Combining Texts

All the ideas for 'works', 'The Philosophy of Mathematics' and 'Some Remarks on Essentialism'

expand these ideas     |    start again     |     specify just one area for these texts


12 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Tell cleverness from answers, but wisdom from questions [Mahfouz]
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 / 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]
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]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R]
9. Objects / F. Identity among Objects / 3. Relative Identity
An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R]