78 ideas
| 13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
| Full Idea: We can learn from the work of philosophers of other periods only if we are prepared to run the risk of radical and almost inevitable misrepresentation of his thought. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Pref) | |
| A reaction: This sounds about right, and a motto for my own approach to Aristotle and Leibniz, but I see the effort as more collaborative than this suggests. Professional specialists in older philosophers are a vital part of the team. Read them! |
| 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 |
| 13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
| Full Idea: The most productive way in which to attempt an understanding of any philosophical idea is to work on its defence. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.vii) | |
| A reaction: Very nice. The key point is that this brings greater understanding than working on attacking an idea, which presumably has the dangers of caricature, straw men etc. It is the Socratic insight that dialectic is the route to wisdom. |
| 10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
| Full Idea: Frege gave up on the attempt to introduce natural numbers by contextual definition, but the project has been revived by neo-logicists. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction II |
| 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. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
| Full Idea: For Wright, an expression refers to an object if it fulfils the 'syntactic role' of a singular term, and if we have fixed the truth-conditions of sentences containing it in such a way that some of them come out true. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michael Dummett - Frege philosophy of mathematics Ch.15 | |
| A reaction: Much waffle is written about reference, and it is nice to hear of someone actually trying to state the necessary and sufficient conditions for reference to be successful. So is it possible for 'the round square' to ever refer? '...is impossible to draw' |
| 13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
| Full Idea: In the Fregean view number theory is a science, aimed at those truths furnished by the essential properties of zero and its successors. The two broad question are then the nature of the objects, and the epistemology of those facts. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: [compressed] I pounce on the word 'essence' here (my thing). My first question is about the extent to which the natural numbers all have one generic essence, and the extent to which they are individuals (bless their little cotton socks). |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
| Full Idea: Someone could be clear about number identities, and distinguish numbers from other things, without conceiving them as ordered in a progression at all. The point of them would be to make comparisons between sizes of groups. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: Hm. Could you grasp size if you couldn't grasp which of two groups was the bigger? What's the point of noting that I have ten pounds and you only have five, if you don't realise that I have more than you? You could have called them Caesar and Brutus. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
| Full Idea: The invitation to number the instances of some non-sortal concept is intelligible only if it is relativised to a sortal. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: I take this to be an essentially Fregean idea, as when we count the boots when we have decided whether they fall under the concept 'boot' or the concept 'pair'. I also take this to be the traditional question 'what units are you using'? |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
| Full Idea: Wright is claiming that HP is a special sort of truth in some way: it is supposed to be the fundamental truth about cardinality; ...in particular, HP is supposed to be more fundamental, in some sense than the Dedekind-Peano axioms. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: Heck notes that although PA can be proved from HP, HP can be proven from PA plus definitions, so direction of proof won't show fundamentality. He adds that Wright thinks HP is 'more illuminating'. |
| 13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
| Full Idea: Informally, Peano's axioms are: 0 is a number, numbers have a successor, different numbers have different successors, 0 isn't a successor, properties of 0 which carry over to successors are properties of all numbers. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: Each statement of the famous axioms is slightly different from the others, and I have reworded Wright to fit him in. Since the last one (the 'induction axiom') is about properties, it invites formalization in second-order logic. |
| 17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
| Full Idea: The intuitive proposal is the essential number theoretic truths are precisely the logical consequences of the Peano axioms, ...but the notion of consequence is a semantic one...and it is not obvious that we possess a semantic notion of the requisite kind. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: (Not sure I understand this, but it is his starting point for rejecting PA as the essence of arithmetic). |
| 17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
| Full Idea: We incline to think of the Peano axioms as truths of some sort; so there has to be a philosophical question how we ought to conceive of the nature of the facts which make those statements true. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) | |
| A reaction: [He also asks about how we know the truths] |
| 13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
| Full Idea: We teach our children to count, sometimes with no attempt to explain what the sounds mean. Doubtless it is this habit which makes it so natural to think of the number series as fundamental. Frege's insight is that sameness of number is fundamental. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: 'When do children understand number?' rather than when they can recite numerals. I can't make sense of someone being supposed to understand number without a grasp of which numbers are bigger or smaller. To make 13='15' do I add or subtract? |
| 10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
| Full Idea: Wright says the Fregean arithmetic can be broken down into two steps: first, Hume's Law may be derived from Law V; and then, arithmetic may be derived from Hume's Law without any help from Law V. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction I.4 | |
| A reaction: This sounds odd if Law V is false, but presumably Hume's Law ends up as free-standing. It seems doubtful whether the resulting theory would count as logic. |
| 8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
| Full Idea: Wright proposed removing Frege's basic law V (which led to paradox), replacing it with Frege's 'number principle' (identity of numbers is one-to-one correspondence). The new system is formally consistent, and the Peano axioms can be derived from it. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.7 | |
| A reaction: The 'number principle' is also called 'Hume's principle'. This idea of Wright's resurrected the project of logicism. The jury is ought again... Frege himself questioned whether the number principle was a part of logic, which would be bad for 'logicism'. |
| 17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
| Full Idea: Wright intends the claim that Hume's Principle (HP) embodies an explanation of the concept of number to imply that it is analytic of the concept of cardinal number - so it is an analytic or conceptual truth, much as a definition would be. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 1 | |
| A reaction: Boolos is quoted as disagreeing. Wright is claiming a fundamental truth. Boolos says something can fix the character of something (as yellow fixes bananas), but that doesn't make it 'fundamental'. I want to defend 'fundamental'. |
| 13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
| Full Idea: What is fundamental to possession of any notion of natural number at all is not the knowledge that the numbers may be arrayed in a progression but the knowledge that they are identified and distinguished by reference to 1-1 correlation among concepts. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xv) | |
| A reaction: My question is 'what is the essence of number?', and my inclination to disagree with Wright on this point suggests that the essence of number is indeed caught in the Dedekind-Peano axioms. But what of infinite numbers? |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| Full Idea: Identifying numbers with extensions will not solve the Caesar problem for numbers unless we have already solved the Caesar problem for extensions. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xiv) |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
| Full Idea: Number-theoretic platonism is just the thesis that natural number is a sortal concept. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: See Crispin Wright on sortals to expound this. An odd way to express platonism, but he is presenting the Fregean version of it. |
| 13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
| Full Idea: We may not be able to settle whether some general form of empiricism is correct independently of natural numbers. It might be precisely our grasp of the abstract sortal, natural number, which shows the hypothesis of empiricism to be wrong. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: A nice turning of the tables. In the end only coherence decides these things. You may accept numbers and reject empiricism, and then find you have opened the floodgates for abstracta. Excessive floodgates, or blockages of healthy streams? |
| 13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
| Full Idea: Treating numbers adjectivally is, in effect, treating the numbers as quantifiers. Frege observes that we can always parse out any apparently adjectival use of a number word in terms of substantival use. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii) | |
| A reaction: The immediate response to this is that any substantival use can equally be expressed adjectivally. If you say 'the number of moons of Jupiter is four', I can reply 'oh, you mean Jupiter has four moons'. |
| 13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
| Full Idea: The Peano Axioms are logical consequences of a statement constituting the core of an explanation of the notion of cardinal number. The infinity of cardinal numbers emerges as a consequence of the way cardinal number is explained. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xix) | |
| A reaction: This, along with Idea 13896, nicely summarises the neo-logicist project. I tend to favour a strategy which starts from ordering, rather than identities (1-1), but an attraction is that this approach is closer to counting objects in its basics. |
| 13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
| Full Idea: We shall endeavour to see whether it is possible to follow through the strategy adumbrated in 'Grundlagen' for establishing the Peano Axioms without at any stage invoking classes. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi) | |
| A reaction: The key idea of neo-logicism. If you can avoid classes entirely, then set theory paradoxes become irrelevant, and classes aren't logic. Philosophers now try to derive the Peano Axioms from all sorts of things. Wright admits infinity is a problem. |
| 7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
| Full Idea: Crispin Wright has reactivated Frege's logistic program, which for decades just about everybody assumed was a lost cause. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by José A. Benardete - Logic and Ontology 3 | |
| A reaction: [This opens Bernadete's section called "Back to Strong Logicism?"] |
| 13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
| Full Idea: Most would cite Russell's paradox, the non-logical character of the axioms which Russell and Whitehead's reconstruction of Frege's enterprise was constrained to employ, and the incompleteness theorems of Gödel, as decisive for logicism's failure. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], Intro) |
| 13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
| Full Idea: The general view is that Russell's Paradox put paid to Frege's logicist attempt, and Russell's own attempt is vitiated by the non-logical character of his axioms (esp. Infinity), and by the incompleteness theorems of Gödel. But these are bad reasons. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xvi) | |
| A reaction: Wright's work is the famous modern attempt to reestablish logicism, in the face of these objections. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
| Full Idea: I have the gravest doubts whether any coherent account could be given of any multiplicity of senses of 'exist'. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 2.x) | |
| A reaction: I thoroughly agree with this thought. Do water and wind exist in different senses of 'exist'? |
| 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. |
| 13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
| Full Idea: When a class of terms functions as singular terms, and the sentences are true, then those terms genuinely refer. Being singular terms, their reference is to objects. There is no further question whether they really refer, and there are such objects. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iii) | |
| A reaction: This seems to be a key sentence, because this whole view is standardly called 'platonic', but it certainly isn't platonism as we know it, Jim. Ontology has become an entirely linguistic matter, but do we then have 'sakes' and 'whereaboutses'? |
| 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. |
| 9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
| Full Idea: Wright says we should accord to contextually defined abstract terms a genuine full-blown reference to objects. | |
| From: report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Michael Dummett - Frege philosophy of mathematics Ch.18 | |
| A reaction: This is the punch line of Wright's neo-logicist programme. See Idea 9868 for his view of reference. Dummett regards this strong view of contextual definition as 'exorbitant'. Wright's view strikes me as blatantly false. |
| 13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
| Full Idea: The claim that no concept counts as sortal if an instance of it can survive its loss, runs foul of so-called phase sortals like 'embryo' and 'chrysalis'. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: The point being that those items only fall under that sortal for one phase of their career, and of their identity. I've always thought such claims absurd, and this gives a good reason for my view. |
| 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. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 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, Castańeda 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... |
| 13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
| Full Idea: Before we can conclude that φ expresses a sortal concept, we need to ensure that 'is the same φ as' generates statements of genuine identity rather than of some other equivalence relation. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) |
| 13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
| Full Idea: A concept is 'sortal' if it exemplifies a kind of object. ..In English predication of a sortal concept needs an indefinite article ('an' elm). ..What really constitutes the distinction is that it involves grasping identity for things which fall under it. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.i) | |
| A reaction: This is a key notion, which underlies the claims of 'sortal essentialism' (see David Wiggins). |
| 13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
| Full Idea: 'Tree' is not a sortal concept under which directions fall since we cannot adequately explain the truth-conditions of any identity statement involving a pair of tree-denoting singular terms by appealing to facts to do with parallelism between lines. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 3.xiv) | |
| A reaction: The idea seems to be that these two fall under 'hedgehog', because that is a respect in which they are identical. I like to notion of explanation as a part of this. |
| 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. |
| 13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
| Full Idea: The fact that it seems possible to establish a sortal notion of direction by reference to lines and parallelism, discloses tacit commitments to directions in statements about parallelism...There is incoherence in the idea that a line might lack direction. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 4.xviii) | |
| A reaction: This seems like a slippery slope into a very extravagant platonism about concepts. Are concepts like direction as much a part of the natural world as rivers are? What other undiscovered concepts await us? |
| 13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
| Full Idea: A mild version of the verification principle would say that it makes sense to think of someone as understanding an expression only if he is able, by his use of the expression, to give the best possible evidence that he understands it. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.vii) | |
| A reaction: That doesn't seem to tell us what understanding actually consists of, and may just be the truism that to demonstrate anything whatsoever will necessarily involve some evidence. |
| 13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
| Full Idea: If the appearance of reference can be misleading, why cannot an apparent lack of reference be misleading? | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 2.xi) | |
| A reaction: A nice simple thought. Analytic philosophy has concerned itself a lot with sentences that seem to refer, but the reference can be analysed away. For me, this takes the question of reference out of the linguistic sphere, which wasn't Wright's plan. |
| 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? |
| 17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |
| Full Idea: The heart of the problem is Frege's assumption that predicates have Bedeutungen at all; and no reason is at present evident why someone who espouses Frege's notion of object is contrained to make that assumption. | |
| From: Crispin Wright (Frege's Concept of Numbers as Objects [1983], 1.iv) | |
| A reaction: This seems like a penetrating objection to Frege's view of reference, and presumably supports the Kripke approach. |
| 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. |