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Single Idea 24036
[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
]
Full Idea
I do not recognise what the proportion of magnitude is between two and three, unless I consider a third term, namely unity, which is the common measure of the one and the other.
Gist of Idea
I can only see the proportion of two to three if there is a common measure - their unity
Source
René Descartes (Rules for the Direction of the Mind [1628], 14)
Book Ref
Descartes,René: 'Rules for the Direction of the Mind' [Newcomb Library 2023], p.56
A Reaction
A striking defence of the concept of the need for the unit in arithmetic. To say 'three is half as big again', you must be discussing the same size of 'half' in each instance.
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]
|
24032
|
Clever scholars can obscure things which are obvious even to peasants
[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]
|
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]
|