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Single Idea 17197
[filed under theme 6. Mathematics / A. Nature of Mathematics / 2. Geometry
]
Full Idea
The idea of the triangle must involve the affirmation that its three angles are equal to two right angles. Therefore this affirmation pertains to the essence of the idea of a triangle.
Gist of Idea
The idea of a triangle involves truths about it, so those are part of its essence
Source
Baruch de Spinoza (The Ethics [1675], II Pr 49)
Book Ref
Spinoza,Benedict de: 'Ethics', ed/tr. White,WH/Stirling,AH [Wordsworth 2001], p.88
A Reaction
This seems to say that the essence is what is inescapable when you think of something. Does that mean that brandy is part of the essence of Napoleon? (Presumably not) Spinoza is ignoring the direction of explanation here.
The
31 ideas
with the same theme
[study of relationships of lines, points, and shapes]:
|
1553
|
No perceptible object is truly straight or curved
[Protagoras]
|
|
9867
|
It is absurd to define a circle, but not be able to recognise a real one
[Plato]
|
|
8726
|
Geometry can lead the mind upwards to truth and philosophy
[Plato]
|
|
9790
|
Geometry studies naturally occurring lines, but not as they occur in nature
[Aristotle]
|
|
12372
|
The essence of a triangle comes from the line, mentioned in any account of triangles
[Aristotle]
|
|
6297
|
Euclid's geometry is synthetic, but Descartes produced an analytic version of it
[Euclid, by Resnik]
|
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17197
|
The idea of a triangle involves truths about it, so those are part of its essence
[Spinoza]
|
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17222
|
The sum of its angles follows from a triangle's nature
[Spinoza]
|
|
18079
|
Newton developed a kinematic approach to geometry
[Newton, by Kitcher]
|
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13163
|
Circles must be bounded, so cannot be infinite
[Leibniz]
|
|
13008
|
Geometry, unlike sensation, lets us glimpse eternal truths and their necessity
[Leibniz]
|
|
8739
|
Geometry studies the Euclidean space that dictates how we perceive things
[Kant, by Shapiro]
|
|
8740
|
Geometry would just be an idle game without its connection to our intuition
[Kant]
|
|
16899
|
Geometrical truth comes from a general schema abstracted from a particular object
[Kant, by Burge]
|
|
16930
|
Geometry is not analytic, because a line's being 'straight' is a quality
[Kant]
|
|
16919
|
Geometry rests on our intuition of space
[Kant]
|
|
9618
|
Bolzano wanted to reduce all of geometry to arithmetic
[Bolzano, by Brown,JR]
|
|
10245
|
One geometry cannot be more true than another
[Poincaré]
|
|
13472
|
Hilbert aimed to eliminate number from geometry
[Hilbert, by Hart,WD]
|
|
14442
|
If straight lines were like ratios they might intersect at a 'gap', and have no point in common
[Russell]
|
|
14151
|
Pure geometry is deductive, and neutral over what exists
[Russell]
|
|
14153
|
In geometry, empiricists aimed at premisses consistent with experience
[Russell]
|
|
14152
|
In geometry, Kant and idealists aimed at the certainty of the premisses
[Russell]
|
|
14154
|
Geometry throws no light on the nature of actual space
[Russell]
|
|
14155
|
Two points have a line joining them (descriptive), a distance (metrical), and a whole line (projective)
[Russell, by PG]
|
|
16949
|
Klein summarised geometry as grouped together by transformations
[Quine]
|
|
8994
|
If analytic geometry identifies figures with arithmetical relations, logicism can include geometry
[Quine]
|
|
16901
|
The equivalent algebra model of geometry loses some essential spatial meaning
[Burge]
|
|
9159
|
You can't simply convert geometry into algebra, as some spatial content is lost
[Burge]
|
|
3332
|
Greeks saw the science of proportion as the link between geometry and arithmetic
[Benardete,JA]
|
|
21444
|
Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori)
[Gardner]
|