38 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. |
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) |
11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
Full Idea: Two ways to see 'all horses are animals' are as picking out all the horses (so that it is a 'horse-quantifier'), ..or as ranging over lots of things in addition to horses, with 'horses' then restricting the things to those that satisfy 'is a horse'. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: Jubien says this gives you two different metaphysical views, of a world of horses etc., or a world of things which 'are horses'. I vote for the first one, as the second seems to invoke an implausible categorical property ('being a horse'). Cf Idea 11116. |
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. |
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. |
11116 | Being a physical object is our most fundamental category [Jubien] |
Full Idea: Being a physical object (as opposed to being a horse or a statue) really is our most fundamental category for dealing with the external world. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: This raises the interesting question of why any categories should be considered to be more 'fundamental' than others. I can only think that we perceive something to be an object fractionally before we (usually) manage to identify it. |
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! |
11117 | Haecceities implausibly have no qualities [Jubien] |
Full Idea: Properties of 'being such and such specific entity' are often called 'haecceities', but this term carries the connotation of non-qualitativeness which I don't favour. | |
From: Michael Jubien (Analyzing Modality [2007], 2) | |
A reaction: The way he defines it makes it sound as if it was a category, but I take it to be more like a bare individual essence. If it has not qualities then it has no causal powers, so there could be no evidence for its existence. |
11119 | De re necessity is just de dicto necessity about object-essences [Jubien] |
Full Idea: I suggest that the de re is to be analyzed in terms of the de dicto. ...We have a case of modality de re when (and only when) the appropriate property in the de dicto formulation is an object-essence. | |
From: Michael Jubien (Analyzing Modality [2007], 5) |
11118 | Modal propositions transcend the concrete, but not the actual [Jubien] |
Full Idea: Where modal propositions may once have seemed to transcend the actual, they now seem only to transcend the concrete. | |
From: Michael Jubien (Analyzing Modality [2007], 4) | |
A reaction: This is because Jubien has defended a form of platonism. Personally I take modal propositions to be perceptible in the concrete world, by recognising the processes involved, not the mere static stuff. |
11108 | Your properties, not some other world, decide your possibilities [Jubien] |
Full Idea: The possibility of your having been a playwright has nothing to do with how people are on other planets, whether in our own or in some other realm. It is only to do with you and the relevant property. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: I'm inclined to think that this simple point is conclusive disproof of possible worlds as an explanation of modality (apart from Jubien's other nice points). What we need to understand are modal properties, not other worlds. |
11111 | Modal truths are facts about parts of this world, not about remote maximal entities [Jubien] |
Full Idea: Typical modal truths are just facts about our world, and generally facts about very small parts of it, not facts about some infinitude of complex, maximal entities. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: I think we should embrace this simple fact immediately, and drop all this nonsense about possible worlds, even if they are useful for the semantics of modal logic. |
11105 | We have no idea how many 'possible worlds' there might be [Jubien] |
Full Idea: As soon as we start talking about 'possible world', we beg the question of their relevance to our prior notion of possibility. For all we know, there are just two such realms, or twenty-seven, or uncountably many, or even set-many. | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11107 | If there are no other possible worlds, do we then exist necessarily? [Jubien] |
Full Idea: Suppose there happen to be no other concrete realms. Would we happily accept the consequence that we exist necessarily? | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11106 | If all possible worlds just happened to include stars, their existence would be necessary [Jubien] |
Full Idea: If all of the possible worlds happened to include stars, how plausible is it to think that if this is how things really are, then we've just been wrong to regard the existence of stars as contingent? | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11112 | Possible worlds just give parallel contingencies, with no explanation at all of necessity [Jubien] |
Full Idea: In the world theory, what passes for 'necessity' is just a bunch of parallel 'contingencies'. The theory provides no basis for understanding why these contingencies repeat unremittingly across the board (while others do not). | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
11109 | If other worlds exist, then they are scattered parts of the actual world [Jubien] |
Full Idea: Any other realms that happened to exist would just be scattered parts of the actual world, not entire worlds at all. It would just happen that physical reality was fragmented in this remarkable but modally inconsequential way. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: This is aimed explicitly at Lewis's modal realism, and strikes me as correct. Jubien's key point here is that they are irrelevant to modality, just as foreign countries are irrelevant to the modality of this one. |
11113 | Worlds don't explain necessity; we use necessity to decide on possible worlds [Jubien] |
Full Idea: The suspicion is that the necessity doesn't arise from how worlds are, but rather that the worlds are taken to be as they are in order to capture the intuitive necessity. | |
From: Michael Jubien (Analyzing Modality [2007], 1) | |
A reaction: It has always seemed to me rather glaring that you need a prior notion of 'possible' before you can start to talk about 'possible worlds', but I have always been too timid to disagree with the combination of Saul Kripke and David Lewis. Thank you, Jubien! |
11110 | We mustn't confuse a similar person with the same person [Jubien] |
Full Idea: If someone similar to Humphrey won the election, that nicely establishes the possibility of someone's winning who is similar to Humphrey. But we mustn't confuse this possibility with the intuitively different possibility of Humphrey himself winning. | |
From: Michael Jubien (Analyzing Modality [2007], 1) |
5495 | Instances of pain are physical tokens, but the nature of pain is more abstract [Putnam, by Lycan] |
Full Idea: In machine functionalism, pain tokens (individual instances of pain) are identical with particular neurophysiological states, but pain itself, the kind, universal, or 'type', can be identified only with something more abstract. | |
From: report of Hilary Putnam (The Mental Life of Some Machines [1967]) by William Lycan - Introduction - Ontology p.6 | |
A reaction: This is where the "what is it like?" question seems important. Pain doesn't seem like a physical object, or an abstract idea. Personally I think the former is more likely to be correct than the latter. Causation by pain is not like causation by gravity. |
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. |