10 ideas
| 13445 | Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD] |
| Full Idea: Descartes founded analytic geometry on the assumption that there is a one-one order-preserving correspondence between the points on a line and the real numbers. | |
| From: report of René Descartes (works [1643]) by William D. Hart - The Evolution of Logic 1 |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 16774 | Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau] |
| Full Idea: Descartes thinks it is a pointless relic of scholastic metaphysics to dispute over the boundaries between substances and mere aggregates. | |
| From: report of René Descartes (works [1643]) by Robert Pasnau - Metaphysical Themes 1274-1671 25.6 | |
| A reaction: This is Pasnau's carefully considered conclusion, with which others may not agree. It presumably captures the attitude of modern science generally to such issues. |
| 7400 | Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck] |
| Full Idea: Descartes argued (in 'The World') that just as words refer to objects, but they do not resemble them, in the same way, visual images or other sensory inputs relate to objects without depicting them. | |
| From: report of René Descartes (works [1643]) by Richard Tuck - Hobbes | |
| A reaction: This strikes me as a rather significant and plausible claim, which might contain the germ of the idea of a language of thought. It is also the basis for the recent view that language is the best route to understanding the mind. |
| 4310 | We have inner awareness of our freedom [Descartes] |
| Full Idea: We have inner awareness of our freedom. | |
| From: René Descartes (works [1643]) | |
| A reaction: This begs a few questions. I may be directly aware that I have not been hypnotised, but no one would accept it as proof. |
| 6553 | Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan] |
| Full Idea: Descartes himself was well aware of the interaction problem, and corresponded uncomfortably with Princess Elizabeth on the matter; …he pointed out that gravity is causal despite not being a physical object. | |
| From: report of René Descartes (works [1643]) by William Lycan - Consciousness n1.3 | |
| A reaction: Lycan observes that at least gravity is in space-time, unlike the Cartesian mind. Pierre Gassendi had pointed out the problem to Descartes in the Fifth Objection to the 'Meditations' (see Idea 3400). |
| 22442 | If lies were ever acceptable, with would undermine all duties based on contract [Kant] |
| Full Idea: Truthfulness is a duty that must be regarded as the basis of all duties to be grounded on a contract, the law of which is made uncertain and useless if even the least exception to it is admitted. | |
| From: Immanuel Kant (On a supposed right to lie [1797], p.30) | |
| A reaction: Should we keep contracts which are made by means of deception and coercion? Where could such absolute authority for contracts come from? Do contracts and treaties tend to lapse after a long period of time? |
| 22441 | The law will protect you if you tell a truth which results in murder [Kant] |
| Full Idea: If you have by a lie prevented someone bent on murder from committing the deed, then you are legally accountable for all the consequences that might arise from it. But if you keep strictly to the truth, then public justice can hold nothing against you. | |
| From: Immanuel Kant (On a supposed right to lie [1797], p.29) | |
| A reaction: Shocking, from a supposedly great thinker. Cowardly hiding behind a perverse law. What would Kant do if the law were changed, to condemn someone who told a truth which would probably lead to a murder? Would he accept a jail sentence? |
| 19676 | Nature is devoid of thought [Descartes, by Meillassoux] |
| Full Idea: It is Descartes who ratifies the idea that nature is devoid of thought. | |
| From: report of René Descartes (works [1643]) by Quentin Meillassoux - After Finitude; the necessity of contingency 5 | |
| A reaction: His dualism is crucial, along with his ontological argument, because they make all mentality supernatural. Remember, for Descartes animals are mindless machines. |
| 6518 | Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes] |
| Full Idea: Notoriously, the Cartesian idea that matter is purely geometrical will not do, for it leaves no distinction between matter and empty volumes: a filler for these volumes is required. | |
| From: comment on René Descartes (works [1643]) by Howard Robinson - Perception IX.3 | |
| A reaction: Descartes thinks of matter as 'extension'. Descartes's error seems so obvious that it is a puzzle why he made it. He may have confused epistemology and ontology - all we can know of matter is its extension in space. |