Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Second Commentary on 'Isagoge'' and 'Remarks on axiomatised set theory'

expand these ideas     |    start again     |     specify just one area for these texts

---

8 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17879

Axiomatising set theory makes it all relative [Skolem]

5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems

17878

If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem]

6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics

17880

Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem]

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

17881

Mathematician want performable operations, not propositions about objects [Skolem]

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 / D. Universals / 5. Universals as Concepts

15035

If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio]

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

19402

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