183 ideas
| 7504 | Modern science comes from Descartes' view that knowledge doesn't need moral purity [Descartes, by Foucault] |
| Full Idea: Before Descartes, one could not be impure, immoral, and know the truth. After Descartes, direct evidence is enough, and we have a nonascetic subject of knowledge; this change makes possible the institutionalisation of modern science. | |
| From: report of René Descartes (Meditations [1641]) by Michel Foucault - On the Genealogy of Ethics | |
| A reaction: I would have thought Gassendi and the British Empiricists would be a more plausible source for this shift of attitude. Plato would relegate modern science to a lower level of knowledge. |
| 1569 | Descartes impoverished the classical idea of logos, and it no longer covered human experience [Roochnik on Descartes] |
| Full Idea: Descartes attacked and fundamentally altered classical logos. The result is an impoverished conception of reason, one that is unable to do justice to the significance and value of human experience. | |
| From: comment on René Descartes (Meditations [1641]) by David Roochnik - The Tragedy of Reason Prol. Xii |
| 2248 | Reason says don't assent to uncertain principles, just as much as totally false ones [Descartes] |
| Full Idea: Reason now persuades me that I should withhold my assent no less carefully from opinions that are not completely certain and indubitable than I would from those that are patently false. | |
| From: René Descartes (Meditations [1641], §1.18) |
| 2857 | Since Plato all philosophers have followed the herd, except Descartes, stuck in superficial reason [Nietzsche on Descartes] |
| Full Idea: Since Plato all philosophers have followed moral 'instinct', or 'faith', or (as I call it) 'the herd'. One might exclude Descartes, the father of rationalism, who recognised only reason - but reason is only an instrument, and Descartes was superficial. | |
| From: comment on René Descartes (Meditations [1641]) by Friedrich Nietzsche - Beyond Good and Evil §191 |
| 3641 | It is circular to make truth depend on believing God's existence is true [Arnauld on Descartes] |
| Full Idea: How does the author avoid reasoning in a circle when he says that we are sure that what we clearly and distinctly perceive is true only because God exists? But we can be sure that God exists only because we clearly and distinctly perceive this. | |
| From: comment on René Descartes (Meditations [1641], §5.71) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 214 |
| 4524 | Descartes is right that in the Christian view only God can guarantee the reliability of senses [Nietzsche on Descartes] |
| Full Idea: Even Descartes had a notion that in a Christian mode of thought (where God is a good creator), only God's veracity guarantees to us the judgements of our senses. | |
| From: comment on René Descartes (Meditations [1641], §5.71) by Friedrich Nietzsche - The Will to Power (notebooks) §436 | |
| A reaction: An unusual defence of the notorious Cartesian Circle. Of course, Descartes claims that God guarantees reason (as 'clear and distinct conception'), not senses, and only reason led Descartes to God. |
| 2290 | Once it is clear that there is a God who is no deceiver, I conclude that clear and distinct perceptions must be true [Descartes] |
| Full Idea: Once I perceived that there is a God,…and that he is no deceiver, I then concluded that everything that I clearly and distinctly perceived is necessarily true. | |
| From: René Descartes (Meditations [1641], §5.70) | |
| A reaction: spotted by Arnauld |
| 2266 | My general rule is that everything that I perceive clearly and distinctly is true [Descartes] |
| Full Idea: I now seem able to posit as a general rule that everything I very clearly and distinctly perceive is true. | |
| From: René Descartes (Meditations [1641], §3.35) |
| 4301 | Someone may think a thing is 'clear and distinct', but be wrong [Leibniz on Descartes] |
| Full Idea: Leibniz objected to Descartes' theory of truth, saying that people may think something is clear and distinct, and yet be wrong. | |
| From: comment on René Descartes (Meditations [1641], §3.36) by Gottfried Leibniz - works | |
| A reaction: Quite so. Descartes has misunderstood what sort of concept 'truth' is meant to be. It's the usual confusion of epistemology and metaphysics. Truth is not a feature of the human mind. |
| 15901 | Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine] |
| Full Idea: The notion of a function evolved gradually from wanting to see what curves can be represented as trigonometric series. The study of arbitrary functions led Cantor to the ordinal numbers, which led to set theory. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 13444 | Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD] |
| Full Idea: Cantor's Theorem says that for any set x, its power set P(x) has more members than x. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 |
| 18098 | Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock] |
| Full Idea: Cantor's diagonalisation argument generalises to show that any set has more subsets than it has members. | |
| From: report of George Cantor (works [1880]) by David Bostock - Philosophy of Mathematics 4.5 | |
| A reaction: Thus three members will generate seven subsets. This means that 'there is no end to the series of cardinal numbers' (Bostock p.106). |
| 15505 | If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis] |
| Full Idea: Cantor taught that a set is 'a many, which can be thought of as one'. ...After a time the unfortunate beginner student is told that some classes - the singletons - have only a single member. Here is a just cause for student protest, if ever there was one. | |
| From: report of George Cantor (works [1880]) by David Lewis - Parts of Classes 2.1 | |
| A reaction: There is a parallel question, almost lost in the mists of time, of whether 'one' is a number. 'Zero' is obviously dubious, but if numbers are for counting, that needs units, so the unit is the precondition of counting, not part of it. |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| Full Idea: Cantor's theories exhibited the contradictions others had claimed to derive from the supposition of infinite sets as confusions resulting from the failure to mark the necessary distinctions with sufficient clarity. | |
| From: report of George Cantor (works [1880]) by Michael Potter - Set Theory and Its Philosophy Intro 1 |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| Full Idea: Cantor discovered that the continuum is the powerset of the integers. While adding or multiplying infinities didn't move up a level of complexity, multiplying a number by itself an infinite number of times did. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 13016 | The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy] |
| Full Idea: Cantor first stated the Union Axiom in a letter to Dedekind in 1899. It is nearly too obvious to deserve comment from most commentators. Justifications usually rest on 'limitation of size' or on the 'iterative conception'. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Believing the Axioms I §1.3 | |
| A reaction: Surely someone can think of some way to challenge it! An opportunity to become notorious, and get invited to conferences. |
| 14199 | Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley] |
| Full Idea: Cantor's definition of a set was a collection of its members into a whole, but within a few years Dedekind had the idea of a set as a container, enclosing its members like a sack. | |
| From: report of George Cantor (works [1880]) by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
| A reaction: As the article goes on to show, these two view don't seem significantly different until you start to ask about the status of the null set and of singletons. I intuitively vote for Dedekind. Set theory is the study of brackets. |
| 10054 | Arithmetic and geometry achieve some certainty without worrying about existence [Descartes] |
| Full Idea: Arithmetic, geometry and sciences of that kind only treat of things without taking any great trouble to ascertain whether they are actually existent or not, and contain some measure of certainty. | |
| From: René Descartes (Meditations [1641], §1), quoted by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: This is Musgrave's earliest quotation which seems to take the if-thenist view. |
| 10082 | There are infinite sets that are not enumerable [Cantor, by Smith,P] |
| Full Idea: Cantor's Theorem (1874) says there are infinite sets that are not enumerable. This is proved by his 1891 'diagonal argument'. | |
| From: report of George Cantor (works [1880]) by Peter Smith - Intro to Gödel's Theorems 2.3 | |
| A reaction: [Smith summarises the diagonal argument] |
| 13483 | Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD] |
| Full Idea: The problem of Cantor's Paradox is that the power set of the universe has to be both bigger than the universe (by Cantor's theorem) and not bigger (since it is a subset of the universe). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 3 | |
| A reaction: Russell eliminates the 'universe' in his theory of types. I don't see why you can't just say that the members of the set are hypothetical rather than real, and that hypothetically the universe might contain more things than it does. |
| 8710 | The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend] |
| Full Idea: Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself. | |
| From: report of George Cantor (works [1880]) by Michčle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly? |
| 2252 | Surely maths is true even if I am dreaming? [Descartes] |
| Full Idea: Surely whether I am asleep or awake, two plus three makes five, and a square does not have more than four sides. | |
| From: René Descartes (Meditations [1641], §1.20) |
| 2430 | I can learn the concepts of duration and number just from observing my own thoughts [Descartes] |
| Full Idea: When I think that I exist now, and recollect that I existed in the past, and when I conceive various thoughts, the number of which I know, then I acquire the ideas of duration and number which I can thereafter transfer to all the other objects I wish. | |
| From: René Descartes (Meditations [1641], §3.44) |
| 15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Cantor, by Lavine] |
| Full Idea: Cantor believed he had discovered that between the finite and the 'Absolute', which is 'incomprehensible to the human understanding', there is a third category, which he called 'the transfinite'. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 15905 | Cantor proved the points on a plane are in one-to-one correspondence to the points on a line [Cantor, by Lavine] |
| Full Idea: In 1878 Cantor published the unexpected result that one can put the points on a plane, or indeed any n-dimensional space, into one-to-one correspondence with the points on a line. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 9983 | Cantor took the ordinal numbers to be primary [Cantor, by Tait] |
| Full Idea: Cantor took the ordinal numbers to be primary: in his generalization of the cardinals and ordinals into the transfinite, it is the ordinals that he calls 'numbers'. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind VI | |
| A reaction: [Tait says Dedekind also favours the ordinals] It is unclear how the matter might be settled. Humans cannot give the cardinality of large groups without counting up through the ordinals. A cardinal gets its meaning from its place in the ordinals? |
| 17798 | Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry] |
| Full Idea: Cantor taught us to regard the totality of natural numbers, which was formerly thought to be infinite, as really finite after all. | |
| From: report of George Cantor (works [1880]) by John Mayberry - What Required for Foundation for Maths? p.414-2 | |
| A reaction: I presume this is because they are (by definition) countable. |
| 9971 | Cantor introduced the distinction between cardinals and ordinals [Cantor, by Tait] |
| Full Idea: Cantor introduced the distinction between cardinal and ordinal numbers. | |
| From: report of George Cantor (works [1880]) by William W. Tait - Frege versus Cantor and Dedekind Intro | |
| A reaction: This seems remarkably late for what looks like a very significant clarification. The two concepts coincide in finite cases, but come apart in infinite cases (Tait p.58). |
| 9892 | Cantor showed that ordinals are more basic than cardinals [Cantor, by Dummett] |
| Full Idea: Cantor's work revealed that the notion of an ordinal number is more fundamental than that of a cardinal number. | |
| From: report of George Cantor (works [1880]) by Michael Dummett - Frege philosophy of mathematics Ch.23 | |
| A reaction: Dummett makes it sound like a proof, which I find hard to believe. Is the notion that I have 'more' sheep than you logically prior to how many sheep we have? If I have one more, that implies the next number, whatever that number may be. Hm. |
| 14136 | A cardinal is an abstraction, from the nature of a set's elements, and from their order [Cantor] |
| Full Idea: The cardinal number of M is the general idea which, by means of our active faculty of thought, is deduced from the collection M, by abstracting from the nature of its diverse elements and from the order in which they are given. | |
| From: George Cantor (works [1880]), quoted by Bertrand Russell - The Principles of Mathematics §284 | |
| A reaction: [Russell cites 'Math. Annalen, XLVI, §1'] See Fine 1998 on this. |
| 15906 | Cantor tried to prove points on a line matched naturals or reals - but nothing in between [Cantor, by Lavine] |
| Full Idea: Cantor said he could show that every infinite set of points on the line could be placed into one-to-one correspondence with either the natural numbers or the real numbers - with no intermediate possibilies (the Continuum hypothesis). His proof failed. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.1 |
| 11015 | Cantor's diagonal argument proved you can't list all decimal numbers between 0 and 1 [Cantor, by Read] |
| Full Idea: Cantor's diagonal argument showed that all the infinite decimals between 0 and 1 cannot be written down even in a single never-ending list. | |
| From: report of George Cantor (works [1880]) by Stephen Read - Thinking About Logic Ch.6 |
| 15903 | A real is associated with an infinite set of infinite Cauchy sequences of rationals [Cantor, by Lavine] |
| Full Idea: Cantor's theory of Cauchy sequences defines a real number to be associated with an infinite set of infinite sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II.6 | |
| A reaction: This sounds remarkably like the endless decimals we use when we try to write down an actual real number. |
| 18251 | Irrational numbers are the limits of Cauchy sequences of rational numbers [Cantor, by Lavine] |
| Full Idea: Cantor introduced irrationals to play the role of limits of Cauchy sequences of rational numbers. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite 4.2 |
| 15902 | Irrationals and the Dedekind Cut implied infinite classes, but they seemed to have logical difficulties [Cantor, by Lavine] |
| Full Idea: From the very nature of an irrational number, it seems necessary to understand the mathematical infinite thoroughly before an adequate theory of irrationals is possible. Infinite classes are obvious in the Dedekind Cut, but have logical difficulties | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite II Intro | |
| A reaction: Almost the whole theory of analysis (calculus) rested on the irrationals, so a theory of the infinite was suddenly (in the 1870s) vital for mathematics. Cantor wasn't just being eccentric or mystical. |
| 15908 | It was Cantor's diagonal argument which revealed infinities greater than that of the real numbers [Cantor, by Lavine] |
| Full Idea: Cantor's 1891 diagonal argument revealed there are infinitely many infinite powers. Indeed, it showed more: it shows that given any set there is another of greater power. Hence there is an infinite power strictly greater than that of the set of the reals. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite III.2 |
| 13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Cantor, by Hart,WD] |
| Full Idea: What we might call 'Cantor's Thesis' is that there won't be a potential infinity of any sort unless there is an actual infinity of some sort. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: This idea is nicely calculated to stop Aristotle in his tracks. |
| 10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
| Full Idea: Cantor showed that the complete totality of natural numbers cannot be mapped 1-1 onto the complete totality of the real numbers - so there are different sizes of infinity. | |
| From: report of George Cantor (works [1880]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.4 |
| 8733 | The Continuum Hypothesis says there are no sets between the natural numbers and reals [Cantor, by Shapiro] |
| Full Idea: Cantor's 'continuum hypothesis' is the assertion that there are no infinite cardinalities strictly between the size of the natural numbers and the size of the real numbers. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Thinking About Mathematics 2.4 | |
| A reaction: The tricky question is whether this hypothesis can be proved. |
| 17889 | CH: An infinite set of reals corresponds 1-1 either to the naturals or to the reals [Cantor, by Koellner] |
| Full Idea: Cantor's Continuum Hypothesis (CH) says that for every infinite set X of reals there is either a one-to-one correspondence between X and the natural numbers, or between X and the real numbers. | |
| From: report of George Cantor (works [1880]) by Peter Koellner - On the Question of Absolute Undecidability 1.2 | |
| A reaction: Every single writer I read defines this differently, which drives me crazy, but is also helpfully illuminating. There is a moral there somewhere. |
| 13447 | Cantor: there is no size between naturals and reals, or between a set and its power set [Cantor, by Hart,WD] |
| Full Idea: Cantor conjectured that there is no size between those of the naturals and the reals - called the 'continuum hypothesis'. The generalized version says that for no infinite set A is there a set larger than A but smaller than P(A). | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: Thus there are gaps between infinite numbers, and the power set is the next size up from any infinity. Much discussion as ensued about whether these two can be proved. |
| 10883 | Cantor's Continuum Hypothesis says there is a gap between the natural and the real numbers [Cantor, by Horsten] |
| Full Idea: Cantor's Continuum Hypothesis states that there are no sets which are too large for there to be a one-to-one correspondence between the set and the natural numbers, but too small for there to exist a one-to-one correspondence with the real numbers. | |
| From: report of George Cantor (works [1880]) by Leon Horsten - Philosophy of Mathematics §5.1 |
| 13528 | Continuum Hypothesis: there are no sets between N and P(N) [Cantor, by Wolf,RS] |
| Full Idea: Cantor's conjecture (the Continuum Hypothesis) is that there are no sets between N and P(N). The 'generalized' version replaces N with an arbitrary infinite set. | |
| From: report of George Cantor (works [1880]) by Robert S. Wolf - A Tour through Mathematical Logic 2.2 | |
| A reaction: The initial impression is that there is a single gap in the numbers, like a hole in ozone layer, but the generalised version implies an infinity of gaps. How can there be gaps in the numbers? Weird. |
| 9555 | Continuum Hypothesis: no cardinal greater than aleph-null but less than cardinality of the continuum [Cantor, by Chihara] |
| Full Idea: Cantor's Continuum Hypothesis was that there is no cardinal number greater than aleph-null but less than the cardinality of the continuum. | |
| From: report of George Cantor (works [1880]) by Charles Chihara - A Structural Account of Mathematics 05.1 | |
| A reaction: I have no view on this (have you?), but the proposal that there are gaps in the number sequences has to excite all philosophers. |
| 18174 | Cantor extended ordinals into the transfinite, and they can thus measure infinite cardinalities [Cantor, by Maddy] |
| Full Idea: Cantor's second innovation was to extend the sequence of ordinal numbers into the transfinite, forming a handy scale for measuring infinite cardinalities. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Struggling with this. The ordinals seem to locate the cardinals, but in what sense do they 'measure' them? |
| 15893 | Cantor's theory concerns collections which can be counted, using the ordinals [Cantor, by Lavine] |
| Full Idea: Cantor's set theory was not of collections in some familiar sense, but of collections that can be counted using the indexes - the finite and transfinite ordinal numbers. ..He treated infinite collections as if they were finite. | |
| From: report of George Cantor (works [1880]) by Shaughan Lavine - Understanding the Infinite I |
| 18173 | Cardinality strictly concerns one-one correspondence, to test infinite sameness of size [Cantor, by Maddy] |
| Full Idea: Cantor's first innovation was to treat cardinality as strictly a matter of one-to-one correspondence, so that the question of whether two infinite sets are or aren't of the same size suddenly makes sense. | |
| From: report of George Cantor (works [1880]) by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: It makes sense, except that all sets which are infinite but countable can be put into one-to-one correspondence with one another. What's that all about, then? |
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| Full Idea: Cantor's theorem entails that there are more property extensions than objects. So there are not enough objects in any domain to serve as extensions for that domain. So Frege's view that numbers are objects led to the Caesar problem. | |
| From: report of George Cantor (works [1880]) by Stewart Shapiro - Philosophy of Mathematics 4.6 | |
| A reaction: So the possibility that Caesar might have to be a number arises because otherwise we are threatening to run out of numbers? Is that really the problem? |
| 18176 | Pure mathematics is pure set theory [Cantor] |
| Full Idea: Pure mathematics ...according to my conception is nothing other than pure set theory. | |
| From: George Cantor (works [1880], I.1), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: [an unpublished paper of 1884] So right at the beginning of set theory this claim was being made, before it was axiomatised, and so on. Zermelo endorsed the view, and it flourished unchallenged until Benacerraf (1965). |
| 8631 | Cantor says that maths originates only by abstraction from objects [Cantor, by Frege] |
| Full Idea: Cantor calls mathematics an empirical science in so far as it begins with consideration of things in the external world; on his view, number originates only by abstraction from objects. | |
| From: report of George Cantor (works [1880]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §21 | |
| A reaction: Frege utterly opposed this view, and he seems to have won the day, but I am rather thrilled to find the great Cantor endorsing my own intuitions on the subject. The difficulty is to explain 'abstraction'. |
| 19482 | Current physics says matter and antimatter should have reduced to light at the big bang [New Sci.] |
| Full Idea: Our best theories of physics imply we shouldn't be here. The big bang ought to have produced equal amounts of matter and antimatter particles, which would have almost immediately annihilated each other, leaving nothing but light. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.05.23) | |
| A reaction: This is not, of course, a rejection of physics, but a puzzle about the current standard model of physics. |
| 19483 | CP violation shows a decay imbalance in matter and antimatter, leading to matter's dominance [New Sci.] |
| Full Idea: The phenomenon of charge-parity (CP) violation says that under certain circumstances antiparticles decay at different rates from their matter counterpart. ...This might explain matter's dominance in the universe, but the effect is too small. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.05.23) | |
| A reaction: Physicists are currently studying CP violations, hoping to explain why there is any matter in the universe. This will not, I presume, explain why matter and antimatter arrived in the first place. |
| 2297 | If I can separate two things in my understanding, then God can separate them in reality [Descartes] |
| Full Idea: My ability clearly and distinctly to understand one thing without another suffices to make me certain that the one thing is different from the other, since they can be separated from each other (at least by God). | |
| From: René Descartes (Meditations [1641], §6.78) |
| 3628 | Substance cannot be conceived or explained to others [Gassendi on Descartes] |
| Full Idea: The alleged naked, or rather hidden, substance of wax is something that we can neither ourselves conceive nor explain to others. | |
| From: comment on René Descartes (Meditations [1641], §2.31) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 273 |
| 16631 | If we remove surface qualities from wax, we have an extended, flexible, changeable thing [Descartes] |
| Full Idea: After taking away what does not belong to the wax, let us see what is left: surely, it is nothing other than a thing that is extended, flexible and changeable. | |
| From: René Descartes (Meditations [1641], (VII:30-1)), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 08.2 | |
| A reaction: Aristotle worried about nothing being left when you 'stripped' an object, so this could be seen as a positive contribution to scholastic philosophy. Why is the substrate 'flexible'? He talks elsewhere of taking the clothes off the wax and seeing it naked. |
| 17865 | Descartes gives an essence by an encapsulating formula [Descartes, by Almog] |
| Full Idea: For Descartes in providing an essence for an item [such as God, wax, or a mathematical kind] we provide an encapsulating formula defining the phenomenon. | |
| From: report of René Descartes (Meditations [1641]) by Joseph Almog - Nature Without Essence I | |
| A reaction: I argue that this is not what Aristotle intended be an essentialist definition, which can be quite long, like a scientific monograph. Descartes firmly rejected Aristotle's 'substantial form' as essence. |
| 2301 | We know by thought that what is done cannot be undone [Descartes] |
| Full Idea: Some ideas belong exclusively to the mind, such as perceiving that what has been done cannot be undone, and everything else that is known by the light of nature. | |
| From: René Descartes (Meditations [1641], §6.82) |
| 3642 | Pythagoras' Theorem doesn't cease to be part of the essence of triangles just because we doubt it [Arnauld on Descartes] |
| Full Idea: You can't reason 'I know the triangle is right-angled, but I doubt Pythagoras' Theorem, therefore it does not belong to the essence of right-angled triangles that the square on the hypotenuse is equal to the sum of the squares on the other two sides'. | |
| From: comment on René Descartes (Meditations [1641], §6.78) by Antoine Arnauld - Objections to 'Meditations' (Fourth) 202 |
| 20190 | Belief is not an intellectual state or act, because propositions are affirmed or denied by the will [Descartes, by Zagzebski] |
| Full Idea: Descartes claimed that belief is not purely an intellectual state or act, since it is not the intellect that affirms or denies a proposition proposed for its consideration, but the will. | |
| From: report of René Descartes (Meditations [1641], IV) by Linda Trinkaus Zagzebski - Virtues of the Mind 4.2 | |
| A reaction: This is the canonical idea of 'doxastic voluntarism' - that we choose what to believe or not believe. In modern times this view has become deeply unfashionable. I don't we should wholly reject the possibility of choosing to believe something. |
| 1585 | Descartes tried to model reason on maths instead of 'logos' [Roochnik on Descartes] |
| Full Idea: Descartes rejects logos because it does not achieve the certainty he craves. He replaces it with his own model of rationality, one modelled essentially on mathematics. | |
| From: comment on René Descartes (Meditations [1641], §1) by David Roochnik - The Tragedy of Reason p.76 |
| 1582 | Labelling slightly doubtful things as false is irrational [Roochnik on Descartes] |
| Full Idea: To declare that which is the least bit dubious as absolutely false is to declare war on logos. | |
| From: comment on René Descartes (Meditations [1641], §1.17) by David Roochnik - The Tragedy of Reason p.72 |
| 2256 | Maybe there is only one certain fact, which is that nothing is certain [Descartes] |
| Full Idea: If I suppose that everything I see is false. Nothing I remember actually existed. I have no senses, and body, shape, extension, movement and place are all chimeras. What then is true? Perhaps just the single fact that nothing is certain. | |
| From: René Descartes (Meditations [1641], §2.24) |
| 6914 | Descartes transformed 'God is thinkable, so he exists' into 'I think, so I exist' [Descartes, by Feuerbach] |
| Full Idea: Descartes transformed the proposition 'because God is thinkable, therefore he exists' into the proposition 'I think, therefore I am'. | |
| From: report of René Descartes (Meditations [1641], 2) by Ludwig Feuerbach - Principles of Philosophy of the Future §18 | |
| A reaction: This implies that Descartes' foundation is the Ontological Argument rather than the Cogito. It certainly shows how a priori synthetic thinking is basic in Descartes - that views of existence derive from pure thought. Was Descartes an idealist? |
| 4641 | In the Meditations version of the Cogito he says "I am; I exist", which avoids presenting it as an argument [Descartes, by Baggini /Fosl] |
| Full Idea: Descartes may have been aware of the danger of begging the question (in claiming "I think therefore I am") because in 'Meditations' he says "I am; I exist", which is not presented in the form of an argument. | |
| From: report of René Descartes (Meditations [1641], 2) by J Baggini / PS Fosl - The Philosopher's Toolkit §3.22 | |
| A reaction: Certainly the word 'therefore' cries out for a strict analysis of what is being inferred from what, but presenting the Cogito as a self-evident intuition for the 'natural light' has its own problems. |
| 6929 | Modern philosophy set the self-conscious ego in place of God [Descartes, by Feuerbach] |
| Full Idea: Modern philosophy set the thinking being, the ego, and the self-conscious mind in the place of the merely ideated being, in place of God. | |
| From: report of René Descartes (Meditations [1641]) by Ludwig Feuerbach - Principles of Philosophy of the Future §37 | |
| A reaction: Descartes would be shocked by this interpretation, but God comes third in his logical priorities, after the existence of his ego, and its reliance on what is clear and distinct. |
| 3849 | "I think therefore I am" is the absolute truth of consciousness [Sartre on Descartes] |
| Full Idea: "I think therefore I am" is the absolute truth of consciousness as it attains to itself. | |
| From: comment on René Descartes (Meditations [1641], §2) by Jean-Paul Sartre - Existentialism and Humanism p.44 |
| 2258 | I must even exist if I am being deceived by something [Descartes] |
| Full Idea: Doubtless I exist if I persuade myself of something. But there is some powerful and cunning deceiver who is deliberately deceiving me. Then too there is no doubt that I exist, if he is deceiving me. | |
| From: René Descartes (Meditations [1641], §2.25) |
| 2259 | "I am, I exist" is necessarily true every time I utter it or conceive it in my mind [Descartes] |
| Full Idea: "I am, I exist" is necessarily true every time I utter it or conceive it in my mind. | |
| From: René Descartes (Meditations [1641], §2.25) |
| 3160 | The Cogito is a transcendental argument, not a piece of a priori knowledge [Rey on Descartes] |
| Full Idea: The Cogito is a transcendental argument; Descartes doesn't claim that it is a priori that he exists, but that any doubt or denial that he exists would presuppose his existence. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Georges Rey - Contemporary Philosophy of Mind 3.2.1 |
| 2260 | If I don't think, there is no reason to think that I exist [Descartes] |
| Full Idea: It could be that if I were to cease all thinking I would then utterly cease to exist. …I am therefore precisely nothing but a thinking thing; that is, a mind, or intellect, or understanding, or reason. | |
| From: René Descartes (Meditations [1641], §2.27) |
| 1117 | The Cogito proves subjective experience is basic, but makes false claims about the Self [Russell on Descartes] |
| Full Idea: The Cogito argument proves that subjective experience is the most reliable, but it makes unjustified claims about the certainty of the Self. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Bertrand Russell - Problems of Philosophy Ch 2 |
| 2873 | Maybe 'I' am not the thinker, but something produced by thought [Nietzsche on Descartes] |
| Full Idea: In the past one said 'I' is the condition, 'think' is the predicate and conditioned - thinking is an activity which the subject causes; but maybe the reverse is true - and 'I' is only a synthesis produced by thinking. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Friedrich Nietzsche - Beyond Good and Evil §54 |
| 3623 | The Cogito only works if you already understand what thought and existence are [Mersenne on Descartes] |
| Full Idea: In order to be certain that you are thinking you must know what thought or thinking is, and what your existence is; but since you do not yet know what these things are, how can you know that you are thinking or that you exist? | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Marin Mersenne - Objections to 'Meditations' (Sixth) 413 |
| 1369 | It is a precondition of the use of the word 'I' that I exist [Ayer on Descartes] |
| Full Idea: In the Cogito the work is all done by the demonstrative word 'I', because it is a precondition of the use of such a word that the thing to which it points has to exist. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by A.J. Ayer - The Problem of Knowledge Ch 2 (iii) |
| 5360 | The thing which experiences may be momentary, and change with the next experience [Russell on Descartes] |
| Full Idea: It might be that the something which sees a brown colour is quite momentary, and not the same thing which has some different experience the next moment. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Bertrand Russell - Problems of Philosophy Ch.2 | |
| A reaction: This has become one of the standard objections to the Cogito. Note that Descartes himself was aware of the problem (Idea 1400). Sometimes experiences make no sense if there isn't something connecting them to previous experiences. |
| 2870 | 'I think' assumes I exist, that thinking is known and caused, and that I am doing it [Nietzsche on Descartes] |
| Full Idea: The sentence "I think" contains a series of unprovable assertions; for example, it is I who think, that it must be something at all which thinks, that thinking is by an entity thought of as a cause, that an 'I' exists, and that I know what thinking is. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Friedrich Nietzsche - Beyond Good and Evil §16 |
| 5188 | A thought doesn't imply other thoughts, or enough thoughts to make up a self [Ayer on Descartes] |
| Full Idea: The fact that a thought occurs at a given moment does not entail that any other thought has occurred at any other moment, still less that there has occurred a series of thoughts sufficient to constitute a single self. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by A.J. Ayer - Language,Truth and Logic Ch.2 | |
| A reaction: This seems to be the main objection to the Cogito. It doesn't refute it, but simply recommends cautious restraint in what is being claimed as its conclusion. I can't make much sense of a thought which has no thinker at all. |
| 3624 | That I perform an activity (thinking) doesn't prove what type of thing I am [Hobbes on Descartes] |
| Full Idea: From the fact that I am thinking it follows that I exist, since that which thinks is not nothing. But when he adds 'that is, I am a mind, or intelligence, or intellect', a doubt arises. ..You might as well say 'I am walking, therefore I am a walk'. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Thomas Hobbes - Objections to 'Meditations' (Third) 172 |
| 3120 | Autistic children seem to use the 'I' concept without seeing themselves as thinkers [Segal on Descartes] |
| Full Idea: It really does not seem (as a result of research into autism) that when one thinks of oneself with one's 'I' concept, one must thereby represent oneself as a thinker. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Gabriel M.A. Segal - A Slim Book about Narrow Content 4.2 |
| 4526 | The Cogito assumes a priori the existence of substance, when actually it is a grammatical custom [Nietzsche on Descartes] |
| Full Idea: Descartes' Cogito posits as 'true a priori' our belief in the concept of substance, but the idea that when there is a thought there has to be something 'that thinks' is simply a formulation of our grammatical custom that adds a doer to every deed. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Friedrich Nietzsche - The Will to Power (notebooks) §484 | |
| A reaction: This anticipates the sort of thing Ayer and the logical positivists said. It is not clear that Descartes does think the mind is a substance, but this pinpoints a possible presupposition in Descartes. |
| 5579 | How can we infer that all thinking involves self-consciousness, just from my own case? [Kant on Descartes] |
| Full Idea: It seems strange that the condition under which I think is to be valid for everything that thinks, and that on an empirical-seeming proposition we can presume to ground a universal judgement, that everything that thinks has self-consciousness. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Immanuel Kant - Critique of Pure Reason A346 | |
| A reaction: Kant is not bothered by this, and says we know it a priori. If it is indeed an empirical proposition, it becomes an induction with one instance, which is the notorious weakness of the 'argument from analogy' to other minds. The Cogito is not empirical. |
| 5580 | My self is not an inference from 'I think', but a presupposition of it [Kant on Descartes] |
| Full Idea: The simplicity of my self is not inferred from the proposition "I think", but rather the former lies in every thought. 'I am simple' is an immediate apperception, just as the Cogito is tautological, since 'cogito' immediately asserts the reality. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Immanuel Kant - Critique of Pure Reason A355 | |
| A reaction: This is why Kant thinks the self is the result of a transcendental deduction, rather than of a direct observation of the self-evident. Personally I side with Descartes. I do not 'observe' my self, but I am acutely aware of its presence and actions. |
| 5587 | We cannot give any information a priori about the nature of the 'thing that thinks' [Kant on Descartes] |
| Full Idea: If anyone asks me: What is the constitution of a thing that thinks? I do not know how to answer a priori, because the answer ought to be synthetic (for an analytic answer explains thinking, but gives no cognition of that on which thinking rests). | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Immanuel Kant - Critique of Pure Reason A398 | |
| A reaction: This has always seemed a problem with Descartes' very thin account of his 'res cogitans', but then what exactly does Kant want to know? Is it a metaphysical disaster if we think of the self as having no more identity than a geometrical point? |
| 5588 | The fact that I am a subject is not enough evidence to show that I am a substantial object [Kant on Descartes] |
| Full Idea: The fact that I am a subject ..does not signify that as object I am a self-subsisting being or substance; the latter goes too far, and hence demands data that are not encountered at all in thinking. | |
| From: comment on René Descartes (Meditations [1641], §2.26) by Immanuel Kant - Critique of Pure Reason B407 | |
| A reaction: This is a key problem with the Cogito - that so little can be said about the 'I' of which the existence has been proved that it is not clear that anything has been proved at all - certainly not that there is a continuous and stable Ego. |
| 13923 | Descartes' claim to know his existence before his essence is misleading or absurd [Descartes, by Lowe] |
| Full Idea: Descartes claimed to know that he existed before he knew what he was - before he grasped his own essence. This is either disingenuous or intended non-literally, if it is not to be dismissed as incomprehensible. | |
| From: report of René Descartes (Meditations [1641], 2) by E.J. Lowe - Two Notions of Being: Entity and Essence 2 n32 | |
| A reaction: If something comes at you from the mist, you can know that it exists before you know what it is. How could you understand the essence of something if you hadn't first encountered its existence? Lowe has it the wrong way round. |
| 6930 | Modern self-consciousness is a doubtful abstraction; only senses and feelings are certain [Feuerbach on Descartes] |
| Full Idea: The self-consciousness of modern philosophy is only a being ideated and mediated through abstraction and thus a doubtful being; certain and immediately assured is only that which is an object of the senses, perception and feeling. | |
| From: comment on René Descartes (Meditations [1641], 2) by Ludwig Feuerbach - Principles of Philosophy of the Future §37 | |
| A reaction: This seems to agree with Hume's empirical doubts about the self (Idea 1316). The comment that 'abstraction' is involved in the Cogito argument is interesting. Descartes said the Cogito was a 'simply intuition of the mind' (Idea 3622). |
| 2261 | My perceiving of things may be false, but my seeming to perceive them cannot be false [Descartes] |
| Full Idea: I now see a light, I hear a noise, I feel heat. Perhaps these things are false, since I am asleep. Yet I certainly do seem to see, hear, and feel warmth. This cannot be false. | |
| From: René Descartes (Meditations [1641], §2.29) |
| 2257 | I myself could be the author of all these self-delusions [Descartes] |
| Full Idea: I myself could be the author of all these self-delusions. | |
| From: René Descartes (Meditations [1641], §2.24) |
| 2279 | A triangle has a separate non-invented nature, shown by my ability to prove facts about it [Descartes] |
| Full Idea: A triangle has a determinate nature, which I did not fabricate, and which does not depend on my mind. This is evident from the fact that various properties can be demonstrated regarding it, such as that its three angles are equal to two right angles. | |
| From: René Descartes (Meditations [1641], §5.64) |
| 6490 | For Descartes, objects have one primary quality, which is geometrical [Descartes, by Robinson,H] |
| Full Idea: Descartes denies any similarity between the physical world and ideas, as matter possesses only geometrical properties; Locke allows more primary qualities, but follows Boyle and the atomists in treating secondary qualities as creations of sense. | |
| From: report of René Descartes (Meditations [1641]) by Howard Robinson - Perception 1.5 | |
| A reaction: The interesting point to note here is that Descartes' geometrical view of objects (they are defined purely by 'extension') is the view that they have one minimal primary quality. I prefer Locke's view, of which the history (given here) is interesting. |
| 2295 | Why does pain make us sad? [Descartes] |
| Full Idea: Why should a certain sadness of spirit arise from a sensation of pain? | |
| From: René Descartes (Meditations [1641], §6.76) |
| 3627 | Dogs can make the same judgements as us about variable things [Gassendi on Descartes] |
| Full Idea: A dog certainly makes similar kinds of judgement to your perceiving men by their hats and cloaks when they see their master's hat or clothes, …and they can recognise their master even if he is standing, sitting, lying down, or crouching. | |
| From: comment on René Descartes (Meditations [1641], §2.32) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 272 |
| 2265 | We perceive objects by intellect, not by senses or imagination [Descartes] |
| Full Idea: Bodies are not, properly speaking, perceived by the senses or by the faculty of imagination, but by the intellect alone. | |
| From: René Descartes (Meditations [1641], §2.34) |
| 2263 | The wax is not perceived by the senses, but by the mind alone [Descartes] |
| Full Idea: The perception of the wax is neither a seeing, nor a touching, nor an imagining. Rather, it is an inspection on the part of the mind alone. | |
| From: René Descartes (Meditations [1641], §2.31) |
| 2264 | We don't 'see' men in heavy clothes, we judge them to be men [Descartes] |
| Full Idea: Were I to look out of my window and observe men crossing the square, I would ordinarily say that I see the men themselves. But what do I see but hats and clothes, which could conceal automata? Yet I judge them to be men. | |
| From: René Descartes (Meditations [1641], §2.32) |
| 2247 | To achieve good science we must rebuild from the foundations [Descartes] |
| Full Idea: Once in my life I had to raze everything to the ground and begin again from the original foundations, if I wanted to establish anything firm and lasting in the sciences. | |
| From: René Descartes (Meditations [1641], §1.17) | |
| A reaction: This sentence is the beginning of the Enlightenment. The project of proving absolutely everything, and in a foundational way, is now met with much scepticism. I will never abandon the project! |
| 2255 | Only one certainty is needed for progress (like a lever's fulcrum) [Descartes] |
| Full Idea: Archimedes sought but one firm and immovable point in order to move the entire earth. Just so, great things are to be hoped for if I succeed in finding just one thing, however slight, that is certain and unshaken. | |
| From: René Descartes (Meditations [1641], §2.24) | |
| A reaction: The classic foundationalist difficulty is that you may find something totally certain, but is it a fulcrum? Or is it just minimal, boring and useless? |
| 2251 | Even if my body and objects are imaginary, there may be simpler things which are true [Descartes] |
| Full Idea: Perhaps even though general things like eyes could be imaginary, still one must admit that certain other things that are even more simple and universal are true. | |
| From: René Descartes (Meditations [1641], §1.20) |
| 6347 | Descartes can't begin again, because sceptics doubt cognitive processes as well as beliefs [Pollock/Cruz on Descartes] |
| Full Idea: Descartes' strategy of starting over will not work, because the skeptic is not just questioning our beliefs, he is also questioning the cognitive processes by which we arrive at our beliefs, and if we start all over again we use the same processes. | |
| From: comment on René Descartes (Meditations [1641], §1) by J Pollock / J Cruz - Contemporary theories of Knowledge (2nd) | |
| A reaction: Scepticism comes in degrees, so there is not one strategy employed by sceptics. It is certainly true, though, that nothing can resist extreme scepticism. The most extreme view is to refuse to accept the meaningfulness of all belief language. |
| 2296 | If pain is felt in a lost limb, I cannot be certain that a felt pain exists in my real limbs [Descartes] |
| Full Idea: I have heard it said by people whose arm or leg has been amputated that they still sensed pain in the lost limb. Thus it does not seem certain that one of my bodily members causes me pain, even though I sense pain in it. | |
| From: René Descartes (Meditations [1641], §6.77) |
| 3620 | We correct sense errors with other senses, not intellect [Mersenne on Descartes] |
| Full Idea: Owing to refraction a stick which is in fact straight appears bent in water. What corrects the error? The intellect? Not at all; it is the sense of touch. | |
| From: comment on René Descartes (Meditations [1641], §1.18) by Marin Mersenne - Objections to 'Meditations' (Sixth) 418 |
| 3619 | The senses can only report, so perception errors are in the judgment [Gassendi on Descartes] |
| Full Idea: Although there is deception or falsity, it is not to be found in the senses; for the sense are quite passive and report only appearances, which must appear the way they do owing to their causes. The error or falsity is in the judgement or the mind. | |
| From: comment on René Descartes (Meditations [1641], §1.18) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 332 |
| 2249 | It is prudent never to trust your senses if they have deceived you even once [Descartes] |
| Full Idea: The senses are sometimes deceptive, and it is a mark of prudence never to place our complete trust in those who have deceived us even once. | |
| From: René Descartes (Meditations [1641], §1.18) |
| 2253 | God may have created nothing, but made his creation appear to me as it does now [Descartes] |
| Full Idea: How do I know that God did not bring it about that there is no earth or heavens, no extension, shape, size or place, and yet that all these things appear to me precisely as they do now? | |
| From: René Descartes (Meditations [1641], §1.21) |
| 2254 | To achieve full scepticism, I imagine a devil who deceives me about the external world and my own body and senses [Descartes] |
| Full Idea: I will suppose an evil genius, supremely powerful and clever, who has directed his entire effort at deceiving me. I will regard all external things as devilish hoaxes, and myself as not possessed of a body or senses, but falsely believing these things. | |
| From: René Descartes (Meditations [1641], §1.22) |
| 2305 | Waking actions are joined by memory to all our other actions, unlike actions of which we dream [Descartes] |
| Full Idea: Dreams are never joined by the memory with all the actions of life, as is the case with those actions that occur when one is awake. | |
| From: René Descartes (Meditations [1641], §6.89) |
| 2294 | I can only sense an object if it is present, and can't fail to sense it when it is [Descartes] |
| Full Idea: Perceptions come upon me without my consent, to the extent that, wish as I may, I could not sense any object unless it was present to a sense organ, nor could I fail to sense it when it was present. | |
| From: René Descartes (Meditations [1641], §6.75) |
| 19737 | A system can infer the structure of the world by making predictions about it [New Sci.] |
| Full Idea: If we can train a system for prediction, it can essentially infer the structure of the world it's looking at by doing this prediction. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.12.12) | |
| A reaction: [AI expert] This seems to be powerful support for the centrality of mathematical laws of nature in achieving understanding of the world. We may downplay the 'mere' ability to predict, but this idea says that the rewards of prediction are very great. |
| 4862 | Can the pineal gland be moved more slowly or quickly by the mind than by animal spirits? [Spinoza on Descartes] |
| Full Idea: I am in ignorance whether the pineal gland can be agitated more slowly or more quickly by the mind than by the animal spirits. | |
| From: comment on René Descartes (Meditations [1641], §6.82) by Baruch de Spinoza - The Ethics V Pref | |
| A reaction: Is this the earliest statement of the problem of double causation? It is a classic difficulty for dualists, highlighted by Ryle, among others. Avoidance of double causation is a classic reason for moving to monism about mind. |
| 3850 | We discovers others as well as ourselves in the Cogito [Sartre on Descartes] |
| Full Idea: It is not only oneself that one discovers in the Cogito, but those of others too. | |
| From: comment on René Descartes (Meditations [1641], §2) by Jean-Paul Sartre - Existentialism and Humanism p.45 | |
| A reaction: The analytical tradition requires a bit more than an instant perception of others in oneself. The problem of 'other minds' must at least be mentioned. However, the way to get to know a universal is to fully study a single instance. |
| 2302 | Faculties of the mind aren't parts, as one mind uses them [Descartes] |
| Full Idea: The faculties of willing, sensing, understanding and so on cannot be called "parts" of the mind, since it is one and the same mind that wills, senses and understands. | |
| From: René Descartes (Meditations [1641], §6.86) | |
| A reaction: It is best here to say that Descartes has confused the 'mind' with the 'person'. These faculties make (I think) no sense without a person to perform them, but the 'mind' surely includes these conscious activities, and many fringe events as well. |
| 3151 | Descartes put thought at the centre of the mind problem, but we put sensation [Rey on Descartes] |
| Full Idea: Descartes confined his dualism to problems of reason and language. Sensation and even imagination seemed to him physically unproblematic. Nowadays it is the reverse: thinking seems easy - but feeling? | |
| From: comment on René Descartes (Meditations [1641], 2) by Georges Rey - Contemporary Philosophy of Mind 2 n16 | |
| A reaction: Thinking only 'seems easy' if it can be done without consciousness, and that is beginning to look like a dubious assumption. The most interesting and promising area is the borderline between a chess-playing machine and a human chess player. |
| 21800 | Descartes mentions many cognitive faculties, but reduces them to will and intellect [Descartes, by Schmid] |
| Full Idea: Although Descartes accepted a variety of cognitive faculties like the intellect, will, power of judgement, imagination, memory, and perception, he took them all to be ultimately reducible to different operations of the will and intellect. | |
| From: report of René Descartes (Meditations [1641], 4) by Stephan Schmid - Faculties in Early Modern Philosophy 2 | |
| A reaction: In Med 4, it is most clear, when he reduces 'judgement' to will and intellect, which enable his to assent to an idea. Nietzsche saw Descartes' view as simplistic. |
| 1399 | Imagination and sensation are non-essential to mind [Descartes] |
| Full Idea: This power of imagination which is in me, in so far as it differs from the power of conceiving, is in no way necessary to my nature or essence. | |
| From: René Descartes (Meditations [1641], §6.73) | |
| A reaction: This is my candidate for the biggest blunder ever made by a great philosopher. But it was thanks to his mistake that I began to realise how totally central imagination is to the very act of thinking. Thank you, René. |
| 19736 | Neural networks can extract the car-ness of a car, or the chair-ness of a chair [New Sci.] |
| Full Idea: Early neural nets were really good at recognising general categories, such as a car or a chair. Those networks are good at extracting the 'chair-ness' or the 'car-ness' of the object. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.12.12) | |
| A reaction: [Interview with Yann LeCun, Facebook AI director] Fregean philosophers such as Geach think that extracting features is a ridiculous idea, but if even a machine can do it then I suspect that human beings can (and do) manage it too. |
| 1400 | Some cause must unite the separate temporal sections of a person [Descartes] |
| Full Idea: Because the entire span of one's life can be divided into countless parts, each one wholly independent of the rest, it does not follow from the fact that I existed a short time ago that I exist now, unless some cause creates and preserves me each moment. | |
| From: René Descartes (Meditations [1641], §3.49) | |
| A reaction: How could I 'prove' that this computer is the same computer as it was five minutes ago, even after I have accepted the straightforward existence of the computer? This is the Enlightenment Project, the mad desire to prove absolutely everything. |
| 1401 | Since I only observe myself to be thinking, I conclude that that is my essence [Descartes] |
| Full Idea: Since I do not observe that any other thing belongs necessarily to my nature or essence except that I am a thinking thing, I rightly conclude that my essence consists in this alone, that I am a thinking thing, or substance whose essence is thinking. | |
| From: René Descartes (Meditations [1641], §6.78) | |
| A reaction: This actually appears to be my favourite confusion - of episemology with ontology. Compare 'whenever I see him he is smiling, so he must be happy'. Personally I am happy to say that my essence is thinking, as long as it needn't be conscious. |
| 2299 | I can exist without imagination and sensing, but they can't exist without me [Descartes] |
| Full Idea: I can understand myself without the faculties of imagining and sensing, but not vice versa; I cannot understand them without me - a substance endowed with understanding. | |
| From: René Descartes (Meditations [1641], §6.78) | |
| A reaction: I think this is a fundamental and important error on Descartes' part. The idea that understanding is possible without imagination (and even sensation) is wrong, and it leads to the misleading concept of 'pure' reason. |
| 6907 | For Descartes a person's essence is the mind because objects are perceived by mind, not senses [Descartes, by Feuerbach] |
| Full Idea: For Descartes the essence of corporeal things is not an object of the senses, but only of the mind; and hence it is not the senses but the mind that is the essence of the perceiving subject, that is, of man. | |
| From: report of René Descartes (Meditations [1641], 2) by Ludwig Feuerbach - Principles of Philosophy of the Future §17 | |
| A reaction: This, of course, is why Descartes' approach can lead to idealism and solipsism, whereas the other approach leads to empiricism and animalism (Idea 6669). |
| 2283 | Our 'will' just consists of the feeling that when we are motivated to do something, there are no external pressures [Descartes] |
| Full Idea: The will consists solely in the fact that when something is proposed to us by our intellect either to affirm or deny, we are moved in such a way that we sense we are determined to it by no external force. | |
| From: René Descartes (Meditations [1641], §4.57) |
| 2282 | My capacity to make choices with my free will extends as far as any faculty ever could [Descartes] |
| Full Idea: I experience that the will or free choice I have received from God is limited by no boundaries whatever, …indeed it is so great in me that I cannot grasp the idea of any greater faculty. | |
| From: René Descartes (Meditations [1641], §4.56) |
| 2276 | The mind is a non-extended thing which thinks [Descartes] |
| Full Idea: My concept of the human mind is a thinking thing, not extended in length, breadth or depth, and having nothing else from the body. | |
| From: René Descartes (Meditations [1641], §4.53) | |
| A reaction: But he admits (in Med 6) that the mind is so closely integrated with the body that they seem inseparable. Perhaps he shouldn't trust his own concept of the thing, because he is too close to the subject matter. You can't count a crowd if you are in it. |
| 2298 | Mind is not extended, unlike the body [Descartes] |
| Full Idea: Since I am clearly a thinking thing and not an extended thing, and on the other hand I have a distinct idea of a body, as merely an extended thing and not a thinking thing, it is certain that I am really distinct from my body, and can exist without it. | |
| From: René Descartes (Meditations [1641], §6.78) | |
| A reaction: How can he be 'certain' for this reason? This is a classic confusion of ontology and epistemology. Given that the mind is a special case, he should be asking WHY his thinking is clear to him, but his body isn't. Maybe it is because of his viewpoint. |
| 3423 | Descartes is a substance AND property dualist [Descartes, by Kim] |
| Full Idea: Descartes' dualism combines substance dualism and property dualism; two disparate domains of substances, and two mutually exclusive families of properties. | |
| From: report of René Descartes (Meditations [1641], §6.78) by Jaegwon Kim - Philosophy of Mind p.211 | |
| A reaction: I would have thought that substance dualism entailed property dualism. How would you distinguish two substances from one another except by their properties? There seems a merely logical possibility that God gives two substances the same properties. |
| 2303 | The mind is utterly indivisible [Descartes] |
| Full Idea: There is a great difference between a mind and a body, in that a body, by its very nature, is always divisible, but the mind is utterly indivisible. | |
| From: René Descartes (Meditations [1641], §6.85) | |
| A reaction: This strikes me as being simply false. I don't just mean that surgeons can split the mind in half. We should think of the mind as a team of conscious and non-conscious processes, which are held together by a self in normal healthy people. Selves change. |
| 6153 | Interaction between mental and physical seems to violate the principle of conservation of energy [Rowlands on Descartes] |
| Full Idea: It is often argued that any interaction between the physical and the mental - as defined by Descartes - would require a violation of the first law of thermodynamics, the principle of conservation of energy. | |
| From: comment on René Descartes (Meditations [1641]) by Mark Rowlands - Externalism Ch.2 | |
| A reaction: This would be because consciousness is adding energy to the system (in order to generate movement) without it having come from anywhere else in the physical system. A good objection, which only a miracle could overcome. |
| 3625 | The 'thinking thing' may be the physical basis of the mind [Hobbes on Descartes] |
| Full Idea: It may be that the thing that thinks is the subject to which mind, reason or intellect belong; and this subject may thus be something corporeal. | |
| From: comment on René Descartes (Meditations [1641], §2.27) by Thomas Hobbes - Objections to 'Meditations' (Third) 173 | |
| A reaction: Of course, Descartes goes on to reject this view. Presumably he is suggesting that mind etc. might be properties of something corporeal, rather than being identical with it. Descartes was well aware of materialism in Hobbes and Gassendi. |
| 2552 | Knowing different aspects of brain/mind doesn't make them different [Rorty on Descartes] |
| Full Idea: Why should an epistemic distinction reflect an ontological distinction? Why should our epistemic privilege of being incorrigible about how things seem to us reflect a distinction between two realms of being? | |
| From: comment on René Descartes (Meditations [1641], §6.78) by Richard Rorty - Philosophy and the Mirror of Nature 1.2 | |
| A reaction: This strikes me as being one of the most important ideas in philosophy, mainly as a corrective to a lot of bad philosophy, rather than as wisdom offered to non-philosophers (for whom Rorty's thought is probably common sense. How is it? How do we know? |
| 4305 | Descartes gives no clear criterion for individuating mental substances [Cottingham on Descartes] |
| Full Idea: Descartes gives no clear criterion for individuating mental substances. | |
| From: comment on René Descartes (Meditations [1641], §6.78) by John Cottingham - The Rationalists p.86 | |
| A reaction: Presumably I can individuate my own mind by the 'natural light' of reason, and the implications of the Cogito. The minds of others do seem to be a problem. Why should they coincide with bodies, and not overlap or blend or swap? |
| 4861 | Does Descartes have a clear conception of how mind unites with body? [Spinoza on Descartes] |
| Full Idea: What does Descartes understand by the union of the mind and the body? What clear and distinct conception has he got of thought in most intimate union with a certain particle of extended matter? | |
| From: comment on René Descartes (Meditations [1641], §6.82) by Baruch de Spinoza - The Ethics V Pref | |
| A reaction: This is the classic, original and strongest objection to Cartesian dualism - that mind and body are held to be too different to interact. Spinoza may have overreacted a bit when he saw the only solution as the total identity of the two things. |
| 6540 | Even Descartes may concede that mental supervenes on neuroanatomical [Lycan on Descartes] |
| Full Idea: Even Descartes may have conceded that the mental supervenes on the neuroanatomical. | |
| From: comment on René Descartes (Meditations [1641], 6) by William Lycan - Consciousness 5.2 | |
| A reaction: This is true (early in Meditation Six) despite his later suggestion of the pineal gland as the linking point. It proves nothing, but I have heard John Cottingham suggest that Descartes might well be a materialist if he came back today. |
| 7733 | Superman's strength is indubitable, Clark Kent's is doubtful, so they are not the same? [Maslin on Descartes] |
| Full Idea: Descartes's claim that mind and body are separate because the first is necessary when thinking and the second isn't, is like arguing 'Superman's strength is indubitable; Clark Kent's strength is widely doubted; so Clark Kent is not Superman'. | |
| From: comment on René Descartes (Meditations [1641], p.156) by Keith T. Maslin - Introduction to the Philosophy of Mind 2.7.1 | |
| A reaction: I've heard people defend Descartes on this, and Kripke is interesting on the subject, but Descartes had better not be following this pattern of argument, or else a great philosopher would really be presenting an absurdity. |
| 5686 | In some thoughts I grasp a subject, but also I will or fear or affirm or deny it [Descartes] |
| Full Idea: Other thoughts are different from ideas, as when I will, or fear, or affirm, or deny, there is always some thing that I grasp as the subject of my thought, yet I embrace in my thought something more than the likeness of that thing. | |
| From: René Descartes (Meditations [1641], §3.37) | |
| A reaction: Note that the class of mental events we call 'propositional attitudes' had already been identified by Descartes. His categories of thinking in Med. Three might be one of his most important contributions, because that is what matters in the mind. |
| 16419 | No one has yet devised a rationality test [New Sci.] |
| Full Idea: The financial sector has been clamouring for a rationality test for years. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.10.29) | |
| A reaction: Many aspects of intelligence tests do actually pick out what I would call rationality (which includes 'rational intuition', a new favourite of mine). But they are mixed in with rather mechanical geeky sort of tests. |
| 4017 | Descartes created the modern view of rationality, as an internal feature instead of an external vision [Descartes, by Taylor,C] |
| Full Idea: Rationality is now an internal property of subjective thinking, rather than its consisting in (according to Plato) its vision of reality. This view of Descartes' has become the standard modern view. | |
| From: report of René Descartes (Meditations [1641]) by Charles Taylor - Sources of the Self §8 | |
| A reaction: Greek 'logos' actually seemed to be both internal and external. We have certainly lost the idea that the universe is rational, even though it is ordered. |
| 2284 | I make errors because my will extends beyond my understanding [Descartes] |
| Full Idea: My errors are owing simply to the fact that, since the will extends further than the intellect, I do not contain the will within the same boundaries, but extend it to things I do not understand. | |
| From: René Descartes (Meditations [1641], §4.58) |
| 16417 | About a third of variation in human intelligence is environmental [New Sci.] |
| Full Idea: Possibly a third of the variation in our intelligence is down to the environment in which we grew up - nutrition and education, for example. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.10.29) | |
| A reaction: This presumably leaves the other two-thirds to derive from genetics. I am a big believer in environment. Swapping babies between extremes of cultural environment would hugely affect intelligence, say I. |
| 16418 | People can be highly intelligent, yet very stupid [New Sci.] |
| Full Idea: You really can be highly intelligent, and at the same time very stupid. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.10.29) | |
| A reaction: This is closely related to my observation (from a lifetime of study) that a talent for philosophy has a very limited correlation with standard notions of high intelligence. What matters is how conscious reasoning and intuition relate. Greek 'phronesis'. |
| 19484 | Psychologists measure personality along five dimensions [New Sci.] |
| Full Idea: Psychologists have long thought that measuring on a scale of just five personality dimensions - agreeableness, extroversion, neuroticism, conscientiousness and openness to new experiences - can capture all human variations in behaviour and attitude. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.06.13) | |
| A reaction: Researchers are considering a sixth - called 'honesty-humility' - which is roughly how devious people are. The five mentioned here seem to be a well entrenched orthodoxy among professional psychologists. Is personality more superficial than character? |
| 5685 | True ideas are images, such as of a man, a chimera, or God [Descartes] |
| Full Idea: Some of my thoughts are like images of things; to these alone does the word 'idea' properly apply, as when I think of a man, or a chimera, or the sky, or an angel, or God. | |
| From: René Descartes (Meditations [1641], §3.37) | |
| A reaction: Descartes is obviously aware of a problem with the application of the word 'idea'. This definition seems rather narrow (and visual), but it is certainly confined to concepts, and does not expand to include propositions. |
| 3629 | All ideas are adventitious, and come from the senses [Gassendi on Descartes] |
| Full Idea: I would go further than you and note that all our ideas seem to be adventitious - to proceed from things which exist outside the mind and come under one of our senses. ..The idea of a giant is a man of ordinary size which the mind enlarges at will. | |
| From: comment on René Descartes (Meditations [1641], §3.38) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 280 | |
| A reaction: A classic early statement of modern empiricism. Gassendi needed to think about logic, maths, and necessities to make his case more secure. Where did his idea to 'enlarge' the giant come from? |
| 8715 | Infinities expand the bounds of the conceivable; we explore concepts to explore conceivability [Cantor, by Friend] |
| Full Idea: Cantor (in his exploration of infinities) pushed the bounds of conceivability further than anyone before him. To discover what is conceivable, we have to enquire into the concept. | |
| From: report of George Cantor (works [1880]) by Michčle Friend - Introducing the Philosophy of Mathematics 6.5 | |
| A reaction: This remark comes during a discussion of Husserl's phenomenology. Intuitionists challenge Cantor's claim, and restrict what is conceivable to what is provable. Does possibility depend on conceivability? |
| 2273 | The ideas of God and of my self are innate in me [Descartes] |
| Full Idea: The idea of God is innate in me, just as the idea of myself is innate in me. | |
| From: René Descartes (Meditations [1641], §3.51) |
| 2285 | I can think of innumerable shapes I have never experienced [Descartes] |
| Full Idea: I can think of countless geometrical figures, concerning which there can be no suspicion of their ever having entered me through the senses. | |
| From: René Descartes (Meditations [1641], §5.64) |
| 2286 | The idea of a supremely perfect being is within me, like the basic concepts of mathematics [Descartes] |
| Full Idea: The idea of God, that is, the idea of a supremely perfect being, is one discovered to be no less within me than the idea of any figure or number. | |
| From: René Descartes (Meditations [1641], §5.65) |
| 13454 | Cantor says (vaguely) that we abstract numbers from equal sized sets [Hart,WD on Cantor] |
| Full Idea: Cantor thought that we abstract a number as something common to all and only those sets any one of which has as many members as any other. ...However one wants to see the logic of the inference. The irony is that set theory lays out this logic. | |
| From: comment on George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: The logic Hart has in mind is the notion of an equivalence relation between sets. This idea sums up the older and more modern concepts of abstraction, the first as psychological, the second as logical (or trying very hard to be!). Cf Idea 9145. |
| 2280 | Many causes are quite baffling, so it is absurd to deduce causes from final purposes [Descartes] |
| Full Idea: God can make unnumerable things whose cause escapes me, and for this reason alone the entire class of causes which people customarily derive from a thing's "end", I judge to be utterly useless in physics. | |
| From: René Descartes (Meditations [1641], §4.55) | |
| A reaction: anti-Aristotle |
| 2272 | There must be at least as much in the cause as there is in the effect [Descartes] |
| Full Idea: There must be at least as much in the cause as there is in the effect. | |
| From: René Descartes (Meditations [1641], §3.49) |
| 19950 | Entropy is the only time-asymmetric law, so time may be linked to entropy [New Sci.] |
| Full Idea: All our physical laws are time-symmetric, ...so things can run forwards or backwards. But entropy is an exception, saying that disorder increases over time. Many physicists therefore suspect that the flow of time is linked to entropy. | |
| From: New Scientist writers (New Scientist articles [2013], 2017.02.04) |
| 19478 | Light moves at a constant space-time speed, but its direction is in neither space nor time [New Sci.] |
| Full Idea: A light ray always moves at one unit of space per unit of time - a constant diagonal on the graph. ...But the direction that light rays travel in is neither space nor time, and is called 'null'. It is on the edge between space and time. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: Don't understand this, but it sounds fun. |
| 19474 | Quantum states are measured by external time, of unknown origin [New Sci.] |
| Full Idea: When we measure the evolution of a quantum state, it is to the beat of an external timepiece of unknown provenance. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: It is best not to leap to philosophical conclusions when studying modern physics. Evidently time has a very different status in quantum mechanics and in relativity theory. |
| 19473 | The Schrödinger equation describes the evolution of an object's wave function in Hilbert space [New Sci.] |
| Full Idea: A quantum object's state is described by a wave function living in Hilbert space, encompassing all of its possible states. We see how the wave function evolves in time, moving from one state to another, using the Schrödinger equation. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: [These idea are basic explanations for non-scientific philosophers - please forgive anything that makes you wince] |
| 19953 | In string theory space-time has a grainy indivisible substructure [New Sci.] |
| Full Idea: String theory suggests that space-time has a grainy substructure - you can't keep chopping it indefinitely into smaller and smaller pieces. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.11.07) | |
| A reaction: Presumably the proposal is that strings are the true 'atoms'. |
| 19954 | It is impossible for find a model of actuality among the innumerable models in string theory [New Sci.] |
| Full Idea: String theory has more than 10-to-the-500th solutions, each describing a different sort of universe, so it is nigh-on impossible to find the one solution that corresponds to our geometrically flat, expanding space-time full of particles. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.11.07) |
| 19476 | String theory needs at least 10 space-time dimensions [New Sci.] |
| Full Idea: String theory needs at least 10 space-time dimensions to be mathematically consistent. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: Apparently because of 'Ads/CFT', it may be possible to swap this situation for a more tractable 4-dimensional version. |
| 19947 | Hilbert Space is an abstraction representing all possible states of a quantum system [New Sci.] |
| Full Idea: The elements of the abstract mathematical entity called Hilbert Space represent all the possible states of a quantum system | |
| From: New Scientist writers (New Scientist articles [2013], 1017.02.04) |
| 10863 | Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg] |
| Full Idea: Cantor proved that one-dimensional space has exactly the same number of points as does two dimensions, or our familiar three-dimensional space. | |
| From: report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14 |
| 19948 | Einstein's merging of time with space has left us confused about the nature of time [New Sci.] |
| Full Idea: Our hunt for the most basic ingredients of reality has left us muddled about the status of time. One culprit for this was Einstein, whose theory of general relativity merged time with space. | |
| From: New Scientist writers (New Scientist articles [2013], 2017.02.04) |
| 19475 | Relativity makes time and space jointly basic; quantum theory splits them, and prioritises time [New Sci.] |
| Full Idea: Relativity says space and time are on the same footing - together they are the fabric of reality. Quantum mechanics, on the other hand, treats time and space differently, with time occasionally seeming more fundamental. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: Interesting. When talking about time, people glibly cite relativistic space-time to tell you that time is just another dimension. Now I can reply 'Aaah, but what about time in quantum mechanics? Eh? Eh?'. Excellent. |
| 19955 | Space-time may be a geometrical manifestation of quantum entanglement [New Sci.] |
| Full Idea: A promising theory (based on the 'Maldacena duality' - that string equations for gravity are the same as quantum equations for surface area) is that space-time is really just geometrical manifestations of quantum entanglement. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.11.07) | |
| A reaction: This is a speculation which might unite the incompatible quantum and general relativity theories. |
| 19949 | Quantum theory relies on a clock outside the system - but where is it located? [New Sci.] |
| Full Idea: After general relativity, quantum mechanics reinstated our familiar notion of time. The buzzing of the quantum world plays out according to the authoritative tick of a clock outside the described system, ...but where is this clock doing its ticking? | |
| From: New Scientist writers (New Scientist articles [2013], 2017.02.04) |
| 19951 | Entropy is puzzling, so we may need to build new laws which include time directionality [New Sci.] |
| Full Idea: Smolin observes that if entropy increases, the early universe must have been highly ordered, which we cannot explain. Maybe we need to build time directionality into the laws, instead of making time depend on entropy. | |
| From: New Scientist writers (New Scientist articles [2013], 2017.02.04) | |
| A reaction: [compressed] |
| 19477 | General relativity predicts black holes, as former massive stars, and as galaxy centres [New Sci.] |
| Full Idea: Black holes are predicted by general relativity, and are thought to exist where massive stars once lived, as well as at the heart of every galaxy. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.06.15) | |
| A reaction: Since black holes now seem to be a certainty, that is one hell of an impressive prediction. |
| 19952 | Black holes have entropy, but general relativity says they are unstructured, and lack entropy [New Sci.] |
| Full Idea: Black holes have a temperature, and hence entropy. ...But if a black hole are just an extreme scrunching of smooth space-time, it should have no substructure, and thus no entropy. This is probably the most obvious incompleteness of general relativity. | |
| From: New Scientist writers (New Scientist articles [2013], 2015.11.07) |
| 16420 | 84.5 percent of the universe is made of dark matter [New Sci.] |
| Full Idea: Dark matter makes up 84.5 percent of the universe's matter. | |
| From: New Scientist writers (New Scientist articles [2013], 2013.10.29) |
| 17604 | We are halfway to synthesising any molecule we want [New Sci.] |
| Full Idea: Ei-ichi Negishi (Nobel chemist of 2010) says 'the ultimate goal is to be able to synthesise any molecule we want. We are probably about halfway there'. | |
| From: New Scientist writers (New Scientist articles [2013], 2010.10.16) |
| 17603 | Chemistry just needs the periodic table, and protons, electrons and neutrinos [New Sci.] |
| Full Idea: Ei-ichi Negishi (Nobel chemist of 2010) says 'I work with the periodic table in front of me at all times, and approach all challenges in terms of three particles, positively charged protons, negatively charged electrons, and neutral neutrinos'. | |
| From: New Scientist writers (New Scientist articles [2013], 2010.10.16) |
| 2269 | God the creator is an intelligent, infinite, powerful substance [Descartes] |
| Full Idea: I understand by the name "God" a certain substance that is infinite, independent, supremely intelligent and supremely powerful, and created me along with everything that exists. | |
| From: René Descartes (Meditations [1641], §3.45) |
| 2289 | Nothing apart from God could have essential existence, and such a being must be unique and eternal [Descartes] |
| Full Idea: I cannot think of anything aside from God alone to whose essence existence belongs, and I cannot conceive of two or more such Gods. I also perceive that God must be eternal, and have other perfect qualities. | |
| From: René Descartes (Meditations [1641], §5.68) |
| 13465 | Only God is absolutely infinite [Cantor, by Hart,WD] |
| Full Idea: Cantor said that only God is absolutely infinite. | |
| From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 1 | |
| A reaction: We are used to the austere 'God of the philosophers', but this gives us an even more austere 'God of the mathematicians'. |
| 2275 | It is self-evident that deception is a natural defect, so God could not be a deceiver [Descartes] |
| Full Idea: It is quite obvious that a perfect God cannot be a deceiver, for it is manifest by the light of nature that all fraud and deception depend on some defect. | |
| From: René Descartes (Meditations [1641], §3.52) |
| 2287 | Existence and God's essence are inseparable, like a valley and a mountain, or a triangle and its properties [Descartes] |
| Full Idea: Existence can no more be separated from God's essence than its having three angles equal to two right angles can be separated from the essence of a triangle, or than the idea of a valley can be separated from the idea of a mountain. | |
| From: René Descartes (Meditations [1641], §5.66) |
| 2274 | The idea of God in my mind is like the mark a craftsman puts on his work [Descartes] |
| Full Idea: In creating me, God has endowed me with the idea of God, so that it would be like the mark of the craftsman impressed upon his work, although this mark need not be something distinct from the work itself. | |
| From: René Descartes (Meditations [1641], §3.51) |
| 2268 | One idea leads to another, but there must be an initial idea that contains the reality of all the others [Descartes] |
| Full Idea: Although one idea can perhaps issue from another, nevertheless no infinite regress is permitted here; eventually some first idea must be reached whose cause is a sort of archetype that contains formally all the reality that is in the idea. | |
| From: René Descartes (Meditations [1641], §3.42) |
| 2288 | I cannot think of a supremely perfect being without the supreme perfection of existence [Descartes] |
| Full Idea: I am not free to think of God without existence, that is, a supremely perfect being without a supreme perfection. | |
| From: René Descartes (Meditations [1641], §5.67) |
| 3632 | We mustn't worship God as an image because we have no idea of him [Hobbes on Descartes] |
| Full Idea: We are forbidden to worship God in the form of an image, for otherwise we might think that we were conceiving of him who is incapable of being conceived. It seems, then, that there is no idea of God in us. | |
| From: comment on René Descartes (Meditations [1641], §5.65) by Thomas Hobbes - Objections to 'Meditations' (Third) 180 |
| 3633 | We can never conceive of an infinite being [Gassendi on Descartes] |
| Full Idea: The human intellect is not capable of conceiving of infinity, and hence it neither has nor can contemplate any idea representing an infinite thing. | |
| From: comment on René Descartes (Meditations [1641], §5.65) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 286 |
| 5036 | Descartes cannot assume that a most perfect being exists without contradictions [Leibniz on Descartes] |
| Full Idea: Descartes' error is in assuming without proof that a most perfect being does not involve a contradiction. | |
| From: comment on René Descartes (Meditations [1641], §5.67) by Gottfried Leibniz - A Specimen of Discoveries p.76 | |
| A reaction: Certainly Descartes seems obliged to grasp the concept of God 'clearly and distinctly', so there must be an absence of contradictions. But does Descartes have to prove that there are no contradictions in his concept of a triangle? Is self-evidence enough? |
| 3638 | Existence is not a perfection; it is what makes perfection possible [Gassendi on Descartes] |
| Full Idea: Existence is not a perfection in God or in anything else; it is that without which no perfections can be present. | |
| From: comment on René Descartes (Meditations [1641], §5.67) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 323 |
| 2277 | Since God does not wish to deceive me, my judgement won't make errors if I use it properly [Descartes] |
| Full Idea: Since God does not wish to deceive me, he assuredly has not given me a faculty of judgement with which I could never make a mistake, when I use it properly. | |
| From: René Descartes (Meditations [1641], §4.54) |
| 2278 | Error arises because my faculty for judging truth is not infinite [Descartes] |
| Full Idea: I make mistakes because the faculty of judging the truth, which I got from God, is not, in my case, infinite. | |
| From: René Descartes (Meditations [1641], §4.54) |
| 3636 | God didn't give us good judgement even about our own lives [Gassendi on Descartes] |
| Full Idea: God is not to be blamed for giving puny man a faculty of judging that is too small to cope with everything, but we may still wonder why our judgement is uncertain, confused and inadequate even for the few matters he did want us to decide upon. | |
| From: comment on René Descartes (Meditations [1641], §4.58) by Pierre Gassendi - Objections to 'Meditations' (Fifth) 314 |
| 2281 | If we ask whether God's works are perfect, we must not take a narrow viewpoint, but look at the universe as a whole [Descartes] |
| Full Idea: Whenever we ask whether the works of God are perfect, we should keep in view not simply some one creature in isolation from the rest, but the universe as a whole. | |
| From: René Descartes (Meditations [1641], §4.55) |