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] |
17197 | The idea of a triangle involves truths about it, so those are part of its essence [Spinoza] |
17222 | The sum of its angles follows from a triangle's nature [Spinoza] |
18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
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] |
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] |
14153 | In geometry, empiricists aimed at premisses consistent with experience [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] |