Combining Texts

All the ideas for 'Commentary on the Metaphysics', 'On the Principles of Indiscernibles' and 'Remarks on axiomatised set theory'

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


9 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Understanding begins with the notion of being and essence [Avicenna]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
Axiomatising set theory makes it all relative [Skolem]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
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
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
Mathematician want performable operations, not propositions about objects [Skolem]
9. Objects / A. Existence of Objects / 5. Simples
The simple's whatness is its very self [Avicenna]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The ultimate material of things has the unity of total formlessness [Avicenna]
9. Objects / D. Essence of Objects / 2. Types of Essence
An essence can either be universal (in the mind) or singular (in concrete particulars) [Avicenna, by Panaccio]
28. God / B. Proving God / 2. Proofs of Reason / a. Ontological Proof
The concept of an existing thing must contain more than the concept of a non-existing thing [Leibniz]