Combining Texts

All the ideas for 'What Numbers Are', 'Some Remarks on Essentialism' and 'Structuralism Reconsidered'

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8 ideas

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17813 Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
8923 Numbers are identified by their main properties and relations, involving the successor function [MacBride]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17812 Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
8926 For mathematical objects to be positions, positions themselves must exist first [MacBride]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
13952 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
13954 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
13955 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
13953 An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R]