70 ideas
| 6979 | Serious metaphysics cares about entailment between sentences [Jackson] |
| Full Idea: Serious metaphysics is committed to views about which sentences entail which other sentences. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
| A reaction: This does not say that metaphysics is only about entailment, or (even worse) only about sentences. Put another way: if we wish to be wise, we must study the implications of our beliefs. Yes. |
| 6980 | Conceptual analysis studies whether one story is made true by another story [Jackson] |
| Full Idea: Conceptual analysis is the very business of addressing when and whether a story told in one vocabulary is made true by one told in some allegedly more fundamental vocabulary. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.2) | |
| A reaction: This is a view of linguistic analysis as focusing on entailments rather than on usage or truth conditions. If philosophy is the attempt to acquire a totally consistent set of beliefs (a plausible view), then Jackson is right. |
| 6983 | Intuitions about possibilities are basic to conceptual analysis [Jackson] |
| Full Idea: Intuitions about possibilities are the bread and butter of conceptual analysis. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: Hence the centrality of the debate over conceivability and possibility. Which seems to reduce to the relationship between 'intuition' and 'imagination'. Imagination is a very weak guide to what is possible, and intuition is very uncertain.... |
| 14707 | Conceptual analysis is needed to establish that metaphysical reductions respect original meanings [Jackson, by Schroeter] |
| Full Idea: On the empiricist view of meaning, the relevance of conceptual analysis to metaphysics is that it establishes that a putative reduction respects the original meaning of the target expression. | |
| From: report of Frank Jackson (From Metaphysics to Ethics [1998], p.28) by Laura Schroeter - Two-Dimensional Semantics 2.2.4 |
| 7005 | Something can only have a place in a preferred account of things if it is entailed by the account [Jackson] |
| Full Idea: The one and only way of having a place in an account told in some set of preferred terms is by being entailed by that account - a view I will refer to as the entry by entailment thesis. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
| A reaction: How do we distinguish between the original account, which seems to be just accepted, and the additions which accrue because they are entailed by it? Why does this club distinguish members from guests? |
| 6994 | Truth supervenes on being [Jackson] |
| Full Idea: Truth supervenes on being. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: A nice slogan for those of us who find the word 'truth' to be meaningful. |
| 8720 | A logic is 'relevant' if premise and conclusion are connected, and 'paraconsistent' allows contradictions [Priest,G, by Friend] |
| Full Idea: Priest and Routley have developed paraconsistent relevant logic. 'Relevant' logics insist on there being some sort of connection between the premises and the conclusion of an argument. 'Paraconsistent' logics allow contradictions. | |
| From: report of Graham Priest (works [1998]) by Michèle Friend - Introducing the Philosophy of Mathematics 6.8 | |
| A reaction: Relevance blocks the move of saying that a falsehood implies everything, which sounds good. The offer of paraconsistency is very wicked indeed, and they are very naughty boys for even suggesting it. |
| 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. |
| 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. |
| 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'. |
| 6984 | Smooth reductions preserve high-level laws in the lower level [Jackson] |
| Full Idea: In a 'smooth' reduction the laws of the reduced theory (thermodynamics of gases) are pretty much preserved in (and isomorphic with) the corresponding laws in the reducing theory (molecular or kinetic theory of gases). | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: Are the 'laws' of weather (e.g. linking humidity, temperature and pressure to rainfall) preserved at the level of physics? One might say that they are not preserved, but they are not lost either (they just fade away). Contradictions would be worrying. |
| 6978 | Baldness is just hair distribution, but the former is indeterminate, unlike the latter [Jackson] |
| Full Idea: Baldness is a much more indeterminate matter than is hair distribution, nevetheless baldness is nothing over and above hair distribution. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], p.22) | |
| A reaction: This seems to support Williamson's view that there is no vagueness in nature, and that 'vague' is an entirely epistemological concept. |
| 6993 | Redness is a property, but only as a presentation to normal humans [Jackson] |
| Full Idea: We typically count things as red just if they have a property that interacts with normal human beings to make the object look red in such a way that their so looking counts as a presentation of the property to normal humans. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.4) | |
| A reaction: This is Jackson's careful statement of the 'Australian' primary property view of colours. He is trying to make red a real property of objects, but personally I take the mention of 'normal' humans as a huge danger sign. Nice try, but no. See Idea 5456. |
| 6987 | We should not multiply senses of necessity beyond necessity [Jackson] |
| Full Idea: We should not multiply senses of necessity beyond necessity. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: It would be nice if there was just one sense of necessity, with the multiplication arising from the different ways in which necessities arise. In chess, checkmate is a necessity which rests on contingencies. Absolute necessities seem different. |
| 6988 | Mathematical sentences are a problem in a possible-worlds framework [Jackson] |
| Full Idea: There is notoriously a problem about what to say concerning mathematical sentences within the possible-worlds framework. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3 n25) | |
| A reaction: Presumably this concerns possible axioms and their combinations. |
| 6975 | Possible worlds could be concrete, abstract, universals, sentences, or properties [Jackson] |
| Full Idea: Possible worlds might be concrete (Lewis), or abstract (Stalnaker), or structured universals (Forrest), or collections of sentences (Jeffrey), or mere combinations of properties and relations (Armstrong). | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
| A reaction: A helpful summary. I don't like concrete, or collections of sentences. Whatever they are, they had better be 'possible', so not any old collection or idea will do. |
| 6982 | Long arithmetic calculations show the a priori can be fallible [Jackson] |
| Full Idea: We know that being fallible and being a priori can co-exist - the results of long numerical additions are well-known examples. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.2) | |
| A reaction: I see this realisation as a good example of progress in philosophy. Russell, who says self-evidence comes in degrees, deserves major credit. It is the key idea that once again makes rationalism respectable. |
| 6991 | We examine objects to determine colour; we do not introspect [Jackson] |
| Full Idea: We examine objects to determine their colour; we do not introspect. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: Interesting, but the theory of secondary qualities did not arise from experience, but from a theory about what is actually going on. Compare pain appearing to be in your foot. |
| 6976 | In physicalism, the psychological depends on the physical, not the other way around [Jackson] |
| Full Idea: Physicalism is associated with various asymmetry doctrines, most famously with the idea that the psychological depends in some sense on the physical, and not the other way around. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
| A reaction: Sounds okay to me. Shadows depend on objects, and not the other way round. It might suggest properties depending on substances (or bare particulars), but I prefer the dependence of processes on mechanisms (waterfalls on liquid water). |
| 6986 | Is the dependence of the psychological on the physical a priori or a posteriori? [Jackson] |
| Full Idea: Should the necessary passage from the physical account of the world to the psychological one that physicalists are committed to, be placed in the a posteriori or the a priori basket? | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: That is, is 'the physical entails the mental' empirical or a priori? See Idea 3989. If we can at least dream of substance dualism, it is hard to see how it could be fully a priori. I think I prefer to see it as an inductive explanation. |
| 6992 | If different states can fulfil the same role, the converse must also be possible [Jackson] |
| Full Idea: It would be strange if having learnt the lesson of multiple realisability that the same role may be filled by different states, we turned around and insisted that the converse - different roles filled by the same state - is impossible. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.4 n3) | |
| A reaction: Good. The world is full of creatures who seem to enjoy the smell of decay etc. Some people (not me) like horror films. The separation of qualia and role leaves type-type physicalism as a possibility. Survival needs similar roles, not similar qualia. |
| 6996 | Folk psychology covers input, internal role, and output [Jackson] |
| Full Idea: Folk psychology has a tripartite nature, with input clauses, internal role clauses, and output clauses. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: Interesting, particularly that folk psychology refers to internal roles, or attempts to explain what is going on inside the 'black box'. The folk have collectively worked out a standard flow diagram for human thought. |
| 6977 | Egocentric or de se content seems to be irreducibly so [Jackson] |
| Full Idea: I have been convinced by arguments (e.g. of Perry, Castañeda and Lewis) that egocentric or de se content is irreducibly so. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.1) | |
| A reaction: This is associated with the use of indexicals (like 'I' and 'now') in language. Quine disagrees, and should not be written off. Any theory of content, concepts, meaning etc. must clearly taken account of such subjective language. |
| 6990 | Keep distinct the essential properties of water, and application conditions for the word 'water' [Jackson] |
| Full Idea: My guess is that objectors to the deflationary account of the Twin Earth parable are confusing the essential properties of water with the question of what is essential for being water. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: That is, we must distinguish between the actual ontology of water's properties and the conditions under which we (in our society) apply the word 'water'. Interesting. The latter issue, though, might push us back towards internalism... |
| 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? |
| 6985 | Analysis is finding necessary and sufficient conditions by studying possible cases [Jackson] |
| Full Idea: Conceptual analysis is sometimes understood as the business of finding necessary and sufficient conditions by the method of possible cases. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: Some (e.g. Stich) reject this, but it seems to me undeniable that the procedure can be very illuminating, even if it is never totally successful. Jackson prefers to see analysis as the study of entailments between stories about the world. |
| 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. |
| 6995 | Successful predication supervenes on nature [Jackson] |
| Full Idea: Successful predication supervenes on nature. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: A nice slogan, but it is in danger of being a tautology. If I say x and y 'are my favourites/are interesting', is that 'successful' predication? Is 'Juliet is the sun' unsuccessful? |
| 6989 | I can understand "He has a beard", without identifying 'he', and hence the truth conditions [Jackson] |
| Full Idea: If I hear someone say "He has a beard", and I don't know whether it is Jackson, Jones, or someone else, I don't know which proposition is being expressed in the sense of not knowing the conditions under which what is said is true. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.3) | |
| A reaction: This is the neatest and simplest problem I have encountered for Davidson's truth-conditions account of meaning. However, we probably just say that we understand the sense but not the reference. The strict-and-literal but not contextual meaning. |
| 6998 | Folk morality does not clearly distinguish between doing and allowing [Jackson] |
| Full Idea: We have, it seems to me, currently no clear sense of the place and rationale of the distinction between doing and allowing in folk morality. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: Does this mean that philosophers should endeavour to appear on television in order to improve folk morality, so that Jackson, back at the ranch, can then infer the meanings of moral terms from the new improved version? |
| 6997 | Moral functionalism says moral terms get their meaning from their role in folk morality [Jackson] |
| Full Idea: Moral functionalism is the view that the meanings of moral terms are given by their place in the network of input, internal clauses, and output that makes up folk psychology. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: Jackson considers this enough to support a cognitivist view of morality. In assuming that there is something stable called 'folk morality' he seems to be ignoring questions about cultural relativism. |
| 7000 | Which are prior - thin concepts like right, good, ought; or thick concepts like kindness, equity etc.? [Jackson] |
| Full Idea: 'Centralists' (e.g. Bernard Williams) say thin ethical concepts (right, good, ought) are conceptually fundamental; 'non-centralists' (e.g. Susan Hurley) say that such concepts are not conceptually prior to kindness, equity and the like. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: My immediate intuition is to side with Susan Hurley, since morality grows out of immediate relationships, not out of intellectual principles and theoretical generalisations. This would go with particularist views of virtue theory. |
| 6999 | It is hard to justify the huge difference in our judgements of abortion and infanticide [Jackson] |
| Full Idea: We allow that abortion is permissible in many circumstances, but infanticide is hardly ever permissible, and yet it is hard to justify this disparity in moral judgement in the sense of finding the relevant difference. | |
| From: Frank Jackson (From Metaphysics to Ethics [1998], Ch.5) | |
| A reaction: The implications of this are tough to face. A foetus is (maybe) just not as important as a new-born babe - and so a new-born babe is of less importance than a five-year old. Birth is (or was) a hugely dangerous hurdle to be cleared. |
| 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'. |