39 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. |
| 4298 | All items of possible human knowledge are interconnected, and can be reached by inference [Descartes] |
| Full Idea: All the items of knowledge that lie within the reach of the human mind are linked together with a marvellous bond, and can be derived from each other by necessary inferences. | |
| From: René Descartes (unfinished dialogue [1649]) | |
| A reaction: It does seem that God ought to be able to infer all empirical facts from first principles. But how do you get started? |
| 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) |
| 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? |
| 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. |
| 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. |
| 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. |
| 9476 | If dispositions are more fundamental than causes, then they won't conceptually reduce to them [Bird on Lewis] |
| Full Idea: Maybe a disposition is a more fundamental notion than a cause, in which case Lewis has from the very start erred in seeking a causal analysis, in a traditional, conceptual sense, of disposition terms. | |
| From: comment on David Lewis (Causation [1973]) by Alexander Bird - Nature's Metaphysics 2.2.8 | |
| A reaction: Is this right about Lewis? I see him as reducing both dispositions and causes to a set of bald facts, which exist in possible and actual worlds. Conditionals and counterfactuals also suffer the same fate. |
| 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! |
| 8425 | For true counterfactuals, both antecedent and consequent true is closest to actuality [Lewis] |
| Full Idea: A counterfactual is non-vacuously true iff it takes less of a departure from actuality to make the consequent true along with the antecedent than it does to make the antecedent true without the consequent. | |
| From: David Lewis (Causation [1973], p.197) | |
| A reaction: Almost every theory proposed by Lewis hangs on the meaning of the word 'close', as used here. If you visited twenty Earth-like worlds (watch Startrek?), it would be a struggle to decide their closeness to ours in rank order. |
| 8424 | Determinism says there can't be two identical worlds up to a time, with identical laws, which then differ [Lewis] |
| Full Idea: By determinism I mean that the prevailing laws of nature are such that there do not exist any two possible worlds which are exactly alike up to that time, which differ thereafter, and in which those laws are never violated. | |
| From: David Lewis (Causation [1973], p.196) | |
| A reaction: This would mean that the only way an action of free will could creep in would be if it accepted being a 'violation' of the laws of nature. Fans of free will would probably prefer to call it a 'natural' phenomenon. I'm with Lewis. |
| 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? |
| 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. |
| 8420 | A proposition is a set of possible worlds where it is true [Lewis] |
| Full Idea: I identify a proposition with the set of possible worlds where it is true. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: As it stands, I'm baffled by this. How can 'it is raining' be a set of possible worlds? I assume it expands to refer to the truth-conditions, among possibilities as well as actualities. 'It is raining' fits all worlds where it is raining. |
| 8405 | A theory of causation should explain why cause precedes effect, not take it for granted [Lewis, by Field,H] |
| Full Idea: Lewis thinks it is a major defect in a theory of causation that it builds in the condition that the time of the cause precede that of the effect: that cause precedes effect is something we ought to explain (which his counterfactual theory claims to do). | |
| From: report of David Lewis (Causation [1973]) by Hartry Field - Causation in a Physical World | |
| A reaction: My immediate reaction is that the chances of explaining such a thing are probably nil, and that we might as well just accept the direction of causation as a given. Even philosophers balk at the question 'why doesn't time go backwards?' |
| 8427 | I reject making the direction of causation axiomatic, since that takes too much for granted [Lewis] |
| Full Idea: One might stipulate that a cause must always precede its effect, but I reject this solution. It won't solve the problem of epiphenomena, it rejects a priori any backwards causation, and it trivializes defining time-direction through causation. | |
| From: David Lewis (Causation [1973], p.203) | |
| A reaction: [compressed] Not strong arguments, I would say. Maybe apparent causes are never epiphenomenal. Maybe backwards causation is impossible. Maybe we must use time to define causal direction, and not vice versa. |
| 10392 | It is just individious discrimination to pick out one cause and label it as 'the' cause [Lewis] |
| Full Idea: We sometimes single out one among all the causes of some event and call it 'the' cause. ..We may select the abnormal causes, or those under human control, or those we deem good or bad, or those we want to talk about. This is invidious discrimination. | |
| From: David Lewis (Causation [1973]) | |
| A reaction: This is the standard view expressed by Mill - presumably the obvious empiricist line. But if we specify 'the pre-conditions' for an event, we can't just mention ANY fact prior to the effect - there is obvious relevance. So why not for 'the' cause as well? |
| 8419 | The modern regularity view says a cause is a member of a minimal set of sufficient conditions [Lewis] |
| Full Idea: In present-day regularity analyses, a cause is defined (roughly) as any member of any minimal set of actual conditions that are jointly sufficient, given the laws, for the existence of the effect. | |
| From: David Lewis (Causation [1973], p.193) | |
| A reaction: This is the view Lewis is about to reject. It seem to summarise the essence of the Mackie INUS theory. This account would make the presence of oxygen a cause of almost every human event. |
| 8421 | Regularity analyses could make c an effect of e, or an epiphenomenon, or inefficacious, or pre-empted [Lewis] |
| Full Idea: In the regularity analysis of causes, instead of c causing e, c might turn out to be an effect of e, or an epiphenomenon, or an inefficacious effect of a genuine cause, or a pre-empted cause (by some other cause) of e. | |
| From: David Lewis (Causation [1973], p.194) | |
| A reaction: These are Lewis's reasons for rejecting the general regularity account, in favour of his own particular counterfactual account. It is unlikely that c would be regularly pre-empted or epiphenomenal. If we build time's direction in, it won't be an effect. |
| 17525 | The counterfactual view says causes are necessary (rather than sufficient) for their effects [Lewis, by Bird] |
| Full Idea: The Humean idea, developed by Lewis, is that rather than being sufficient for their effects, causes are (counterfactual) necessary for their effects. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.162 |
| 17524 | Lewis has basic causation, counterfactuals, and a general ancestral (thus handling pre-emption) [Lewis, by Bird] |
| Full Idea: Lewis's basic account has a basic causal relation, counterfactual dependence, and the general causal relation is the ancestral of this basic one. ...This is motivated by counterfactual dependence failing to be general because of the pre-emption problem. | |
| From: report of David Lewis (Causation [1973]) by Alexander Bird - Causation and the Manifestation of Powers p.161 | |
| A reaction: It is so nice when you struggle for ages with a topic, and then some clever person summarises it clearly for you. |
| 8397 | Counterfactual causation implies all laws are causal, which they aren't [Tooley on Lewis] |
| Full Idea: Some counterfactuals are based on non-causal laws, such as Newton's Third Law of Motion. 'If no force one way, then no force the other'. Lewis's counterfactual analysis implies that one force causes the other, which is not the case. | |
| From: comment on David Lewis (Causation [1973]) by Michael Tooley - Causation and Supervenience 5.2 | |
| A reaction: So what exactly does 'cause' my punt to move forwards? Basing causal laws on counterfactual claims looks to me like putting the cart before the horse. |
| 8423 | My counterfactual analysis applies to particular cases, not generalisations [Lewis] |
| Full Idea: My (counterfactual) analysis is meant to apply to causation in particular cases; it is not an analysis of causal generalizations. Those presumably quantify over particulars, but it is hard to match natural language to the quantifiers. | |
| From: David Lewis (Causation [1973], p.195) | |
| A reaction: What authority could you have for asserting a counterfactual claim, if you only had one observation? Isn't the counterfactual claim the hallmark of a generalisation? For one case, 'if not-c, then not-e' is just a speculation. |
| 8426 | One event causes another iff there is a causal chain from first to second [Lewis] |
| Full Idea: One event is the cause of another iff there exists a causal chain leading from the first to the second. | |
| From: David Lewis (Causation [1973], p.200) | |
| A reaction: It will be necessary to both explain and identify a 'chain'. Some chains are extremely tenuous (Alexander could stop a barrel of beer). Go back a hundred years, and the cause of any present event is everything back then. |
| 4795 | Lewis's account of counterfactuals is fine if we know what a law of nature is, but it won't explain the latter [Cohen,LJ on Lewis] |
| Full Idea: Lewis can elucidate the logic of counterfactuals on the assumption that you are not at all puzzled about what a law of nature is. But if you are puzzled about this, it cannot contribute anything towards resolving your puzzlement. | |
| From: comment on David Lewis (Causation [1973]) by L. Jonathan Cohen - The Problem of Natural Laws p.219 | |
| A reaction: This seems like a penetrating remark. The counterfactual theory is wrong, partly because it is epistemological instead of ontological, and partly because it refuses to face the really difficult problem, of what is going on out there. |