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Single Idea 24030
[filed under theme 10. Modality / C. Sources of Modality / 4. Necessity from Concepts
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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.
The
19 ideas
from 'Rules for the Direction of the Mind'
24018
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One truth leads us to another
[Descartes]
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24019
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If we accept mere probabilities as true we undermine our existing knowledge
[Descartes]
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24020
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We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding
[Descartes]
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24022
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Our souls possess divine seeds of knowledge, which can bear spontaneous fruit
[Descartes]
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24021
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The method starts with clear intuitions, followed by a process of deduction
[Descartes]
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24023
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All the sciences searching for order and measure are related to mathematics
[Descartes]
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24024
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The secret of the method is to recognise which thing in a series is the simplest
[Descartes]
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24025
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Clear and distinct truths must be known all at once (unlike deductions)
[Descartes]
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24029
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Among the simples are the graspable negations, such as rest and instants
[Descartes]
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24030
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3+4=7 is necessary because we cannot conceive of seven without including three and four
[Descartes]
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24032
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Clever scholars can obscure things which are obvious even to peasants
[Descartes]
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24027
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Nerves and movement originate in the brain, where imagination moves them
[Descartes]
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24026
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Our four knowledge faculties are intelligence, imagination, the senses, and memory
[Descartes]
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24028
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The force by which we know things is spiritual, and quite distinct from the body
[Descartes]
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24031
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When Socrates doubts, he know he doubts, and that truth is possible
[Descartes]
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24033
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Most scholastic disputes concern words, where agreeing on meanings would settle them
[Descartes]
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24036
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I can only see the proportion of two to three if there is a common measure - their unity
[Descartes]
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24035
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Unity is something shared by many things, so in that respect they are equals
[Descartes]
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24034
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If someone had only seen the basic colours, they could deduce the others from resemblance
[Descartes]
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