Combining Texts

All the ideas for 'The Roots of Reference', 'A world of truthmakers?' and 'The Theory of Transfinite Numbers'

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4 ideas

3. Truth / B. Truthmakers / 6. Making Negative Truths

15549	If it were true that nothing at all existed, would that have a truthmaker? [Lewis]
	Full Idea: If there was absolutely nothing at all, then it would have been true that there was nothing. Would there have been a truthmaker for this truth?
	From: David Lewis (A world of truthmakers? [1998], p.220)
	A reaction: This is a problem for Lewis's own claim that 'truth supervenes on being', as well as the more restricted truthmakers invoked by Armstrong.

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
	Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought.
	From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2
	A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896	Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
	Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
	From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
	A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.

8. Modes of Existence / C. Powers and Dispositions / 3. Powers as Derived

14296	Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine]
	Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition.
	From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3
	A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers?