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All the ideas for 'Frege's Theory of Numbers', 'The Human Animal' and 'works'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17447	Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
	Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
	From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
	A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18086	Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
	Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
	From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18092	Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
	Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
	From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
	A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.

16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body

16236	Maybe our persistence conditions concern bodies, rather than persons [Olson, by Hawley]
	Full Idea: Instead of attributing person-like persistence conditions to bodies, we could attribute body-like persistence conditions to persons, …so human persons are identical with human organisms.
	From: report of Eric T. Olson (The Human Animal [1997]) by Katherine Hawley - How Things Persist 5.10
	A reaction: In the case of pre-birth and advanced senility, Olson thinks we could have the body without the person, so person is a 'phase sortal' of bodies. A good theory, which seems to answer a lot of questions. 'Person' may be an abstraction.

6669	For 'animalism', I exist before I became a person, and can continue after it, so I am not a person [Olson, by Lowe]
	Full Idea: According to 'animalism', I existed before I was a person and I may well go one existing for some time after I cease to be a person; hence, I am not essentially a person, but a human organism.
	From: report of Eric T. Olson (The Human Animal [1997]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.10
	A reaction: There is a very real sense in which an extremely senile person has 'ceased to exist' (e.g. as the person I used to love). On the whole, though, I think that Olson is right, and yet 'person' is an important concept. Neither concept is all-or-nothing.