37 ideas
| 17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
| Full Idea: As Kreisel has remarked, what is important is not the existence of mathematical objects, but the objectivity of mathematical statements. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: [see Maddy 2011:115 for the history of this idea] It seems rather unclear where Frege stands on objectivity. Maddy embraces it, following up this idea, and Tyler Burge's fat book on objectivity. |
| 13985 | A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle] |
| Full Idea: Whereas there might be just one fact that a true proposition was like, we would have to say that a false proposition was unlike any fact. We could not speak of the fact that it was false of, so we could not speak of its being false of anything at all. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Objections') | |
| A reaction: Ryle brings out very nicely the point Russell emphasised so much, that the most illuminating studies in philosophy are of how falsehood works, rather than of how truths work. If I say 'the Queen is really a man' it is obvious what that is false of. |
| 13984 | Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle] |
| Full Idea: One map of Sussex is like another, but it is not true of that other map, but only of the county. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Objections') | |
| A reaction: One might question whether a map is in any sense 'true' of Sussex, though one must admit that there are good and bad maps of Sussex. The point is a nice one, which shows that there is no simple account of truth as correspondence. |
| 10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
| Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
| Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 13979 | Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle] |
| Full Idea: Logic studies the way in which one thing follows from another, in which one thing is compatible with another, contradicts, corroborates or necessitates another, is a special case of another or the nerve of another. And so on. | |
| From: Gilbert Ryle (Are there propositions? [1930], IV) | |
| A reaction: I presume that 'and so on' would include how one thing proves another. This is quite a nice list, which makes me think a little more widely about the nature of logic (rather than just about inference). Incompatibility isn't a process. |
| 10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
| Full Idea: In the intuitionist view, the notion of an intuitive proof cannot be expected to coincide with that of a proof in a formal system, and Gödel's incompleteness theorem is thus unsurprising from an intuitionist point of view. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) |
| 10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
| Full Idea: From the intuitionist point of view natural numbers are mental constructions, so their totality is only potential, but it is neverthless a fully determinate totality. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This could only be if the means of constructing the numbers was fully determinate, so how does that situation come about? |
| 10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
| Full Idea: Dummett distinguishes, roughly, between those concrete objects which can be possible objects of ostension, and abstract objects which can only be referred to by functional expressions whose argument is some other object. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: At least someone has proposed a theory! Hale gives a nice critical discussion of the proposal. It is a moot point whether in the second case, when you pick out the 'other object', you are thereby able to refer to some new abstract object. |
| 10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
| Full Idea: The dichotomy between concrete and abstract objects comes to seem far too crude: to which of the two categories should we assign the Mistral, for instance? | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He has previously given colours and points as difficult borderline cases. We can generalise this particular problem case as the question of whether a potentiality or possibility is abstract or concrete. |
| 10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
| Full Idea: There is no reason for wanting a sharp distinction between concrete and abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This rather depends on your ontology. If you are happy for reality to be full of weird non-physical entities, then the blurring won't bother you. If the boundary is blurred but still real, it is a very interesting one. |
| 10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
| Full Idea: If abstractions were defined by whether they could affect human sense-organs, light-waves would be concrete but radio waves abstract. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is a pretty good baseline example. No account should draw an abstract/concrete line through the electromagnetic spectrum. |
| 13988 | Many sentences do not state facts, but there are no facts which could not be stated [Ryle] |
| Full Idea: There are many sentences which do not state facts, while there are no facts which (in principle) could not be stated. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Substitute') | |
| A reaction: Hm. This seems like a nice challenge. The first problem would be infinite facts. Then complex universal facts, beyond the cognizance of any mind. Then facts that change faster than thinking can change. Do you give up yet? Then there's.... |
| 10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
| Full Idea: The dictum that a name has meaning only in the context of a sentence repudiates the conception of a special philosophical sense of 'existence', which claims that numbers do not exist while affirming existential statements about them. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He refers to Frege's Context Principle. Personally I would say you could make plenty of 'affirmations' about arithmetic without them having to be 'existential'. I can say there 'is' a number between 6 and 8, without huge existential claims. |
| 10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
| Full Idea: What objects we recognise the world as containing depends upon the structure of our language. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: The background to this claim is the Fregean idea that there are no objects for us if there are no concepts. Dummett is adding that there are no concepts if there is no language. I say animals have concepts and recognise objects. |
| 10532 | We can understand universals by studying predication [Dummett] |
| Full Idea: It is by the study of the character of predication that we shall come to understand the essential nature of universals. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I haven't founded a clearer manifesto for linguistic philosophy than that! Personally I find it highly dubious, given the shifting nature of linguistic forms, and the enormous variation between remote languages. |
| 10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
| Full Idea: The original sense of 'nominalism' is the denial of universals, that is the denial of reference to either predicates or to abstract nouns. The modern sense (of Nelson Goodman) is the denial of the existence of abstract objects. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is why you find loads of modern philosophers vigorous attacking nominalism, only to gradually realise that they don't actually believe in universals, as traditionally understood. It's hard to keep up, when words shift their meaning. |
| 10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
| Full Idea: We cannot simply distinguish concrete objects as objects of ostension, if it literally involves a pointing gesture, as this would exclude a colourless gas, a sound or a smell. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: He shifts to verbal ostension as a result, since we can talk of 'this smell'. On p.491 he suggests that affecting our senses is a sufficient condition to be concrete, but not a necessary one. |
| 10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
| Full Idea: To say that an abstract object cannot be the cause of change seems plausible enough, but the thesis that it cannot be the subject of change is problematic. The shape of an object can change, or the number of sheep on a hill. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This seems a pretty crucial difficulty for the standard notion of abstracta as non-causal. I would say that it is an acid which could eat away the whole edifice if you thought about it for long enough. He shifts shape-change to the physical object. |
| 10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
| Full Idea: For intuitionists, it ceases to be true that abstract objects are not observable and cannot be involved in causal interaction, since such intuitive apprehension of them may be regarded as just such an interaction. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I would say that since abstract objects can be involved in causal interactions, in the mind, and since the mind is entirely physical (oh yes), this makes abstract objects entirely physical, which may come as a shock to some people. |
| 10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
| Full Idea: For an object to be abstract, we require only that an understanding of any name of that object involves a recognition that the object is in the range of some functional expression. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: I'm not sure I understand this, but a function must involve a relation between some objects, such that a unique object is consequently picked out. |
| 10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
| Full Idea: Dummett's best argument for excluding abstract nouns relies upon the entirely Fregean requirement that with any genuine singular term there must be associated a criterion of identity. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Bob Hale - Abstract Objects Ch.2.II | |
| A reaction: This sounds a rather rigid test. Must the criteria be logically precise, or must you just have some vague idea of what you are talking about? |
| 10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
| Full Idea: An abstract object can be referred to only by means of a verbal phrase, ...and no confrontation with an abstract object is possible. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: So does this mean that animals are incapable of entertaining abstract concepts? Some research suggests otherwise. Does a dog understand what a 'walk' is, without use of the word? Dummett disgracefully neglects animals in his theories. |
| 10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
| Full Idea: The notion of 'object', as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: If we say 'objects exist', I think it is crucial that if we are going to introduce 'object' as a term of art, then 'exist' had better stick to normal usage. If that drifts into a term of art as well (incorporating 'subsist', or some such) we have no hope! |
| 13983 | Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle] |
| Full Idea: The theory of Representative Ideas begs the whole question, by assuming a) that we can know these 'Ideas', b) that we can know the realities they represent, and c) we can know a particular 'idea' to be representative of a particular reality. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Objections') | |
| A reaction: Personally I regard the ideas as immediate (rather than acquired by some knowledge process), and I am dimly hoping that they represent reality (or I'm in deep trouble), and I am struggling to piece together the reality they represent. I'm happy with that. |
| 13980 | If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle] |
| Full Idea: Those who find 'judgments' everywhere and propositions nowhere find that some judgments cohere whereas others are incoherent. What is the status of the terms between which these relations hold? | |
| From: Gilbert Ryle (Are there propositions? [1930], IV) | |
| A reaction: Ryle is playing devil's advocate, but this strikes me as a nice point. I presume Russell after 1906 is the sort of thinker he has in mind. |
| 19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
| Full Idea: Real functions map objects onto objects, but concepts map objects onto truth value, ...so Dummett says that concepts are not functions, but that they have a 'functional character'. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973]) by Donald Davidson - Truth and Predication 6 |
| 10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
| Full Idea: Since we cannot pick an abstract object out from its surrounding, all that we need to master is the use of statements of identity between objects of a certain kind. | |
| From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) | |
| A reaction: This is the necessary Fregean preliminary to using a principle of abstraction to identify two objects which are abstract (when the two objects are in an equivalence relation). Presumably circular squares and square circles are identical? |
| 13978 | Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle] |
| Full Idea: It is argued by Husserl and (virtually) by Meinong that only if there are such entities as objective Meanings - and propositions are just a species of Meaning - is there anything for Logic to be about. | |
| From: Gilbert Ryle (Are there propositions? [1930], IV) | |
| A reaction: It is presumably this proposal which led to the scepticism about meanings in Wittgenstein, Quine and Kripke. The modern view, which strikes me as right, is that logic is about inference, and so doesn't need a subject-matter. |
| 13977 | When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle] |
| Full Idea: If I have uttered my sentence aloud, a listener can both understand what I say or grasp my meaning, and also infer to my state of mind. | |
| From: Gilbert Ryle (Are there propositions? [1930], I) | |
| A reaction: This simple observations seems rather important. If we shake written words onto the floor, they might add up to a proper sentence, but half of the point of a sentence is missing. Irony trades on the gap between meaning and state of mind. |
| 10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
| Full Idea: Dummett claims that a realistic conception of reference can be sustained for concrete objects (possible objects of ostension), but breaks down for (putative) names of (pure) abstract objects. | |
| From: report of Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14) by Bob Hale - Abstract Objects Ch.3.II | |
| A reaction: An extremely hard claim to evaluate, because a case must first be made for abstract objects which are fundamentally different in kind. Realistic reference must certainly deal with these hard cases. Field rejects Dummett's abstract points. |
| 13976 | 'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle] |
| Full Idea: As the orthodox terms 'thoughts' and 'judgments' are equivocal, since they may equally well denote 'thinkings' as 'what-is-thought', the 'accusatives' of acts of thinking have come to be called 'propositions'. | |
| From: Gilbert Ryle (Are there propositions? [1930], I) | |
| A reaction: I have understood propositions to be capable of truth or falsity. 'What is thought' could be a right old jumble of images and disjointed fragments. Propositions are famous for their unity! |
| 13981 | Several people can believe one thing, or make the same mistake, or share one delusion [Ryle] |
| Full Idea: We ordinarily find no difficulty in saying of a given thing that several people believe it and so, if they think it false, 'make the same mistake' or 'labour under the same delusion'. | |
| From: Gilbert Ryle (Are there propositions? [1930], IV) | |
| A reaction: Ryle is playing devil's advocate, but this (like 13980) strikes me as quite good support for propositions. I suppose you can describe these phenomena as assent to sentences, but they might be very different sentences to express the same delusion. |
| 13987 | We may think in French, but we don't know or believe in French [Ryle] |
| Full Idea: Although we speak of thinking in French, we never talk of knowing or believing or opining in French. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Substitute') | |
| A reaction: Once again Ryle is playing devil's advocate, but he does it rather well, and offers good support for my belief in propositions. I love this. 'I know, in French, a bank where the wild thyme blows'. |
| 13989 | There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle] |
| Full Idea: There are no substantial propositions...There is just a relation between grammatical structure and the logical structure of facts. 'Proposition' denotes the same as 'sentence' or 'statement'. A proposition is not what I think, but what I think or talk in. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Conclusions') | |
| A reaction: The conclusion of Ryle's discussion, but I found his support for propositions much more convincing than his critique of them, or his attempt at an alternative linguistic account. He never mentioned animals, so he self-evidently hasn't grasped the problem. |
| 13982 | If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle] |
| Full Idea: All the arguments for the subsistence of true propositions seem to hold good for the subsistence of false ones. We might even have to find room for absurd or nonsensical ones like 'some round squares are not red-headed'. | |
| From: Gilbert Ryle (Are there propositions? [1930], 'Objections') | |
| A reaction: A particularly nice example of a Category Mistake from the man who made them famous. Why can't we just make belief a proposition attitude, so I equally believe 'sea is blue', 'grass is pink' and 'trees are bifocal', but the status of my belief varies? |
| 18545 | The disinterested attitude of the judge is the hallmark of a judgement of beauty [Shaftesbury, by Scruton] |
| Full Idea: Shaftesbury explained the peculiar features of the judgement of beauty in terms of the disinterested attitude of the judge. | |
| From: report of 3rd Earl of Shaftesbury (Characteristics [1711]) by Roger Scruton - Beauty: a very short introduction 1 | |
| A reaction: Good. I take our vocabulary to mark a distinction between expressions of subjective preference, and expressions of what aspire to be objective facts. 'I love this' versus 'this is good or beautiful'. |