60 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! |
| 19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
| Full Idea: I defend the thesis that questions about what kinds of things there are cannot be properly understood or adequately answered without recourse to considerations about possibility and necessity. | |
| From: Bob Hale (Necessary Beings [2013], Intro) | |
| A reaction: Good. I would say that this is a growing realisation in contemporary philosophy. The issue is focused when we ask what are the limitations of Quine's approach to metaphysics. If you don't see possibilities around you, you are a fool. |
| 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. |
| 19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
| Full Idea: One might think of a full dress, or canonical, definition as specifying what type of thing it is, and what distinguishes it from everything else within its type. | |
| From: Bob Hale (Necessary Beings [2013], 06.4) | |
| A reaction: Good! At last someone embraces the Aristotelian ideas that definitions are a) quite extensive and detailed (unlike lexicography), and b) they aim to get right down to the individual. In that sense, an essence is captured by a definition. |
| 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 |
| 19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
| Full Idea: If the Brouwersche principle, p ⊃ □◊p is adjoined to a standard quantified vesion of the weakest modal logic K, then one can prove both the Barcan principle, and its converse. | |
| From: Bob Hale (Necessary Beings [2013], 09.2) | |
| A reaction: The Brouwersche principle (that p implies that p must be possible) sounds reasonable, but the Barcan principles strike me as false, so something has to give. They are theorems of S5. Hale proposes giving up classical logic. |
| 19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
| Full Idea: I reject both Barcan and Converse Barcan by adopting a negative free logic. | |
| From: Bob Hale (Necessary Beings [2013], 11.3) | |
| A reaction: See section 9.2 of Hale's book, where he makes his case. I can't evaluate this bold move, though I don't like the Barcan Formulae. We can anticipate objections to Hale: are you prepared to embrace the unexpected consequences of your new logic? |
| 19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
| Full Idea: Contrary to what Quine supposes, it is neither necessary nor desirable to interpret bound higher-order variables as ranging over sets. Sets are a species of object. They should range over entities of a completely different type: properties and relations. | |
| From: Bob Hale (Necessary Beings [2013], 08.2) | |
| A reaction: This helpfully clarifies something which was confusing me. If sets are objects, then 'second-order' logic just seems to be the same as first-order logic (rather than being 'set theory in disguise'). I quantify over properties, but deny their existence! |
| 19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
| Full Idea: An old objection to conventionalism claims that it confuses sentences with propositions, confusing what makes sentences mean what they do with what makes them (as propositions) true. | |
| From: Bob Hale (Necessary Beings [2013], 05.2) | |
| A reaction: The conventions would presumably apply to the sentences, but not to the propositions. Since I think that focusing on propositions solves a lot of misunderstandings in modern philosophy, I like the sound of this. |
| 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' |
| 19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
| Full Idea: In contrast with axiomatic systems, in natural deductions systems of logic neither the premises nor the conclusions of steps in a derivation need themselves be logical truths or theorems of logic. | |
| From: Bob Hale (Necessary Beings [2013], 09.2 n7) | |
| A reaction: Not sure I get that. It can't be that everything in an axiomatic proof has to be a logical truth. How would you prove anything about the world that way? I'm obviously missing something. |
| 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. |
| 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'? |
| 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) |
| 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. |
| 19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
| Full Idea: The existence of the natural numbers is not a matter of pure logic - it cannot be proved in pure logic. It can be proved in second-order logic plus Hume's principle. Truths of arithmetic are not logic - they depend on the nature of natural numbers. | |
| From: Bob Hale (Necessary Beings [2013], 07.4) | |
| A reaction: Hume's principles needs entities which can be matched to one another, so a certain ontology is needed to get neo-logicism off the ground. |
| 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'? |
| 19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
| Full Idea: Any intereresting supervenience thesis requires that the class of facts on which the allegedly supervening facts supervene be characterizable independently, without use or presupposition of the notions involved in stating the supervening facts. | |
| From: Bob Hale (Necessary Beings [2013], 03.4.1) | |
| A reaction: There might be intermediate cases here, since having descriptions which are utterly unconnected (at any level) might be rather challenging. |
| 19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
| Full Idea: There is no clear gap between its being a fact that p and its being true that p, no obvious way to individuate the fact a true statement records other than via that statement's truth-conditions. | |
| From: Bob Hale (Necessary Beings [2013], 03.2) | |
| A reaction: Typical of philosophers of language. The concept of a fact is of something mind-independent; the concept of a truth is of something mind-dependent. They can't therefore be the same thing (by the contrapositive of the indiscernability of identicals!). |
| 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'? |
| 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. |
| 19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
| Full Idea: How shall we prevent a sorites taking us to the conclusion that a chair might have originated in a completely disjoint lot of wood, or even in some other material altogether? | |
| From: Bob Hale (Necessary Beings [2013], 11.3.7) | |
| A reaction: This seems a good criticism of Kripke's implausible claim that his lectern is necessarily (or essentially) made of the piece of wood it is made of. Could his lectern have had a small piece of plastic inserted in it? |
| 19290 | Absolute necessities are necessarily necessary [Hale] |
| Full Idea: I argue that any absolute necessity is necessarily necessary. | |
| From: Bob Hale (Necessary Beings [2013], 05.5.2) | |
| A reaction: This requires the principle of S4 modal logic, that necessity implies necessary necessity. He argues that S5 is the logical of absolute necessity. |
| 19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
| Full Idea: The strength of the claim that p is 'absolutely necessary' derives from the fact that in its expression as a universally quantified counterfactual ('everything will necessitate p'), the quantifier ranges over all propositions whatever. | |
| From: Bob Hale (Necessary Beings [2013], 04.1) | |
| A reaction: Other philosophers don't seem to use the term 'absolute necessity', but it seems a useful concept, in contrast to conditional or local necessities. You can't buy chocolate on the sun. |
| 19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
| Full Idea: The difference between logical and metaphysical necessities lies, not in the range of possibilities for which they hold, but - at the linguistic level - in the kind of vocabulary essential to their expression, and the kinds of entities that explain them. | |
| From: Bob Hale (Necessary Beings [2013], 04.5) | |
| A reaction: I don't think much of the idea that the difference is just linguistic, and I don't like the idea of 'entities' as grounding them. I see logical necessities as arising from natural deduction rules, and metaphysical ones coming from the nature of reality. |
| 19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
| Full Idea: We can identify the belief that the proposition that p is logically necessary, where p may be of any logical form, with the belief that, no matter what else was the case, it would be true that p. | |
| From: Bob Hale (Necessary Beings [2013], 04.1) | |
| A reaction: I find this surprising. I take it that logical necessity must be the consequence of logic. That all squares have corners doesn't seem to be a matter of logic. But then he seems to expand logical necessity to include conceptual necessity. Why? |
| 19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
| Full Idea: We can distinguish between narrower and broader kinds of logical necessity. There are, for example, the logical necessities of propostional logic, those of first-order logic, and so on. Maybe they are necessities expressed using logical vocabulary. | |
| From: Bob Hale (Necessary Beings [2013], 04.5) | |
| A reaction: Hale goes on to prefer a view that embraces conceptual necessities. I think in philosophy we should designate the necessities according to their sources. This might clarify a currently rather confused situation. First-order includes propositional logic. |
| 19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
| Full Idea: I think we may conclude that there is no significant version of modal supervenience which both commands acceptance and implies that all modal facts depend asymmetrically on non-modal ones. | |
| From: Bob Hale (Necessary Beings [2013], 03.4.3) | |
| A reaction: This is the conclusion of a sustained and careful discussion, recorded here for interest. I'm inclined to think that there are very few, if any, non-modal facts in the world, if those facts are accurately characterised. |
| 19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
| Full Idea: Whether the essentialist theory can account for all absolute necessities depends in part on whether the theory can explain the necessities of existence (of certain objects, properties and entities). | |
| From: Bob Hale (Necessary Beings [2013], Intro) | |
| A reaction: Hale has a Fregean commitment to all sorts of abstract objects, and then finds difficulty in explaining them from his essentialist viewpoint. His book didn't convince me. I'm more of a nominalist, me, so I sleep better at nights. |
| 19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
| Full Idea: The point of the essentialist theory is not to provide a reductive explanation of necessities. It is, rather, to locate a base class of necessities - those which directly reflect the natures of things - in terms of which the remainder may be explained. | |
| From: Bob Hale (Necessary Beings [2013], 06.6) | |
| A reaction: My picture is of most of the necessities being directly explained by the natures of things, rather than a small core of natures generating all the derived ones. All the necessities of squares derive from the nature of the square. |
| 19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
| Full Idea: If the essentialist theory of necessity is to be adequate, it must be able to explain how the existence of certain objects - such as the natural numbers - can itself be absolutely necessary. | |
| From: Bob Hale (Necessary Beings [2013], 07.1) | |
| A reaction: Hale and his neo-logicist pals think that numbers are 'objects', and they necessarily exist, so he obviously has a problem. I don't see any alternative for essentialists to treating the existing (and possible) natures as brute facts. |
| 19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
| Full Idea: We need an explanation of what worlds are that makes clear why being true at all of them should be necessary and sufficient for being necessary (and true at one of them suffices for being possible). | |
| From: Bob Hale (Necessary Beings [2013], 03.3.2) | |
| A reaction: Hale is introducing combinatorial accounts of worlds, as one possible answer to this. Hale observes that all the worlds might be identical to our world. It is always assumed that the worlds are hugely varied. But maybe worlds are constrained. |
| 19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
| Full Idea: The standard conception of worlds incorporates the assumption of bivalence - every proposition is either true or false. But it is infelicitous to build into one's basic semantic machinery a principle endorsing classical logic against its rivals. | |
| From: Bob Hale (Necessary Beings [2013], 10.3) | |
| A reaction: No wonder Dummett (with his intuitionist logic) immediately spurned possible worlds. This objection must be central to many recent thinkers who have begun to doubt possible worlds. I heard Kit Fine say 'always kick possible worlds where you can'. |
| 19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
| Full Idea: What it is to be (pure) water is to be explained in terms of being composed of H2O molecules, but this is not what the word 'water' means. | |
| From: Bob Hale (Necessary Beings [2013], 11.2) | |
| A reaction: Hale says when the real and verbal definitions match, we can know the essence a priori. If they come apart, presumably we need a posteriori research. Interesting. It is certainly dubious to say a stuff-word means its chemical composition. |
| 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. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |