Combining Texts

All the ideas for 'Necessary Existents', 'Building Blocks of Mathematical Logic' and 'What Numbers Are'

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4 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

17699

Variables are auxiliary notions, and not part of the 'eternal' essence of logic [Schönfinkel]

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]

19. Language / D. Propositions / 3. Concrete Propositions

19216

Propositions (such as 'that dog is barking') only exist if their items exist [Williamson]