Combining Texts

All the ideas for '', 'Summa Contra Gentiles' and 'The Philosophy of Mathematics'

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14 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
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
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
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
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Without God's influence every operation would stop, so God causes everything [Aquinas]
19. Language / F. Communication / 3. Denial
We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas]