Combining Texts

All the ideas for 'works', 'What Numbers Are' and 'Structuralism Reconsidered'

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9 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor

6806	Do not multiply entities beyond necessity [William of Ockham]

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]

8. Modes of Existence / D. Universals / 5. Universals as Concepts

22132

Species and genera are individual concepts which naturally signify many individuals [William of Ockham]

27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time

19381

The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham]

28. God / A. Divine Nature / 6. Divine Morality / d. God decrees morality

8010	William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham]

29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels

16679

Even an angel must have some location [William of Ockham, by Pasnau]