Combining Texts

All the ideas for 'Explaining the A Priori', 'Rechnungsmethoden (dissertation)' and 'On 'Generation and Corruption''

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4 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

18256	Quantity is inconceivable without the idea of addition [Frege]
	Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.
	From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'
	A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

9831	Geometry appeals to intuition as the source of its axioms [Frege]
	Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.
	From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics
	A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.

8. Modes of Existence / B. Properties / 9. Qualities

16705	Whiteness isn't created in an alteration, because it is just this-being-white [Oresme]
	Full Idea: If it is said that whiteness begins to be through alteration, this does not hold, because whiteness is nothing other than this-being-white.
	From: Nicole Oresme (On 'Generation and Corruption' [1349], I.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.3
	A reaction: This innocent-looking remark is dynamite, because it rejects the separability of qualities, which threatens the doctrine of Transubstantiation.

18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts

17722	The concept 'red' is tied to what actually individuates red things [Peacocke]
	Full Idea: The possession conditions for the concept 'red' of the colour red are tied to those very conditions which individuate the colour red.
	From: Christopher Peacocke (Explaining the A Priori [2000], p.267), quoted by Carrie Jenkins - Grounding Concepts 2.5
	A reaction: Jenkins reports that he therefore argues that we can learn something about the word 'red' from thinking about the concept 'red', which is his new theory of the a priori. I find 'possession conditions' and 'individuation' to be very woolly concepts.