14 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 |
| 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. |
| 14280 | The probability of two events is the first probability times the second probability assuming the first [Bayes] |
| Full Idea: The probability that two events will both happen is the probability of the first [multiplied by] the probability of the second on the supposition that the first happens. | |
| From: Thomas Bayes (Essay on a Problem in the Doctrine of Chances [1763]), quoted by Dorothy Edgington - Conditionals (Stanf) 3.1 |
| 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). |
| 19271 | No rule can be fully explained [Kripke] |
| Full Idea: Every explanation of a rule could conceivably be misunderstood. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 3) | |
| A reaction: This is Kripke's summary of what he takes to be Wittgenstein's scepticism about rules. |
| 19269 | 'Quus' means the same as 'plus' if the ingredients are less than 57; otherwise it just produces 5 [Kripke] |
| Full Idea: I will define 'quus' by x-quus-y = x + y, if x, y < 57, and otherwise it equals 5. Who is to say that this is not the function I previously meant by '+'? | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Kripke's famous example, to illustrate the big new scepticism introduced by Wittgenstein's questions about the rationality of following a rule. I suspect that you have to delve into psychology to understand rule-following, rather than logic. |
| 7305 | Kripke's Wittgenstein says meaning 'vanishes into thin air' [Kripke, by Miller,A] |
| Full Idea: Quine and Kripke's Wittgenstein attempt to argue that there are no facts about meaning, that the notion of meaning, as Kripke puts it, 'vanishes into thin air'. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Alexander Miller - Philosophy of Language Pref | |
| A reaction: A tempting solution to the problem. If, though, it is possible for someone to say something that is self-evidently meaningless, or to accuse someone of speaking (deep down) without meaning, then that needs explaining. |
| 19270 | If you ask what is in your mind for following the addition rule, meaning just seems to vanish [Kripke] |
| Full Idea: What can there be in my mind that I make use of when I follow a general rule to add in the future? It seems that the entire idea of meaning vanishes into thin air. | |
| From: Saul A. Kripke (Wittgenstein on Rules and Private Language [1982], 2) | |
| A reaction: Introspection probably isn't the best way to investigate the phenomenon of meaning. Indeed it seems rather old-fashioned and Cartesian. Kripke says, though, that seeking 'tacit' rules is even worse [end of note 22]. |
| 11076 | Community implies assertability-conditions rather than truth-conditions semantics [Kripke, by Hanna] |
| Full Idea: If we take account of the fact that a speaker is in a community, then we must adopt an assertability-conditions semantics (based on what is legitimately assertible), and reject truth-conditional semantics (based on correspondence to the facts). | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: [Part of Hanna's full summary of Kripke's argument] This sounds wrong to me. There are conditions where it is agreed that a lie should be told. Two people can be guilty of the same malapropism. |
| 11075 | The sceptical rule-following paradox is the basis of the private language argument [Kripke, by Hanna] |
| Full Idea: Kripke argues that the 'rule-following paradox' is essential to the more controversial private language argument, and introduces a radically new form of scepticism. | |
| From: report of Saul A. Kripke (Wittgenstein on Rules and Private Language [1982]) by Robert Hanna - Rationality and Logic 6.1 | |
| A reaction: It certainly seems that Kripke is right to emphasise the separateness of the two, as the paradox is quite persuasive, but the private language argument seems less so. |
| 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. |