Metaethics / B. Value / 2. Values / i. Self-interest
7398 Carneades said that after a shipwreck a wise man would seize the only plank by force [Carneades, by Tuck]
25. Social Practice / D. Justice / 1. Basis of justice
21392 People change laws for advantage; either there is no justice, or it is a form of self-injury [Carneades, by Lactantius]