Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Review of Bob Hale's 'Abstract Objects'' and 'Letters to Pierre Bayle'

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4 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis

9184	We can't presume that all interesting concepts can be analysed [Williamson]
	Full Idea: We have no prior reason to suppose that philosophically significant concepts have interesting analyses into necessary and sufficient conditions.
	From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
	A reaction: We might think that they are either analysable or primitive, and that failure of analysis invites us to take a concept as primitive. But maybe God can analyse it and we can't.

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 / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

9183	Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
	Full Idea: The Fregean argument for platonism is that some true assertions contain singular terms which denote abstract objects if they denote anything; since the assertions are true, the singular terms denote.
	From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
	A reaction: I am perplexed that anyone would rest their view of reality on such an argument. The obvious comparison would be with true remarks about blatantly fictional characters, or blatantly invented concepts such as 'checkmate'.

16. Persons / F. Free Will / 5. Against Free Will

19413	If we know what is good or rational, our knowledge is extended, and our free will restricted [Leibniz]
	Full Idea: The more perfect one is, the more one is determined to the good, and so is more free at the same time. ...Our power and knowledge are more extended, and our will much the more limited within the bounds of perfect reason.
	From: Gottfried Leibniz (Letters to Pierre Bayle [1702], 1702)
	A reaction: I like this idea, which seems to me to derive from Aquinas. When I choose to eat and drink each day, or agree that 7+5 is 12, I don't complain about my lack of freedom in the choices. Goodness and reason are constraints I welcome.