Combining Texts

All the ideas for 'fragments/reports', 'Reference and Generality (3rd ed)' and 'What Numbers Are'

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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 / 4. Using Numbers / c. Counting procedure

17812

Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP]

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts

12154

Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]

9. Objects / A. Existence of Objects / 6. Nihilism about Objects

8969	We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]

9. Objects / F. Identity among Objects / 3. Relative Identity

16075

Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]

12152

Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]

9. Objects / F. Identity among Objects / 8. Leibniz's Law

16073

Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]