Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Letters to Thomasius' and 'What is 'naturalized epistemology'?'

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4 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'.

9. Objects / D. Essence of Objects / 1. Essences of Objects

13432	The essence of a circle is the equality of its radii [Leibniz]
	Full Idea: The essence of a circle consists in the equality of all lines drawn from its centre to its circumference.
	From: Gottfried Leibniz (Letters to Thomasius [1669], 1669)
	A reaction: Compare Locke in Idea 13431 and Spinoza in Idea 13073 on the essence of geometrical figures. A key question is whether the essence is in the simplest definition, or in a complex and wide-ranging account, e.g. including conic sections for circles.

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique

8825	It seems impossible to logically deduce physical knowledge from indubitable sense data [Kim]
	Full Idea: It is agreed on all hands that the classical epistemological project, conceived as one of deductively validating physical knowledge from indubitable sensory data, cannot succeed.
	From: Jaegwon Kim (What is 'naturalized epistemology'? [1988], p.304)
	A reaction: This is the 'Enlightenment Project', which had a parallel in morality. Kim refers to the difficulty as 'The Humean Predicament'. Hume also hoped that induction might be deductive. One obvious move is to expand from 'deduction' to 'reason'.

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

12696	Bodies are recreated in motion, and don't exist in intervening instants [Leibniz]
	Full Idea: I have demonstrated that whatever moves is continuously created and that bodies are nothing at any time between the instants in motion.
	From: Gottfried Leibniz (Letters to Thomasius [1669], 1669.04), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1
	A reaction: Leibniz is a little over-confident about what he has 'demonstrated', but I think (from this remark) that he would not have been displeased with quantum theory, and the notion of a 'quantum leap' and a 'Planck time'. A 'conatus' is a 'smallest motion'.