Combining Texts

All the ideas for 'Universals and Particulars', 'What Numbers Are' and 'Rechnungsmethoden (dissertation)'

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5 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 / c. Priority of numbers

18256

Quantity is inconceivable without the idea of addition [Frege]

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 / C. Sources of Mathematics / 2. Intuition of Mathematics

9831	Geometry appeals to intuition as the source of its axioms [Frege]

8. Modes of Existence / D. Universals / 6. Platonic Forms / c. Self-predication

4442	Most thinkers now reject self-predication (whiteness is NOT white) so there is no Third Man problem [Armstrong]