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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.
Gist of Idea
3+4=7 is necessary because we cannot conceive of seven without including three and four
Source
René Descartes (Rules for the Direction of the Mind [1628], 12)
Book Ref
Descartes,René: 'Rules for the Direction of the Mind' [Newcomb Library 2023], p.39
A Reaction
This seems to make the truths of arithmetic conceptual, and hence analytic.
| 24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
| 18796 | Formal experience conditions show what is possible, and general conditions what is necessary [Kant] |
| 22018 | Necessary truths derive from basic assertion and negation [Fichte, by Pinkard] |
| 15216 | Is conceptual necessity just conventional, or does it mirror something about nature? [Harré/Madden] |
| 15235 | There is a conceptual necessity when properties become a standard part of a nominal essence [Harré/Madden] |
| 16422 | The necessity of a proposition concerns reality, not our words or concepts [Stalnaker] |
| 16423 | Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker] |
| 13810 | The source of de dicto necessity is not concepts, but the actual properties of the thing [Forbes,G] |
| 12028 | De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G] |
| 11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
| 15087 | Conceptual necessities are made true by all concepts [Hale] |
| 12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
| 15033 | Humeans says mathematics and logic are necessary because that is how our concept of necessity works [Sider] |