41 ideas
| 9847 | A contextual definition permits the elimination of the expression by a substitution [Dummett] |
| Full Idea: The standard sense of a 'contextual definition' permits the eliminating of the defined expression, by transforming any sentence containing it into an equivalent one not containing it. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.11) | |
| A reaction: So the whole definition might be eliminated by a single word, which is not equivalent to the target word, which is embedded in the original expression. Clearly contextual definitions have some problems |
| 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. |
| 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. |
| 9820 | In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett] |
| Full Idea: For sentential or first-order logic, the logical truths are represented by valid formulas; in higher-order logics, by sentences formulated in purely logical terms. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 3) |
| 9896 | A prime number is one which is measured by a unit alone [Dummett] |
| Full Idea: A prime number is one which is measured by a unit alone. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 11) | |
| A reaction: We might say that the only way of 'reaching' or 'constructing' a prime is by incrementing by one till you reach it. That seems a pretty good definition. 64, for example, can be reached by a large number of different routes. |
| 18255 | Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett] |
| Full Idea: It is essential to a quantitative domain of any kind that there should be an operation of adding its elements; that this is more fundamental thaat that they should be linearly ordered by magnitude is apparent from cyclic domains like that of angles. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |
| 9895 | A number is a multitude composed of units [Dummett] |
| Full Idea: A number is a multitude composed of units. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 7 Def 2) | |
| A reaction: This is outdated by the assumption that 0 and 1 are also numbers, but if we say one is really just the 'unit' which is preliminary to numbers, and 0 is as bogus a number as i is, we might stick with the original Greek distinction. |
| 9852 | We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett] |
| Full Idea: A child understands 'there are just as many nuts as apples' as easily by pairing them off as by counting them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: I find it very intriguing that you could know that two sets have the same number, without knowing any numbers. Is it like knowing two foreigners spoke the same words, without understanding them? Or is 'equinumerous' conceptually prior to 'number'? |
| 9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
| Full Idea: The identity of a mathematical object may sometimes be fixed by its relation to what lies outside the structure to which it belongs. It is more fundamental to '3' that if certain objects are counted, there are three of them. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This strikes me as Dummett being pushed (by his dislike of the purely abstract picture given by structuralism) back to a rather empiricist and physical view of numbers, though he would totally deny that. |
| 9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
| Full Idea: The number 0 is not differentiated from 1 by its position in a progression, otherwise there would be no difference between starting with 0 and starting with 1. That is enough to show that numbers are not identifiable just as positions in structures. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 5) | |
| A reaction: This sounds conclusive, but doesn't feel right. If numbers are a structure, then where you 'start' seems unimportant. Where do you 'start' in St Paul's Cathedral? Starting sounds like a constructivist concept for number theory. |
| 9876 | Set theory isn't part of logic, and why reduce to something more complex? [Dummett] |
| Full Idea: The two frequent modern objects to logicism are that set theory is not part of logic, or that it is of no interest to 'reduce' a mathematical theory to another, more complex, one. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Dummett says these are irrelevant (see context). The first one seems a good objection. The second one less so, because whether something is 'complex' is a quite different issue from whether it is ontologically more fundamental. |
| 9884 | The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett] |
| Full Idea: The distinction between concrete and abstract objects, or Frege's corresponding distinction between actual and non-actual objects, is not a sharp dichotomy, but resembles a scale upon which objects occupy a range of positions. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This might seem right if you live (as Dummett chooses to) in the fog of language, but it surely can't be right if you think about reality. Is the Equator supposed to be near the middle of his scale? Either there is an equator, or there isn't. |
| 9869 | Realism is just the application of two-valued semantics to sentences [Dummett] |
| Full Idea: Fully fledged realism depends on - indeed, may be identified with - an undiluted application to sentences of the relevant kind of straightforwards two-valued semantics. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: This is the sort of account you get from a whole-heartedly linguistic philosopher. Personally I would say that Dummett has got it precisely the wrong way round: I adopt a two-valued semantics because my metaphysics is realist. |
| 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.... |
| 9880 | Nominalism assumes unmediated mental contact with objects [Dummett] |
| Full Idea: The nominalist superstition is based ultimately on the myth of the unmediated presentation of genuine concrete objects to the mind. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: Personally I am inclined to favour nominalism and a representative theory of perception, which acknowledges some 'mediation', but of a non-linguistic form. Any good theory here had better include animals, which seem to form concepts. |
| 9885 | The existence of abstract objects is a pseudo-problem [Dummett] |
| Full Idea: The existence of abstract objects is a pseudo-problem. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.18) | |
| A reaction: This remark follows after Idea 9884, which says the abstract/concrete distinction is a sliding scale. Personally I take the distinction to be fairly sharp, and it is therefore probably the single most important problem in the whole of human thought. |
| 9858 | Abstract objects nowadays are those which are objective but not actual [Dummett] |
| Full Idea: Objects which are objective but not actual are precisely what are now called abstract objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Why can there not be subjective abstract objects? 'My favourites are x, y and z'. 'I'll decide later what my favourites are'. 'I only buy my favourites - nothing else'. |
| 9859 | It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett] |
| Full Idea: If someone argued that assuming the existence of the Equator explains nothing, and it has no causal powers, so everything would be the same if it didn't exist, so we needn't accept its existence, we should gape at the crudity of the misunderstanding. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: Not me. I would gape if someone argued that latitude 55° 14' (and an infinity of other lines) exists for the same reasons (whatever they may be) that the Equator exists. A mode of description can't create an object. |
| 9860 | 'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett] |
| Full Idea: 'We've crossed the Equator' is judged true if we are nearer the other Pole, so it not for philosophers to deny that the Earth has an equator, and we see that the Equator is not a concept or relation or function, so it must be classified as an object. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.15) | |
| A reaction: A lovely example of linguistic philosophy in action (and so much the worse for that, I would say). A useful label here, I suggest (unoriginally, I think), is that we should label such an item a 'semantic object', rather than a real object in our ontology. |
| 9872 | Abstract objects need the context principle, since they can't be encountered directly [Dummett] |
| Full Idea: To recognise that there is no objection in principle to abstract objects requires acknowledgement that some form of the context principle is correct, since abstract objects can neither be encountered nor presented. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: I take this to be an immensely important idea. I consider myself to be a philosopher of thought rather than a philosopher of language (Dummett's distinction, he being one of the latter). Thought connects to the world, but does it connect to abstracta? |
| 9848 | Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett] |
| Full Idea: Husserl says the only ground for assuming the replaceability of one content by another is their identity; we are therefore not entitled to define their identity as consisting in their replaceability. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by Michael Dummett - Frege philosophy of mathematics Ch.12 | |
| A reaction: This is a direct challenge to Frege. Tricky to arbitrate, as it is an issue of conceptual priority. My intuition is with Husserl, but maybe the two are just benignly inerdefinable. |
| 9842 | Frege introduced criteria for identity, but thought defining identity was circular [Dummett] |
| Full Idea: In his middle period Frege rated identity indefinable, on the ground that every definition must take the form of an identity-statement. Frege introduced the notion of criterion of identity, which has been widely used by analytical philosophers. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.10) | |
| A reaction: The objection that attempts to define identity would be circular sounds quite plausible. It sounds right to seek a criterion for type-identity (in shared properties or predicates), but token-identity looks too fundamental to give clear criteria. |
| 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. |
| 9849 | Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett] |
| Full Idea: One powerful argument for a thesis that one notion is conceptually prior to another is the possibility of defining the first without reference to the second. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: You'd better check whether you can't also define the second without reference to the first before you rank their priority. And maybe 'conceptual priority' is conceptually prior to 'definition' (i.e. definition needs a knowledge of priority). Help! |
| 9850 | An argument for conceptual priority is greater simplicity in explanation [Dummett] |
| Full Idea: An argument for conceptual priority is greater simplicity in explanation. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.12) | |
| A reaction: One might still have to decide priority between two equally simple (or complex) concepts. I begin to wonder whether 'priority' has any other than an instrumental meaning (according to which direction you wish to travel - is London before Edinburgh?). |
| 9873 | Abstract terms are acceptable as long as we know how they function linguistically [Dummett] |
| Full Idea: To recognise abstract terms as perfectly proper items of a vocabulary depends upon allowing that all that is necessary for the lawful introduction of a range of expressions into the language is a coherent account of how they are to function in sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.16) | |
| A reaction: Why can't the 'coherent account' of the sentences include the fact that there must be something there for the terms to refer to? How else are we to eliminate nonsense words which obey good syntactical rules? Cf. Idea 9872. |
| 9993 | There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait] |
| Full Idea: Dummett uses the term 'logical abstraction' for the construction of the abstract objects as equivalence classes, but it is not clear why we should call this construction 'logical'. | |
| From: report of Michael Dummett (Frege philosophy of mathematics [1991]) by William W. Tait - Frege versus Cantor and Dedekind n 14 | |
| A reaction: This is a good objection, and Tait offers a much better notion of 'logical abstraction' (as involving preconditions for successful inference), in Idea 9981. |
| 9857 | We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett] |
| Full Idea: We arrive at the concept of suicide by considering both occurrences in the sentence 'Cato killed Cato' of the proper name 'Cato' as simultaneously replaceable by another name, say 'Brutus', and so apprehending the pattern common to both sentences. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch.14) | |
| A reaction: This is intended to illustrate Frege's 'logical abstraction' technique, as opposed to wicked psychological abstraction. The concept of suicide is the pattern 'x killed x'. This is a crucial example if we are to understand abstraction... |
| 9833 | To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett] |
| Full Idea: To get units by abstraction, units arrived at by abstraction from forks must the identical to that abstracted from spoons, with no trace of individuality. But if spoons can no longer be differentiated from forks, they can't differ from one another either. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: [compressed] Dummett makes the point better than Frege did. Can we 'think of a fork insofar as it is countable, ignoring its other features'? What are we left thinking of? Frege says it must still be the whole fork. 'Nice fork, apart from the colour'. |
| 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. |
| 9836 | Fregean semantics assumes a domain articulated into individual objects [Dummett] |
| Full Idea: A Fregean semantics assumes a domain already determinately articulated into individual objects. | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], Ch. 8) | |
| A reaction: A more interesting criticism than most of Dummett's other challenges to the Frege/Davidson view. I am beginning to doubt whether the semantics and the ontology can ever be divorced from the psychology, of thought, interests, focus etc. |
| 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? |
| 22818 | Liberals are not too individualistic, because people recognise and value social relations [Kymlicka] |
| Full Idea: It is alleged that liberals fail to recognise that people are naturally social or communal. …But liberals believe that people form and join social relations in which they come to understand and pursue the good. | |
| From: Will Kymlicka (Liberal Individualism and Liberal Neutrality [1989], Conc) | |
| A reaction: This is particulary aimed at communitarians, who see liberalism as based on a distorted concept of people as isolated beings. Personally I am beginning to shift my views from Aristotelian communitarianism to modern liberalism, so I like this idea. |
| 18257 | Why should the limit of measurement be points, not intervals? [Dummett] |
| Full Idea: By what right do we assume that the limit of measurement is a point, and not an interval? | |
| From: Michael Dummett (Frege philosophy of mathematics [1991], 22 'Quantit') |