Combining Texts

All the ideas for 'fragments/reports', 'On 'Insolubilia' and their solution' and 'The Philosophy of Mathematics'

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12 ideas

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]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
The 'no classes' theory says the propositions just refer to the members [Russell]
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 / 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]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / d. Richard's paradox
Richard's puzzle uses the notion of 'definition' - but that cannot be defined [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
Vicious Circle: what involves ALL must not be one of those ALL [Russell]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]