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2 ideas
24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
Full Idea: When I say that four and three make seven, this connection is necessary, because one cannot conceive the number seven distinctly without including in it in a confused way the number four and the number three. | |
From: René Descartes (Rules for the Direction of the Mind [1628], 12) | |
A reaction: This seems to make the truths of arithmetic conceptual, and hence analytic. |
22018 | Necessary truths derive from basic assertion and negation [Fichte, by Pinkard] |
Full Idea: Fichte thought that everything that involves necessary truths - even mathematics and logic - should be shown to follow from the more basic principles involved in assertion and negation. | |
From: report of Johann Fichte (The Science of Knowing (Wissenschaftslehre) [1st ed] [1794]) by Terry Pinkard - German Philosophy 1760-1860 05 | |
A reaction: An interesting proposal, though I am struggling to see how it works. Fichte sees assertion and negation as foundational (Idea 22017), but I take them to be responses to the real world. |