122 ideas
| 19695 | The devil was wise as an angel, and lost no knowledge when he rebelled [Whitcomb] |
| Full Idea: The devil is evil but nonetheless wise; he was a wise angel, and through no loss of knowledge, but, rather, through some sort of affective restructuring tried and failed to take over the throne. | |
| From: Dennis Whitcomb (Wisdom [2011], 'Argument') | |
| A reaction: ['affective restructuring' indeed! philosophers- don't you love 'em?] To fail at something you try to do suggests a flaw in the wisdom. And the new regime the devil wished to introduce doesn't look like a wise regime. Not convinced. |
| 23657 | The existence of tensed verbs shows that not all truths are necessary truths [Reid] |
| Full Idea: If all truths were necessary truths, there would be no occasion for different tenses in the verbs by which they are expressed. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: This really is like modern linguistic analysis. Of course the tensed verbs might only indicate times when the universal necessities have been noticed by speakers. …But then the noticing would be contingent! |
| 23655 | An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid] |
| Full Idea: It is a good argument ad hominem, if it can be shewn that a first principle which a man rejects, stands upon the same footing with others which he admits, …for he must then be guilty of an inconsistency. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4) | |
| A reaction: Good point. You can't divorce 'pure' reason from the reasoners, because the inconsistency of two propositions only matters when they are both asserted together. …But attacking the ideas isn't quite the same as attacking the person. |
| 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 |
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞..... | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2 |
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 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 |
| 17831 | Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake] |
| Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another. | |
| From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6 | |
| A reaction: Lake suggests that it should therefore be called CZF. |
| 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. |
| 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 Michèle 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? |
| 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. |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence). | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 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 |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 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 |
| 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. |
| 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. |
| 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 |
| 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? |
| 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? |
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| Full Idea: The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate. | |
| From: George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind | |
| A reaction: Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!). |
| 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'. |
| 23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
| Full Idea: The belief of the existence of anything seems to suppose a notion of existence - a notion too abstract, perhaps, to enter into the mind of an infant. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 05) | |
| A reaction: But even a small infant has to cope with the experience of waking up from a dream. I don't see how existence can be anything other than a primitive concept in any system of ontology. |
| 23664 | Powers are quite distinct and simple, and so cannot be defined [Reid] |
| Full Idea: Power is a thing so much of its own kind, and so simple in its nature, as to admit of no logical definition. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: True. And this makes Powers ideally suited for the role of primitives in a metaphysics of nature. |
| 23669 | Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid] |
| Full Idea: Those philosophers who attribute to matter the power of gravitation, and other active powers, teach us, at the same time, that matter is a substance altogether inert, and merely passive; …that those powers are impressed on it by some external cause. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: This shows the dilemma of the period, when 'laws of nature' were imposed on passive matter by God, and yet gravity and magnetism appeared as inherent properties of matter. |
| 23666 | It is obvious that there could not be a power without a subject which possesses it [Reid] |
| Full Idea: It is evident that a power is a quality, and cannot exist without a subject to which it belongs. That power may exist without any being or subject to which that power may be attributed, is an absurdity, shocking to every man of common understanding. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: This is understandble in the 18th C, when free-floating powers were inconceivable, but now that we have fields and plasmas and whatnot, we can't rule out pure powers as basic. However, I incline to agree with Reid. Matter is active. |
| 23651 | Universals are not objects of sense and cannot be imagined - but can be conceived [Reid] |
| Full Idea: A universal is not an object of any sense, and therefore cannot be imagined; but it may be distinctly conceived. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
| A reaction: If you try to imagine whiteness, what size is it, and what substance embodies it? Neither are needed to think of whiteness, so Reid is right. A nice observation. |
| 23650 | Only individuals exist [Reid] |
| Full Idea: Everything that really exists is an individual. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
| A reaction: Locke is the probable inspiration for this nominalist affirmation. Not sure how high temperature plasma, or the oceans of the world, fit into this. On the whole I agree with him. He is mainly rejecting abstract universals. |
| 23649 | No one thinks two sheets possess a single whiteness, but all agree they are both white [Reid] |
| Full Idea: If we say that the whiteness of this sheet is the whiteness of another sheet, every man perceives this to be absurd; but when he says both sheets are white, this is true and perfectly understood. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 3) | |
| A reaction: Well said. Only a philosopher could think the whiteness of one sheet is exactly the same entity as the whiteness of a different sheet. We seem to have brilliantly and correctly labelled them both as white, and then thought that one word implies one thing. |
| 23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
| Full Idea: Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition. |
| 1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
| Full Idea: Identity supposes an uninterrupted continuance of existence….Otherwise we must suppose a being to exist after it has ceased to exist, and to have existed before it was produced, which are manifest contradictions. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: I take the point to be that if something is supposed to survive a gap in its existence, that must imply that it somehow exists during the gap. If a light flashes on and off, is it really a new entity each time? |
| 21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
| Full Idea: All bodies, as they consist of innumerable parts, are subject to continual changes of their substance. When such changes are gradual, because language could not afford a different name for each state, it retains the same name and is considered the same. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: This is hard to deny. We could hardly rename a child each morning. Simlarly, we can't have a unique name for each leaf on a tree. Economy of language explains a huge amount in philosophy. |
| 21320 | Identity is familiar to common sense, but very hard to define [Reid] |
| Full Idea: Every man of common sense has a clear and distinct notion of identity. If you ask for a definition of identity, I confess I can give none. It is too simple a notion. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: 'Identical' seems to be a two-place predicate, but the only strict way two things can be identical is if there is actually just one thing. In which case just drop the word 'identity' (instead of defining it), and say there is just one thing here. |
| 1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
| Full Idea: Identity can only be affirmed of things which have a continued existence. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: This doesn't mean that Reid thinks there is nothing more to the identity than their similitude. But he, like Hume, denies that there is personal identity at any given instant. Reid is better at criticism than at formulating his own theory. |
| 11874 | Real identity admits of no degrees [Reid] |
| Full Idea: Wherever identity is real, it admits of no degrees. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785]), quoted by David Wiggins - Sameness and Substance Renewed 6 epig | |
| A reaction: Wiggins quotes this with strong approval. Personally I am inclined to think that identity may admit of no degrees in human thought, because that is the only way we can do it, but the world is full of uncertain identities, at every level. |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| Full Idea: Reid pointed out how easily conceivable mathematical and geometric impossibilities are. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], IV.III) by George Molnar - Powers 11.3 | |
| A reaction: The defence would be that you have to really really conceive them, and the only way the impossible can be conceived is by blurring it at the crucial point, or by claiming to conceive more than you actually can |
| 23659 | If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid] |
| Full Idea: If any man could be found so frantic as to deny that he thinks, while he is conscious of it, I may wonder, I may laugh, or I may pity him, but I cannot reason the matter with him. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: An example of the influence of Descartes' Cogito running through all subsequent European philosophy. There remain the usual questions about personal identity which then arise, but Reid addresses those. |
| 23662 | The existence of ideas is no more obvious than the existence of external objects [Reid] |
| Full Idea: If external objects be perceived immediately, we have the same reason to believe their existence as philosophers have to believe the existence of ideas. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: He doesn't pay much attention to mirages and delusions, but in difficult conditions of perception we are confident of our experiences but doubtful about the objects they represent. |
| 23661 | We are only aware of other beings through our senses; without that, we are alone in the universe [Reid] |
| Full Idea: We can have no communication, no correspondence or society with any created being, but by means of our senses. And, until we rely on their testimony, we must consider ourselves as being alone in the universe. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: I'm not aware of any thinker before this so directly addressing solipsism. Even the champion of direct and common sense realism has to recognise the intermediary of our senses when accepting other minds. |
| 23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
| Full Idea: Self-evident propositions are those which appear evident to every man of sound understanding who apprehends the meaning of them distinctly, and attends to them without prejudice. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 10) | |
| A reaction: I suspect that there are some truths which are self-evident to dogs. There are also truths which are self-evident to experts, but not to ordinary persons of good understanding. Self-evidence is somewhat contextual. Self-evidence can be empirical. |
| 7631 | Sensation is not committed to any external object, but perception is [Reid] |
| Full Idea: Sensation, by itself, implies neither the conception nor belief of any external object. ...Perception implies a conviction and belief of something external. ...Things so different in their nature ought to be distinguished. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], II.16), quoted by Barry Maund - Perception | |
| A reaction: Maund sees this as the origin of the two-stage view of perception, followed by Chisholm, Evans, Dretske and Lowe. It implies that 'looks', 'tastes', 'sounds' etc. are ambiguous words, having either phenomenal or realist meanings. I like it. |
| 23637 | Primary qualities are the object of mathematics [Reid] |
| Full Idea: The primary qualities are the object of the mathematical sciences. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: He spells out this crucial point, which is not so obvious in Locke. The sciences totally rely on the primary qualities, so it is ridiculous to reject the distinction (which Reid accepts). |
| 23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
| Full Idea: The thought of a secondary quality always carries us back to the sensation which it produces.We give the same name to both, and are apt to confound them. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 17) | |
| A reaction: 'Redness', for example. Reid puts the point very nicely. Secondary qualities are not entirely mental; they pick out features of the world, but are much harder to understand than the primary qualities. The qualia question lurks. |
| 23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
| Full Idea: If it be made a question whether the toothache be in the mind that feels it, or in tooth that is affected, much might be said on both sides, while it is not observed that the word has two meanings. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 18) | |
| A reaction: I'm glad Reid was struck by the weird phenomenon of the brain apparently 'projecting' a pain into a tooth. Presumably before the brain's role was known, people were unaware of this puzzle. There certainly are not two distinct experiences. |
| 6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
| Full Idea: Reid is often represented by modern opponents of the empiricists as the outstanding protagonist of direct or naïve realism and common sense in the eighteenth century. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 2: Senses [1785]) by Howard Robinson - Perception 1.6 | |
| A reaction: Robinson does not deny that this is Reid's view. Keith Lehrer is a great fan of Reid. Personally I think direct realism is quite clearly false, so I find myself losing interest in Reid's so-called 'common sense'. |
| 23633 | Many truths seem obvious, and point to universal agreement - which is what we find [Reid] |
| Full Idea: There are many truths so obvious to the human faculties, that it should be expected that men should universally agree in them. And this is actually found to be the case with regard to many truths, against which we find no dissent. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 2) | |
| A reaction: He says that a few sceptical philosophers may disagree. This is a nice statement of his creed of common sense. I agree with him, and Aristotle observes the same fact. |
| 23654 | In obscure matters the few must lead the many, but the many usually lead in common sense [Reid] |
| Full Idea: In matters beyond the reach of common understanding, the many are led by the few, and willingly yield to their authority. But, in matters of common sense, the few must yield to the many, when local and temporary prejudices are removed. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4) | |
| A reaction: Wishful thinking in the 21st century, when the many routinely deny the authority of the expert few, and the expert few occasionally prove that the collective common sense of the many is delusional. I still sort of agree with Reid. |
| 23644 | Without memory we could have no concept of duration [Reid] |
| Full Idea: It is impossible to show how we could acquire a notion of duration if we had no memory. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], 1) | |
| A reaction: We would probably not have a notion of duration if we possessed a memory, but nothing ever changed. Maybe in Shoemaker's frozen worlds they retain memories, but nothing happens? |
| 23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
| Full Idea: Every man feels he must believe what he distinctly remembers, though he can give no other reason for his belief, but that he remembers the thing distinctly; whereas, when he merely distinctly imagines a thing, he has no belief in it upon that account. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], 1) | |
| A reaction: The word 'distinct' is doing some heavy work here. I fear that believing the memory is the only criterion we have for calling it distinct. As a boy I was persuaded to change my testimony about a car accident, and I realised I was not distinct about it. |
| 23660 | The theory of ideas, popular with philosophers, means past existence has to be proved [Reid] |
| Full Idea: The theory concerning ideas, so generally received by philosophers, destroys all the authority of memory. …This theory made it necessary for them to find out arguments to prove the existence of external objects …and of things past. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: Reid was a very articulate direct realist. He seems less aware than the rest of us of the problem of delusions and false memories. Our strong sense that immediate memories are reliable is certainly inexplicable. |
| 23641 | People dislike believing without evidence, and try to avoid it [Reid] |
| Full Idea: To believe without evidence is a weakness which every man is concerned to avoid, and which every man wishes to avoid. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: It seems to be very common, though, for people to believe things on incredibly flimsy evidence, if they find the belief appealing. This is close to Clifford's Principle, but not quite as dogmatic. |
| 23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
| Full Idea: If Nature gives us information of things that concern us, by other means that by reasoning, reason itself will direct us to receive that information with thankfulness, and to make the best use of it. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 20) | |
| A reaction: This is more of a claim than an argument, but it is hard to see how anything could even be seen as evidence if some sort of rational judgement has not been made. The clever detective sees which facts are evidence. |
| 23549 | We treat testimony with a natural trade off of belief and caution [Reid, by Fricker,M] |
| Full Idea: Reid says we naturally operate counterpart principles of veracity and credulity in our testimonial exchanges. | |
| From: report of Thomas Reid (An Enquiry [1764], 6.24) by Miranda Fricker - Epistemic Injustice 1.3 n11 | |
| A reaction: What you would expect from someone who believed in common sense. Fricker contrasts this with Tyler Burge's greater confidence, and then criticises both (with Reid too cautious and Burge over-confident). She defends a 'low-level' critical awareness. |
| 1356 | A person is a unity, and doesn't come in degrees [Reid] |
| Full Idea: The identity of a person is a perfect identity: wherever it is real, it admits of no degrees; and it is impossible that a person should be in part the same, and in part different; because a person is a 'monad', and is not divisible into parts. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: I don't accept this, because I don't accept the metaphysics needed to underpin it. To watch a person with Alzheimer's disease fade out of existence before they die seems sufficient counter-evidence. I believe in personal identity, but it isn't 'perfect'. |
| 23658 | Consciousness is an indefinable and unique operation [Reid] |
| Full Idea: Consciousness is an operation of the understanding of its own kind, and cannot be logically defined. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 5) | |
| A reaction: It is interesting that has tried to define consciousness, rather than just assuming it. I note that he calls consciousness an 'operation', rather than an entity. Good. |
| 23665 | Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid] |
| Full Idea: Consciousness is that power of the mind by which it has an immediate knowledge of its own operations. …Every operation of the mind is the exertion of some power of the mind. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 1) | |
| A reaction: I strongly favour this account of the mind and consciousness in terms of powers, because they give the best basis for their dynamic nature, and seem to be primitives which terminate all of our explanations. Science identifies the powers for us. |
| 1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
| Full Idea: Identity, when applied to persons, has no ambiguity, and admits of no degrees. It is the foundation of all rights and obligations, and of all accountableness. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: This seems to me to be one of the key mistakes in all of philosophy - thinking that items must always be all-or-nothing. If a person deteriorates through Alzheimer's, there seem to be obvious degrees of personhood. Responsibility comes in degrees, too. |
| 21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
| Full Idea: The conviction of personal identity is indispensably necessary to all exercise of reason. Reasoning is made up of successive parts. Without the conviction that the antecedent have been seen by me, I could have no reason to proceed to the consequent. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: Society needs philosophers precisely to point such things out. It isn't conclusive, but populist waffle about the self not existing undermines the very concept of a 'train of thought', which everybody is signed up to. Trains of thought can take years. |
| 21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
| Full Idea: A man challenges a thief in possession of his horse only on similarity. The testimony of witnesses to the identity of a person is commonly grounded on no other evidence. ...Evidence of our own identity is grounded in memory, and gives undoubted certainty. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: With other people the best we can hope for is type-identity, hoping that each individual being is a unique type, but with otherselves we are always confident of establishing token identity. Could I have been someone different yesterday, without realising? |
| 21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
| Full Idea: Although memory gives the most irresistible evidence of my being the identical person that did such a thing, I may have other good evidence of things which befell me. I know who bare me and suckled me, but I do not remember those events. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: A splendidly accurate and simple observation. Reid's criticisms of Locke are greatly superior to those of Butler. We now have vast collections of photographs showing our past identities. |
| 21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
| Full Idea: If the same consciousness can be transferred from one intelligent being to another, then two or twenty beings may be the same person. If he may lose the consciousness of actions done by him, one intelligent being may be two or twenty different persons. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: Reid says Locke was aware of these two implications of his theory of personal identity (based on consciousness). The first example is me replicated like software. The second is if I forget that I turned the light off, then who did turn the light off? |
| 21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
| Full Idea: Suppose a brave officer, flogged as a boy for robbing an orchard, to have captured a standard in his first campaign, and become a general in advanced life. [If the general forgets the flogging] he is and at the same time is not the same as the boy. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: The point is that strict identity has to be transitive, and if the general forgets his boyhood that breaks the transitivity. If identity is less strict there is no problem. The general may only have memories related to some part of his boyhood. |
| 21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
| Full Idea: When a stolen horse is claimed, the only evidence that this is the same horse is similitude. But would it not be ridiculous from this to infer that the identity of a horse consists in similitude only? | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: Actually that is exactly Hume's view of the matter (Idea 21292). For a strict empiricist there is nothing else be close resemblance over time. I prefer Reid's account to Hume's. - but then I am not a 'strict' empiricist. |
| 1366 | If consciousness is personal identity, it is continually changing [Reid] |
| Full Idea: Is it not strange that the identity of a person should consist in a thing (consciousness) which is continually changing? | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 6) | |
| A reaction: This is the panicky slippery slope view of Locke, that sees his doctrine as the first step to the destruction of religion. The fact is, though, that parts of my consciousness changes continually, but other parts stay the same for years on end. |
| 1352 | Thoughts change continually, but the self doesn't [Reid] |
| Full Idea: My thoughts, and actions, and feelings, change every moment: they have no continued, but a successive, existence: but that self, or I, to which they belong, is permanent. | |
| From: Thomas Reid (Essays on Intellectual Powers 3: Memory [1785], III.Ch 4) | |
| A reaction: The word 'permanent' may be excessive, but one could hardly say there is nothing more to personal identity than the contents of consciousnes, given how much and how quickly those continually fluctuate. |
| 23681 | The first motion or effect cannot be produced necessarily, so the First Cause must be a free agent [Reid] |
| Full Idea: That the first motion, or the first effect, whatever it be, cannot be produced necessarily, and, consequently, that the First Cause must be a free agent, has been demonstrated clearly and unanswerably. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 8) | |
| A reaction: He has said that the First Cause can only be conceived by us as an 'agent'. If there is an agential First Cause, then he must be right. It is this need for God to be free which makes scepticism about free will unacceptable to many. |
| 23676 | A willed action needs reasonable understanding of what is to be done [Reid] |
| Full Idea: There can be no will without such a degree of understanding, at least, as gives the conception of that which we will. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 1) | |
| A reaction: Presumably this 'conception' includes an understanding of the probable consequences, but they are of infinite complexity. I see this as an objection to 'ultimate' free will and responsibility, because there are only ever degrees of understanding. |
| 23668 | Our own nature attributes free determinations to our own will [Reid] |
| Full Idea: Every man is led by nature to attribute to himself the free determination of his own will, and to believe those events to be in his power which depend upon his will. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: I'm happy to say we are all responsible for those actions which are caused by the conscious decisions of our own will (our mental decision mechanisms), but personally I would drop the word 'free', which adds nothing. We are not 'ultimately' responsible. |
| 23680 | We are morally free, because we experience it, we are accountable, and we pursue projects [Reid] |
| Full Idea: I believe in moral liberty first because we have a natural conviction of belief that in many cases we act freely, second because we are accountable, and third because we can prosecute an end by a long series of means adapted. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 5) | |
| A reaction: This is his final summary of why he believes in free will. Why didn't Plato and Aristotle have this natural belief? He could only believe we are 'accountable' because he believes in free will. Ants and bees pursue lengthy projects. Hm. |
| 23652 | We must first conceive things before we can consider them [Reid] |
| Full Idea: No man can consider a thing which he does not conceive. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 6) | |
| A reaction: This seems to imply concepts, but we should not take this to be linguistic, since animals obviously consider things and make judgements. |
| 23656 | The structure of languages reveals a uniformity in basic human opinions [Reid] |
| Full Idea: What is common in the structure of languages, indicates an uniformity of opinion in those things upon which that structure is grounded. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 4) | |
| A reaction: Reid was more interested than his contemporaries in the role of language in philosophy. The first idea sounds like Chomsky. I would add to this that the uniformity of common opinion reflects uniformities in the world they are talking about. |
| 23630 | Only philosophers treat ideas as objects [Reid] |
| Full Idea: The vulgar allow that an 'idea' implies a mind that thinks, an act of mind which we call thinking, and an object about which we think. But the philosopher conceives a fourth - the idea, which is the immediate object. …I believe this to be a mere fiction. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 1) | |
| A reaction: Another example, to add to Yablo's list, of abstract objects invented by philosophers to fill holes in their theories. This one is illuminating, because we all say 'I've got an idea'. Cf discussions of the redundancy of truth. Cf propositions. |
| 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 Michèle 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? |
| 23648 | First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising') [Reid] |
| Full Idea: First we resolve or analyse a subject into its known attributes, and give a name to each attribute. Then we observe one or more attributes to be common to many subjects. The first philosophers call 'abstraction', and the second is 'generalising'. | |
| From: Thomas Reid (Essays on Intellectual Powers 5: Abstraction [1785], 3) | |
| A reaction: It is very unfashionable in analytic philosophy to view universals in this way, but it strikes me as obviously correct. There are not weird abstract entities awaiting a priori intuition. There are just features of the world to be observed and picked out. |
| 23653 | If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid] |
| Full Idea: If you perceive an object, white, round, and a foot in diameter, if you had not been able to distinguish the colour from the figure, and both from the magnitude, your senses would only give you one complex and confused notion of all these mingled together | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 1) | |
| A reaction: His point is that if you reject the 'abstraction' of these qualities, you still cannot deny that distinguishing them is an essential aspect of perceiving complex things. Does this mean that animals distinguish such things? |
| 23640 | Only mature minds can distinguish the qualities of a body [Reid] |
| Full Idea: I think it requires some ripeness of understanding to distinguish the qualities of a body from the body; perhaps this distinction is not made by brutes, or by infants. | |
| From: Thomas Reid (Essays on Intellectual Powers 2: Senses [1785], 19) | |
| A reaction: I'm glad the brutes get a mention in his assessment of these questions. I take such thinking to arise from what can be labelled the faculty of abstraction, which presumably only appears in a mature brain. It is second-level thinking. |
| 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. |
| 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
| Full Idea: We call 'cardinal number' the general concept which, by means of our active faculty of thought, arises when we make abstraction from an aggregate of its various elements, and of their order. From this double abstraction the number is an image in our mind. | |
| From: George Cantor (Beitrage [1915], §1), quoted by Kit Fine - Cantorian Abstraction: Recon. and Defence Intro | |
| A reaction: [compressed] This is the great Cantor, creator of set theory, endorsing the traditional abstractionism which Frege and his followers so despise. Fine offers a defence of it. The Frege view is platonist, because it refuses to connect numbers to the world. |
| 23629 | The ambiguity of words impedes the advancement of knowledge [Reid] |
| Full Idea: There is no greater impediment to the advancement of knowledge than the ambiguity of words. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 1) | |
| A reaction: He means that ambiguity leads to long pointless disagreements. |
| 23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
| Full Idea: An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: [compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade. |
| 23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
| Full Idea: The meaning of a word (such as 'felony') is the thing conceived; and that meaning is the conception affixed to it by those who best understand the language. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: He means legal experts. This is precisely that same as Putnam's account of the meaning of 'elm tree'. His discussion here of reference is the earliest I have encountered, and it is good common sense (for which Reid is famous). |
| 20051 | Reid said that agent causation is a unique type of causation [Reid, by Stout,R] |
| Full Idea: Thomas Reid said that an agent's causing something involves a fundamentally different kind of causation from inanimate causing. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Rowland Stout - Action 4 'Agent' | |
| A reaction: I'm afraid the great philosopher of common sense got it wrong on this one. Introducing a new type of causation into our account of nature is crazy. |
| 23678 | A motive is merely an idea, like advice, and not a force for action [Reid] |
| Full Idea: A motive is equally incapable of action and of passion; because it is not a thing that exists, but a thing that is conceived. …Motives may be compared to advice or exhortation. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 4) | |
| A reaction: We say people are motivated by greed or anger or love, which seems a bit stronger than mere advice. |
| 23663 | There are axioms of taste - such as a general consensus about a beautiful face [Reid] |
| Full Idea: I think there are axioms, even in matters of taste. …I never heard of any man who thought it a beauty in a human face to want a nose, or an eye, or to have the mouth on one side. | |
| From: Thomas Reid (Essays on Intellectual Powers 6: Judgement [1785], 6) | |
| A reaction: It is hard to disagree, but the human face may be a special case, since it is so deeply embedded in the minds of even the youngest infants. More recent artists seem able to discover beauty in very unlikely places. |
| 23674 | If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid] |
| Full Idea: If a man should give to his neighbour a potion which he really believes will poison him, but which, in the event, proves salutary, and does much good; in moral estimation, he is a poisoner, and not a benefactor. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: I take Reid to mean that morality concerns how we assess the agent, and not the results of his actions. Mill and Bentham concede that we judge people this way, but don't think morality mainly concerns judging people. |
| 23675 | We shouldn't do to others what would be a wrong to us in similar circumstances [Reid] |
| Full Idea: It is a first principle of morals, that we ought not to do to another what we should think wrong to be done to us in like circumstances. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 6) | |
| A reaction: This negative form of the rule is more plausible than the positive form, presumably because there is more consensus about what we all dislike than what we all prefer. But presents for people that they would like, not that you like. |
| 23672 | To be virtuous, we must care about duty [Reid] |
| Full Idea: A man cannot be virtuous, if he has no regard to duty. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: Thus are Aristotle and Kant united in a simple sentence. Aristotle thinks that a virtuous person thereby sees what is the right thing to do, but I take 'duty' to imply a requirement which comes not from good character but from external society. |
| 23673 | Every worthy man has a principle of honour, and knows what is honourable [Reid] |
| Full Idea: I presume it will be granted, that, in every man of real worth, there is a principle of honour, a regard to what is honourable or dishonourable, very distinct from a regard to his interest. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: Note that there is a 'principle' of honour in a person's character, and there are also actions which are intrinsically honourable or not. I fear that only the worthy are honourable, and only the honourable are worthy! |
| 23632 | Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid] |
| Full Idea: A first principle is that similar effects proceed from the same or similar causes; that we ought to admit of no other causes …but such as are sufficient to account for the effects. | |
| From: Thomas Reid (Essays on Intellectual Powers 1: Preliminary [1785], 2) | |
| A reaction: He treats these as a priori axioms of natural philosophy. In evolution similar causes seem to produce startlingly divergent effects, such as the mating needs of male birds. |
| 8383 | Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane] |
| Full Idea: A famous example of Thomas Reid: day regularly follows night, and night regularly follows day. There is therefore a constant conjunction between night and day. But day does not cause night, nor does night cause day. | |
| From: report of Thomas Reid (Essays on Active Powers 1: Active power [1788]) by Tim Crane - Causation 1.2.2 | |
| A reaction: Not a fatal objection to Hume, of course, because in the complex real world there are huge numbers of nested constant conjunctions. Night and the rotation of the Earth are conjoined. But how do you tell which constant conjunctions are causal? |
| 23677 | We all know that mere priority or constant conjunction do not have to imply causation [Reid] |
| Full Idea: Every man who understands the language knows that neither priority, nor constant conjunction, nor both taken together, imply efficiency. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 2) | |
| A reaction: This invites the question of how we do know causal events, if none of our experiences are enough to prove it. Reid says we have an innate knowledge that all events are caused, but that isn't much help. The presence of power? |
| 23667 | Regular events don't imply a cause, without an innate conviction of universal causation [Reid] |
| Full Idea: A train of events following one another ever so regularly, could never lead us to the notion of a cause, if we had not, from our constitution, a conviction of the necessity of a cause for every event. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 5) | |
| A reaction: Presumably a theist like Reid must assume that the actions of God are freely chosen, rather than necessities. It's hard to see why this principle should be innate in us, and hard to see why it must thereby be true. A bit Kantian, this idea. |
| 23679 | The principle of the law of nature is that matter is passive, and is acted upon [Reid] |
| Full Idea: The law of nature respecting matter is grounded upon this principle: That matter is an inert, inactive substance, which does not act, but is acted upon. | |
| From: Thomas Reid (Essays on Active Powers 4: Liberty of Agents [1788], 5) | |
| A reaction: A clear statement (alongside Euler's) of the 18th century view, still with us, but strikes me as entirely wrong. Their view needs the active power of God to drive the laws. Matter has intrinsic primitive powers, and laws describe patterns of behaviour. |
| 23670 | Scientists don't know the cause of magnetism, and only discover its regulations [Reid] |
| Full Idea: A Newtonian philosopher …confesses his ignorance of the true cause of magnetic motion, and thinks that his business, as a philosopher, is only to find from experiment the laws by which it is regulated in all cases. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Since there is a 'true cause', that implies that the laws don't actively 'regulate' the magnetism, but only describe its regularity, which I think is the correct view of laws. |
| 23671 | Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid] |
| Full Idea: The laws of nature are the rules according to which the effects are produced; but there must be a cause which operates according to these rules. The rules of navigation never navigated a ship. | |
| From: Thomas Reid (Essays on Active Powers 1: Active power [1788], 6) | |
| A reaction: Very nice. No enquirer should be satisfied with merely discovering patterns; the point is to explain the patterns. |
| 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 |
| 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'. |