Combining Texts

All the ideas for 'fragments/reports', 'Remarks on axiomatised set theory' and 'Logical Necessity: Some Issues'

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16 ideas

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]
10. Modality / A. Necessity / 6. Logical Necessity
Logical necessity overrules all other necessities [McFetridge]
The fundamental case of logical necessity is the valid conclusion of an inference [McFetridge, by Hale]
In the McFetridge view, logical necessity means a consequent must be true if the antecedent is [McFetridge, by Hale]
Logical necessity requires that a valid argument be necessary [McFetridge]
Traditionally, logical necessity is the strongest, and entails any other necessities [McFetridge]
It is only logical necessity if there is absolutely no sense in which it could be false [McFetridge]
The mark of logical necessity is deduction from any suppositions whatever [McFetridge]
10. Modality / B. Possibility / 2. Epistemic possibility
We assert epistemic possibility without commitment to logical possibility [McFetridge]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Objectual modal realists believe in possible worlds; non-objectual ones rest it on the actual world [McFetridge]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Modal realists hold that necessities and possibilities are part of the totality of facts [McFetridge]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]