Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Protagoras' and 'Counterpart theory and Quant. Modal Logic'

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27 ideas

2. Reason / B. Laws of Thought / 4. Contraries
192 Only one thing can be contrary to something [Plato]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9195 Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
9186 First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication
190 If asked whether justice itself is just or unjust, you would have to say that it is just [Plato]
9. Objects / D. Essence of Objects / 1. Essences of Objects
11976 Aristotelian essentialism says essences are not relative to specification [Lewis]
10. Modality / A. Necessity / 7. Natural Necessity
11978 Causal necessities hold in all worlds compatible with the laws of nature [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
11979 It doesn't take the whole of a possible Humphrey to win the election [Lewis]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
16994 Counterpart theory is bizarre, as no one cares what happens to a mere counterpart [Kripke on Lewis]
11974 Counterparts are not the original thing, but resemble it more than other things do [Lewis]
11975 If the closest resembler to you is in fact quite unlike you, then you have no counterpart [Lewis]
11977 Essential attributes are those shared with all the counterparts [Lewis]
11. Knowledge Aims / A. Knowledge / 3. Value of Knowledge
20184 The only real evil is loss of knowledge [Plato]
20185 The most important things in life are wisdom and knowledge [Plato]
15. Nature of Minds / C. Capacities of Minds / 7. Seeing Resemblance
191 Everything resembles everything else up to a point [Plato]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
203 Courage is knowing what should or shouldn't be feared [Plato]
22. Metaethics / B. Value / 2. Values / j. Evil
202 No one willingly and knowingly embraces evil [Plato]
22. Metaethics / C. The Good / 1. Goodness / h. Good as benefit
193 Some things are good even though they are not beneficial to men [Plato]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
197 Some pleasures are not good, and some pains are not evil [Plato]
200 People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / d. Teaching virtue
188 Socrates did not believe that virtue could be taught [Plato]
204 Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato]
189 If we punish wrong-doers, it shows that we believe virtue can be taught [Plato]