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Single Idea 24030

[filed under theme 10. Modality / C. Sources of Modality / 4. Necessity from Concepts ]

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.

The 19 ideas from 'Rules for the Direction of the Mind'

24018 One truth leads us to another [Descartes]
24019 If we accept mere probabilities as true we undermine our existing knowledge [Descartes]
24020 We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes]
24022 Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes]
24021 The method starts with clear intuitions, followed by a process of deduction [Descartes]
24023 All the sciences searching for order and measure are related to mathematics [Descartes]
24024 The secret of the method is to recognise which thing in a series is the simplest [Descartes]
24025 Clear and distinct truths must be known all at once (unlike deductions) [Descartes]
24028 The force by which we know things is spiritual, and quite distinct from the body [Descartes]
24027 Nerves and movement originate in the brain, where imagination moves them [Descartes]
24026 Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes]
24031 When Socrates doubts, he know he doubts, and that truth is possible [Descartes]
24029 Among the simples are the graspable negations, such as rest and instants [Descartes]
24030 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes]
24032 Clever scholars can obscure things which are obvious even to peasants [Descartes]
24033 Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes]
24035 Unity is something shared by many things, so in that respect they are equals [Descartes]
24036 I can only see the proportion of two to three if there is a common measure - their unity [Descartes]
24034 If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes]