Combining Texts

All the ideas for 'What Numbers Are', 'Concepts and Counting' and 'Human Society in Ethics and Politics'

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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 / 4. Using Numbers / c. Counting procedure

17812

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

17462

A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

17461

Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt]

28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question

2609	If God's decrees are good, and this is not a mere tautology, then goodness is separate from God's decrees [Russell]