Combining Texts

All the ideas for 'Quaestiones de Potentia Dei', 'An Axiomatization of Set Theory' and 'Disputed questions about truth'

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5 ideas

3. Truth / C. Correspondence Truth / 1. Correspondence Truth

22104	Truth is the conformity of being to intellect [Aquinas]
	Full Idea: The word 'true' expresses the conformity of a being to intellect.
	From: Thomas Aquinas (Disputed questions about truth [1267], I.1c), quoted by Kretzmann/Stump - Aquinas, Thomas 09
	A reaction: I believe in a 'robust' theory of truth, but accept that the concept of 'correspondence' has major problems. So I embrace with delight the word 'conformity'. I offer the world The Conformity Theory of Truth! 'Conform' is suitably vague.

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size

15943	Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
	Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong.
	From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

13672	All the axioms for mathematics presuppose set theory [Neumann]
	Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.
	From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2
	A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this.

7. Existence / A. Nature of Existence / 3. Being / f. Primary being

22103	Being is basic to thought, and all other concepts are additions to being [Aquinas]
	Full Idea: Being is inherently intellect's most intelligible object, in which it finds the basis of all conceptions. ...All of intellect's other conceptions must be arrived at by adding to being, insofar as they express what is not expressed by 'being' itself.
	From: Thomas Aquinas (Disputed questions about truth [1267], I.1c), quoted by Kretzmann/Stump - Aquinas, Thomas 09
	A reaction: I like the word 'intelligible' here. We might know reality, or be aware of appearances, but what is intelligible lies nicely in between. What would Berkeley make of that? I presume 'intelligible' means 'makes good sense'.

9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates

17555	'One' can mean undivided and not a multitude, or it can add measurement, giving number [Aquinas]
	Full Idea: There are two sorts of one. There is the one which is convertible with being, which adds nothing to being except being undivided; and this deprives of multitude. Then there is the principle of number, which to the notion of being adds measurement.
	From: Thomas Aquinas (Quaestiones de Potentia Dei [1269], q3 a16 ad 3-um)
	A reaction: [From a lecture handout] I'm not sure I understand this. We might say, I suppose, that insofar as water is water, it is all one, but you can't count it. Perhaps being 'unified' and being a 'unity' are different?