Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'The Foundations of Mathematics (2nd ed)' and 'Logicism, Some Considerations (PhD)'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

13412

Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]

13413

We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

13411

If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism

13415

An adequate account of a number must relate it to its series [Benacerraf]

7. Existence / A. Nature of Existence / 5. Reason for Existence

19400

Possibles demand existence, so as many of them as possible must actually exist [Leibniz]

19401

God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]

8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation

18465

An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]

10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds

19402

The actual universe is the richest composite of what is possible [Leibniz]