71 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! |
| 6891 | Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner] |
| Full Idea: Quine has aimed at a naturalistic and empirical world-view, and claims that first-order logic and set theory provide a framework sufficient for the articulation of our knowledge of the world. | |
| From: report of Willard Quine (Word and Object [1960]) by Thomas Mautner - Penguin Dictionary of Philosophy p.465 | |
| A reaction: Consequently he is fairly eliminativist about meaning and mental states, and does without universals in his metaphysics. An impressively puritanical enterprise, taking Ockham's Razor to the limit, but I find it hard to swallow. |
| 6310 | Enquiry needs a conceptual scheme, so we should retain the best available [Quine] |
| Full Idea: No enquiry is possible without some conceptual scheme, so we may as well retain and use the best one we know. | |
| From: Willard Quine (Word and Object [1960], §01) | |
| A reaction: This remark leads to Davidson's splendid paper 'On the Very Idea of a Conceptual Scheme'. Quine's remark raises the question of how we know which conceptual scheme is 'best'. |
| 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 |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 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' |
| 12798 | Plurals can in principle be paraphrased away altogether [Quine] |
| Full Idea: By certain standardizations of phrasing the contexts that call for plurals can in principle be paraphrased away altogether. | |
| From: Willard Quine (Word and Object [1960], §19) | |
| A reaction: Laycock, who quotes this, calls it 'unduly optimistic', but I presume that it was the standard view of plural reference until Boolos raised the subject. |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 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). |
| 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. |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| Full Idea: The condition on an explication of number can be put succinctly: any progression will do nicely. Russell once held that one must also be able to measure multiplicity, but this was a mistake; any progression can be fitted to that further condition. | |
| From: Willard Quine (Word and Object [1960], §54) | |
| A reaction: [compressed] This is the strongest possible statement that the numbers are the ordinals, and the Peano Axioms will define them. The Fregean view that cardinality comes first is redundant. |
| 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'? |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 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] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 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) |
| 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? |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| Full Idea: Mathematics, except for very trivial portions such as very elementary arithmetic, is irredeemably committed to quantification over abstract objects. | |
| From: Willard Quine (Word and Object [1960], §55) | |
| A reaction: Personally I would say that we are no more committed to such things than actors in 'The Tempest' are committed to the existence of Prospero and Caliban (which is quite a strong commitment, actually). |
| 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. |
| 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'? |
| 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'? |
| 16462 | The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine] |
| Full Idea: The quest of a simplest, clearest overall pattern of canonical notation is not to be distinguished from a quest of ultimate categories, a limning of the most general traits of reality. | |
| From: Willard Quine (Word and Object [1960], §33) | |
| A reaction: I won't disagree, as long as we recognise that reality calls the shots, not the notation, and that even animals must have some sort of system of categories, achieved without 'notation'. |
| 15723 | Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine] |
| Full Idea: The further a disposition is from those that can confidently be pinned on molecular structure or something comparably firm, the more our talk of it tends to depend on a vague factor of 'caeteris paribus' | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: I approve of this. It is precisely the point of scientific essentialism, I take it. We are faced with innumerable uncertain dispositions, but once the underlying mechanisms are known, their role in nature becomes fairly precise. |
| 15490 | Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB] |
| Full Idea: Quine claims that an unmanifested disposition is explicable in terms of an object having a structure similar to a structure of an object that has manifested the supposed disposition. | |
| From: report of Willard Quine (Word and Object [1960], §46) by C.B. Martin - The Mind in Nature 07.4 | |
| A reaction: This is probably the best account available for the firm empiricist who denies modal features in the actual world. In other words, a disposition is the result of an induction, not a conditional statement. |
| 8504 | Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt] |
| Full Idea: Quine is not an 'ostrich', because his strategy for dealing with property sentences is clear enough: all talk of attributes is to be dispensed with in favour of talk of eternal open sentences or talk of classes. | |
| From: report of Willard Quine (Word and Object [1960], §43) by Michael Devitt - 'Ostrich Nominalism' or 'Mirage Realism'? p.100 | |
| A reaction: [See p.209 'Word and Object'] The proposal seems to be that a property like being-human (a category) would be dealt with by classes, and qualitative properties would be dealt with simply as predicates. I like the split, and the first half, not the second. |
| 8464 | Physical objects in space-time are just events or processes, no matter how disconnected [Quine] |
| Full Idea: Physical objects, conceived four-dimensionally in space-time, are not to be distinguished from events or concrete processes. Each comprises simply the content, however heterogeneous, of a portion of space-time, however disconnected and gerrymandered. | |
| From: Willard Quine (Word and Object [1960], §36) | |
| A reaction: I very much like the suggestion that objects should be thought of as 'processes', but I dislike the idea that they can be gerrymandered. This is a refusal to cut nature at the joints (Idea 7953), which I find very counterintuitive. |
| 7924 | The notion of a physical object is by far the most useful one for science [Quine] |
| Full Idea: In a contest of sheer systematic utility to science, the notion of physical object still leads the field. | |
| From: Willard Quine (Word and Object [1960], §48) | |
| A reaction: A delightful circumlocution from someone who seems terrified to assert that there just are objects. Not that I object to Quine's caution. It would be disturbing if his researches had revealed that we could manage without objects. But compare Idea 6124. |
| 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. |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| Full Idea: Mathematicians are necessarily rational, and not necessarily two-legged; cyclists are the opposite. But what of an individual who counts among his eccentricities both mathematics and cycling? | |
| From: Willard Quine (Word and Object [1960], §41) | |
| A reaction: Quine's view is that the necessity (and essence) depends on how this eccentric is described. If he loses a leg, he must give up cycling; if he loses his rationality, he must give up the mathematics. Quine is wrong. |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| Full Idea: Cyclists are not essentially two-legged (a one-legged cyclist exists, but can't cycle any more), and mathematicians are not essentially rational (as they can lose rationality and continue to exist, though unable to do mathematics). | |
| From: comment on Willard Quine (Word and Object [1960], §41.5) by Baruch Brody - Identity and Essence 5.1 | |
| A reaction: Was Quine thinking of the nominal essence of this person - that 'cyclists' necessarily cylce, and 'mathematicians' necessarily do some maths? It is as bad to confuse 'necessary' with 'essential' as to confuse 'use' with 'mention'. |
| 17594 | We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine] |
| Full Idea: For general terms write 'if Fx then Fy' and vice versa, and 'if Fxz then Fyz'..... The conjunction of all these is coextensive with 'x=y' if any formula constructible from the vocabulary is; and we can adopt that conjunction as our version of identity. | |
| From: Willard Quine (Word and Object [1960], §47) | |
| A reaction: [first half compressed] The main rival views of equality are this and Wiggins (1980:199). Quine concedes that his account implies a modest version of the identity of indiscernibles. Wiggins says identity statements need a sortal. |
| 15725 | Normal conditionals have a truth-value gap when the antecedent is false. [Quine] |
| Full Idea: In its unquantified form 'If p then q' the indicative conditional is perhaps best represented as suffering a truth-value gap whenever its antecedent is false. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: That is, the clear truth-functional reading of the conditional (favoured by Lewis, his pupil) is unacceptable. Quine favours the Edgington line, that we are only interested in situations where the antecedent might be true. |
| 15722 | Conditionals are pointless if the truth value of the antecedent is known [Quine] |
| Full Idea: The ordinary conditional loses its point when the truth value of its antecedent is known. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: A beautifully simple point that reveals a lot about what conditionals are. |
| 15719 | We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine] |
| Full Idea: The subjunctive conditional depends, like indirect quotation and more so, on a dramatic projection: we feign belief in the antececent and see how convincing we then find the consequent. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems accurate. It means that we are only interested in when the antecedent is true, and when it is false is irrelevant. |
| 15721 | Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine] |
| Full Idea: The subjunctive conditional is seen at its most respectable in the disposition terms. ...The reason is that they are conceived as built-in, enduring structural traits. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Surprisingly, this is very sympathetic to a metaphysical view that seems a long way from Quine, since dispositions seem to invite commitment to modal features of reality. But the structural traits are not, of course, modal, in any way! |
| 15724 | Counterfactuals have no place in a strict account of science [Quine] |
| Full Idea: The subjunctive conditional has no place in an austere canonical notation for science - but that ban is less restrictive than would at first appear. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: Idea 15723 shows what he has in mind - that what science aims for is accounts of dispositional mechanisms, which then leave talk of other possible worlds (in Lewis style) as unnecessary. I may be with Quine one this one. |
| 15720 | What stays the same in assessing a counterfactual antecedent depends on context [Quine] |
| Full Idea: The traits to suppose preserved in a counterfactual depend on sympathy for the fabulist's purpose. Compare 'If Caesar were in command, he would use the atom bomb', and 'If Caesar were in command, he would use catapults'. | |
| From: Willard Quine (Word and Object [1960], §46) | |
| A reaction: This seems to be an important example for the Lewis approach, since you are asked to consider the 'nearest' possible world, but that will depend on context. |
| 4630 | Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl] |
| Full Idea: Duhem and Quine have maintained that it may be possible to develop two or more theories that are 1) internally consistent, 2) inconsistent with one another, and 3) perfectly consistent with all the data we can muster. | |
| From: report of Willard Quine (Word and Object [1960]) by J Baggini / PS Fosl - The Philosopher's Toolkit §1.06 | |
| A reaction: Obviously this may be a contingent truth about our theories, but why not presume that this is because we are unable to collect the crucial data (e.g. about prehistoric biology), rather than denigrate the whole concept of a theory, and undermine science? |
| 3131 | Quine expresses the instrumental version of eliminativism [Quine, by Rey] |
| Full Idea: Quine expresses the instrumental version of eliminativism. | |
| From: report of Willard Quine (Word and Object [1960]) by Georges Rey - Contemporary Philosophy of Mind Int.3 |
| 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. |
| 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. |
| 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. |
| 3988 | Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine] |
| Full Idea: Quine's thesis of the indeterminacy of radical translation carries all the way in, as the thesis of the indeterminacy of radical interpretation of mental states and processes. | |
| From: comment on Willard Quine (Word and Object [1960]) by Daniel C. Dennett - Daniel Dennett on himself p.239 | |
| A reaction: Strong scepticism seems wrong here. Davidson's account of charity in interpretation, and the role of truth, seems closer. |
| 6311 | The firmer the links between sentences and stimuli, the less translations can diverge [Quine] |
| Full Idea: The firmer the direct links of a sentence with non-verbal stimulation, the less drastically its translations can diverge from one another from manual to manual. | |
| From: Willard Quine (Word and Object [1960], §07) | |
| A reaction: This implies (plausibly) that talk about farming will have fairly determinate translations into foreign languages, but talk of philosophy will not. An interesting case is logic, where we might expect tight translation with little non-verbal stimulation. |
| 6312 | We can never precisely pin down how to translate the native word 'Gavagai' [Quine] |
| Full Idea: There is no evident criterion whereby to strip extraneous effects away and leave just the meaning of 'Gavagai' properly so-called - whatever meaning properly so-called may be. | |
| From: Willard Quine (Word and Object [1960], §09) | |
| A reaction: Quine's famous assertion that translation is ultimately 'indeterminate'. Huge doubts about meaning and language and truth follow from his claim. Personally I think it is rubbish. People become fluent in very foreign languages, and don't have breakdowns. |
| 6313 | Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine] |
| Full Idea: Stimulus synonymy of the occasion sentences 'Gavagai' and 'Rabbit' does not even guarantee that 'gavagai' and 'rabbit' are coextensive terms, terms true of the same things. | |
| From: Willard Quine (Word and Object [1960], §12) | |
| A reaction: Since this scepticism eventually seems to result in the reader no longer knowing what they mean themselves by the word 'rabbit', I doubt Quine's claim. Problems after hearing one word of a foreign language disappear after years of residence. |
| 6317 | Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine] |
| Full Idea: Rival systems of analytical hypotheses can fit the totality of speech behaviour to perfection, and can fit the totality of dispositions to speech behaviour as well, and still specify mutually incompatible translations of countless sentences. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: This is Quine's final assertion of indeterminacy, having explored charity, bilingual speakers etc. It seems to me that he is a victim of his underlying anti-realism, which won't allow nature to dictate ways of cutting up the world. |
| 6315 | We should be suspicious of a translation which implies that a people have very strange beliefs [Quine] |
| Full Idea: The more absurd or exotic the beliefs imputed to a people, the more suspicious we are entitled to be of the translations. | |
| From: Willard Quine (Word and Object [1960], §15) | |
| A reaction: Quine is famous for his relativist and indeterminate account of translation, but he gradually works his way towards the common sense which Davidson later brought out into the open. |
| 6314 | Weird translations are always possible, but they improve if we impose our own logic on them [Quine] |
| Full Idea: Wanton translation can make natives sound as queer as one pleases; better translation imposes our logic upon them. | |
| From: Willard Quine (Word and Object [1960], §13) | |
| A reaction: This begins to point towards the principle of charity, on which Davidson is so keen, and even on doubts whether two different conceptual schemes are possible. Personally I think there is only one logic (deep down), and the natives will have it. |