Combining Texts

All the ideas for 'Through the Looking Glass', 'The Theory of Transfinite Numbers' and 'Natural Kinds and Biological Realism'

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6 ideas

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.

7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing

21982	I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
	Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
	From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
	A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.

26. Natural Theory / B. Natural Kinds / 1. Natural Kinds

17371	Some kinds are very explanatory, but others less so, and some not at all [Devitt]
	Full Idea: Explanatory significance, hence naturalness, comes in degrees: positing some kinds may be very explanatory, positing others, only a little bit explanatory, positing others still, not explanatory at all.
	From: Michael Devitt (Natural Kinds and Biological Realism [2009], 4)
	A reaction: He mentions 'cousin' as a natural kind that is not very explanatory of anything. It interests us as humans, but not at all in other animals, it seems. ...Nice thought, though, that two squirrels might be cousins...

27. Natural Reality / G. Biology / 5. Species

17372	The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt]
	Full Idea: The signs are that the higher categories are not natural kinds and so the Linnaean hierarchy must be abandoned. ...This is not abandoning a hierarchy altogether, it is not abandoning a tree of life.
	From: Michael Devitt (Natural Kinds and Biological Realism [2009], 6)
	A reaction: Devitt's underlying point is that the higher and more general kinds do not have an essence (a specific nature), which is the qualification to be a natural kind. They explain nothing. Essence is the hallmark of natural kinds. Hmmm.

17373	Species pluralism says there are several good accounts of what a species is [Devitt]
	Full Idea: Species pluralism is the view that there are several equally good accounts of what it is to be a species.
	From: Michael Devitt (Natural Kinds and Biological Realism [2009], 7)
	A reaction: Devitt votes for it, and cites Dupré, among many other. Given the existence of rival accounts, all making good points, it is hard to resist this view.