53 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! |
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 |
13134 | We negate predicates but do not negate names [Westerhoff] |
Full Idea: We negate predicates but do not negate names. | |
From: Jan Westerhoff (Ontological Categories [2005], §88) | |
A reaction: This is a point for anyone like Ramsey who wants to collapse the distinction between particulars and universals, or singular terms and their predicates. |
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). |
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. |
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'? |
13117 | How far down before we are too specialised to have a category? [Westerhoff] |
Full Idea: How far down are we allowed to go before the categories become too special to qualify as ontological categories? | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: A very nice question, because we can't deny a category to a set with only one member, otherwise the last surviving dodo would not have been a dodo. |
13116 | Maybe objects in the same category have the same criteria of identity [Westerhoff] |
Full Idea: There is an idea that objects belonging to the same category have the same criteria of identity. This view was first explicitly endorsed by Frege (1884), and was later systematized by Dummett (1981). | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: This approach is based on identity between equivalence classes. Westerhoff says it means, implausibly, that the resulting categories cannot share properties. |
13118 | Categories are base-sets which are used to construct states of affairs [Westerhoff] |
Full Idea: My fundamental idea is that 'form-sets' are intersubstitutable constituents of states of affairs with the same form, and 'base-sets' are special form-sets which can be used to construct other form-sets. Ontological categories are the base-sets. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: The spirit of this is, of course, to try to achieve the kind of rigour that is expected in contemporary professional philosophy, by aiming for some sort of axiom-system that is related to a well established precise discipline like set theory. Maybe. |
13125 | Categories are held to explain why some substitutions give falsehood, and others meaninglessness [Westerhoff] |
Full Idea: It is usually assumed of ontological categories that they can explain why certain substitutions make a statement false ('prime' for 'odd'), while others make it meaningless ('sweet' for 'odd', of numbers). | |
From: Jan Westerhoff (Ontological Categories [2005], §05) | |
A reaction: So there is a strong link between big ontological questions, and Ryle's famous identification of the 'category mistake'. The phenomenon of the category mistake is undeniable, and should make us sympathetic to the idea of categories. |
13126 | Categories systematize our intuitions about generality, substitutability, and identity [Westerhoff] |
Full Idea: Systems of ontological categories are systematizations of our intuitions about generality, intersubstitutability, and identity. | |
From: Jan Westerhoff (Ontological Categories [2005], §23) | |
A reaction: I think we might be able to concede this without conceding the relativism about categories which Westerhoff espouses. I would claim that our 'intuitions' are pretty accurate about the joints of nature, and hence accurate about these criteria. |
13130 | Categories as generalities don't give a criterion for a low-level cut-off point [Westerhoff] |
Full Idea: Categories in terms of generality, dependence and containment are unsatisfactory because of the 'cut-off point problem': they don't give an account of how far down the order we can go and be sure we are still dealing with categories. | |
From: Jan Westerhoff (Ontological Categories [2005], §27) | |
A reaction: I don't see why this should be a devastating objection to any theory. I have a very clear notion of a human being, but a very hazy notion of how far back towards its conception a human being extends. |
13124 | Categories can be ordered by both containment and generality [Westerhoff] |
Full Idea: Categories are usually not assumed to be ordered by containment, but also be generality. | |
From: Jan Westerhoff (Ontological Categories [2005], §02) | |
A reaction: I much prefer generality, which is responsive to the full picture, whereas containment seems to appeal too much to the orderly and formalised mind. Containments overlap, so we can't dream of a perfectly neat system. |
13131 | The aim is that everything should belong in some ontological category or other [Westerhoff] |
Full Idea: It seems to be one of the central points of constructing systems of ontological categories that everything can be placed in some category or other. | |
From: Jan Westerhoff (Ontological Categories [2005], §49) | |
A reaction: After initial resistance to this, I suppose I have to give in. The phoenix (a unique mythological bird) is called a 'phoenix', though it might just be called 'John' (cf. God). If there were another phoenix, we would know how to categorise it. |
13123 | All systems have properties and relations, and most have individuals, abstracta, sets and events [Westerhoff] |
Full Idea: Surveyed ontological systems show overlaps: properties and relations turn up in every system; individuals form part of five systems; abstracta, collections/sets and events are in four; facts are in two. | |
From: Jan Westerhoff (Ontological Categories [2005], §02) | |
A reaction: Westerhoff is a hero for doing such a useful survey. Of course, Quine challenges properties, and relations are commonly given a reductive analysis. Individuals can be challenged, and abstracta reduced. Sets are fictions. Events or facts? Etc. |
13115 | Ontological categories are like formal axioms, not unique and with necessary membership [Westerhoff] |
Full Idea: I deny the absolutism of a unique system of ontological categories and the essentialist view of membership in ontological categories as necessary features. ...I regard ontological categories as similar to axioms of formalized theories. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: The point is that modern axioms are not fundamental self-evident truths, but an economic set of basic statements from which some system can be derived. There may be no unique set of axioms for a formal system. |
13119 | Categories merely systematise, and are not intrinsic to objects [Westerhoff] |
Full Idea: My conclusion is that categories are relativistic, used for systematization, and that it is not an intrinsic feature of an object to belong to a category, and that there is no fundamental distinction between individuals and properties. | |
From: Jan Westerhoff (Ontological Categories [2005], Intro) | |
A reaction: [compressed] He calls his second conclusion 'anti-essentialist', but I think we can still get an account of (explanatory) essence while agreeing with his relativised view of categories. Wiggins might be his main opponent. |
13135 | A thing's ontological category depends on what else exists, so it is contingent [Westerhoff] |
Full Idea: What ontological category a thing belongs to is not dependent on its inner nature, but dependent on what other things there are in the world, and this is a contingent matter. | |
From: Jan Westerhoff (Ontological Categories [2005], §89) | |
A reaction: This is aimed at those, like Wiggins, who claim that category is essential to a thing, and there is no possible world in which that things could belong to another category. Sounds good, till you try to come up with examples. |
14596 | Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr] |
Full Idea: Just as there are no numbers or properties, there are no relations (like 'being heavier than' or 'betweenness'), or sets. I will provisionally use 'nominalism' for the conjunction of these four claims. | |
From: Cian Dorr (There Are No Abstract Objects [2008], 1) | |
A reaction: If you are going to be a nominalist, do it properly! My starting point in metaphysics is strong sympathy with this view. Right now [Tues 22nd Nov 2011, 10:57 am GMT] I think it is correct. |
14597 | Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr] |
Full Idea: Natural Class Nominalists take as primitive the notion of a 'natural' class - a class of things that all resemble one another in some one respect and resemble nothing else in that respect. | |
From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
A reaction: Dorr rejects this view because he doesn't believe in 'classes'. How committed to classes do you have to be before you are permitted to talk about them? All vocabulary (such as 'resemble') seems metaphysically tainted in this area. |
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. |
13129 | Essential kinds may be too specific to provide ontological categories [Westerhoff] |
Full Idea: Essential kinds can be very specific, and arguably too specific for the purposes of ontological categories. | |
From: Jan Westerhoff (Ontological Categories [2005], §27) | |
A reaction: Interesting. There doesn't seem to be any precise guideline as to how specific an essential kind might be. In scientific essentialism, each of the isotopes of tin has a distinct essence, but why should they not be categories |
14598 | Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr] |
Full Idea: If there are abstract objects, there are necessary truths about these things that cannot be reduced to truths of logic. So only the nominalist, who denies that there are any such things, can adequately respect the idea that there are no brute necessities. | |
From: Cian Dorr (There Are No Abstract Objects [2008], 4) | |
A reaction: This is where two plates of my personal philosophy grind horribly against one another. I love nominalism, and I love natural necessities. They meet like a ring-species in evolution. I'll just call it a 'paradox', and move on (swiftly). |
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. |