49 ideas
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right. | |
| From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong. |
| 19160 | A comprehensive theory of truth probably includes a theory of predication [Davidson] |
| Full Idea: Theories of truth and theories of predication are closely related: it seems probable that any comprehensive theory of truth will include a theory of predication. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: Davidson defends the view that it is this way round. It is tempting to label them both as 'primitive'. Davidson distinguishes a 'theory' about truth from a 'definition'. |
| 19151 | Antirealism about truth prevents its use as an intersubjective standard [Davidson] |
| Full Idea: Antirealism, with its limitations of truth to what can be ascertained, deprives truth of its role as an intersubjective standard. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: I like this, because it lifts truth out of individual minds. I take truth to be an ideal - a simple one with little content, which is thus fairly uncontroversial. Truth is the main general purpose of thinking. |
| 19144 | 'Epistemic' truth depends what rational creatures can verify [Davidson] |
| Full Idea: The 'epistemic' view of truth asserts an essential tie to epistemology, and introduces a dependence of truth on what can somehow be verified by finite rational creatures. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: This view, which seems to be widely held, strikes me as an elementary confusion. I take truth to be fully successful belief. If you say belief can never be fully successful, then we can't know the truth - but that doesn't destroy the concept of truth. |
| 19148 | There is nothing interesting or instructive for truths to correspond to [Davidson] |
| Full Idea: The real objection to the correspondence theory of truth is that there is nothing interesting or instructive to which true sentences correspond. (C.I. Lewis challenged defenders to locate the fact or part of reality to which a truth corresponded). | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson defended a correspondence view in 'True to the Facts'. Davidson evidently also thinks the same objection applies to claims about truthmakers. If you say 'gold is shiny', the gold is very dispersed, but it is still there. |
| 19166 | The Slingshot assumes substitutions give logical equivalence, and thus identical correspondence [Davidson] |
| Full Idea: The Slingshot argument (of Frege, Church and Gödel) assumes that if two sentences are logically equivalent, they correspond to the same thing, and what a sentence corresponds to is not changed if a singular term is replaced by a coreferring term. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: This obviously won't work for 'Oedipus thinks he ought to marry Jocasta'. Sentences correspond, I presume, to what they are about, which is often a matter of emphasis or phrasing. Hence the Slingshot sounds like nonsense to me. |
| 19167 | Two sentences can be rephrased by equivalent substitutions to correspond to the same thing [Davidson] |
| Full Idea: Slingshot: 'Scott is the author of Waverley' and 'The number of counties in Utah is twenty-nine' can be rephrased by substitution so that they are both about the number twenty-nine, and are thus correspond to the same thing. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: [my paraphrase of Davidson's quote from Church 1956:24] These sentences clearly do not correspond to the same thing, so something has gone wrong with the idea that logically equivalent sentences have identical correspondents. |
| 19150 | Coherence truth says a consistent set of sentences is true - which ties truth to belief [Davidson] |
| Full Idea: A pure coherence theory of truth says that all sentences in a consistent set of sentences are true. ...I class this with epistemic views, because it ties truth directly to what is believed. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: [He cites Neurath] I would have thought that coherence is rather more than mere consistency. Truths which have nothing whatever in common can be consistent with one another. [but see his p.43 n14] |
| 19145 | We can explain truth in terms of satisfaction - but also explain satisfaction in terms of truth [Davidson] |
| Full Idea: Truth is easily defined in terms of satisfaction (as Tarski showed), but, alternatively, satisfaction can be taken to be whatever relation yields a correct account of truth. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson is assessing which is the prior 'primitive' concept, and he votes for truth. A perennial problem in philosophy, and very hard to find reasons for a preference. The axiomatic approach grows from taking truth as primitive. Axioms for satisfaction? |
| 19146 | Satisfaction is a sort of reference, so maybe we can define truth in terms of reference? [Davidson] |
| Full Idea: That the truth of sentences is defined by appeal to the semantic properties of words suggests that, if we could give an account of the semantic properties of words (essentially, of reference or satisfaction), we would understand the concept of truth. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: If you thought that words were prior to sentences, this might be the route to go. Davidson gives priority to sentences, and so prefers to work from the other end, which treats truth as primitive, and then defines reference and meaning. |
| 19174 | Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths [Davidson] |
| Full Idea: Axioms specify how each unstructured predicate is satisfied by a particular sequence. Then recursive axioms characterise complex sentences built from simpler ones. Closed sentences have no free variables, so true sentences are satisfied by all sequences. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: I take 'all sequences' to mean all combinations of objects in the domain. Thus nothing in domain contradicts the satisfied sentences. Hence Tarski's truth is said to be 'true in a model', where the whole system vouches for the sentence. |
| 19136 | Many say that Tarski's definitions fail to connect truth to meaning [Davidson] |
| Full Idea: It is complained that Tarski's definitions do not establish the connection between truth and meaning that many philosophers hold to be essential. | |
| From: Donald Davidson (Truth and Predication [2005], 1) | |
| A reaction: This, of course, was Davidson's big mission - to build on Tarski's theory a view of truth which dovetailed it with theories of meaning and reference. |
| 19139 | Tarski does not tell us what his various truth predicates have in common [Davidson] |
| Full Idea: There is no indication in Tarski's formal work of what it is that his various truth predicates have in common, and this is part of the content of the concept. | |
| From: Donald Davidson (Truth and Predication [2005], 1) | |
| A reaction: This seems like a good question to raise. If I list all the 'red' things, I can still ask what qualifies them to all appear on the same list. |
| 19147 | Truth is the basic concept, because Convention-T is agreed to fix the truths of a language [Davidson] |
| Full Idea: The key role of Convention-T in determining that truth, as characterised by the theory, has the same extension as the intuitive concept of truth makes it seem that it is truth rather than reference that is the basic primitive. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: The key strength of Tarski's account is that it specifies the extension of 'true' for a given language (as expressed in a richer meta-language). |
| 19172 | To define a class of true sentences is to stipulate a possible language [Davidson] |
| Full Idea: When we enquire whether a truth definition defines the class of true sentences in a particular language, we are thinking of the truth definition as stipulating a possible language. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Thus I might say "Nij wonk yang" is true if and only if snow is white, and make my first step towards a new language. An interesting way of looking at Tarski's project. |
| 19153 | Truth is basic and clear, so don't try to replace it with something simpler [Davidson] |
| Full Idea: Truth is one of the clearest and most basic concepts we have, so it is fruitless to dream of eliminating it in favor of something simpler or more fundamental. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: For redundancy theorists, I suppose, truth would be eliminated in favour of 'assertion'. Replacing it with 'satisfaction' doesn't seem very illuminating. Davidson would say 'reference' is more tricky and elusive than truth. |
| 19170 | Tarski is not a disquotationalist, because you can assign truth to a sentence you can't quote [Davidson] |
| Full Idea: It is clearly a mistake to call Tarski a disquotationalist. ...We say of a sentence not at hand (such as 'You gave the right answer to this question last night, but I can't remember what you said') that it is true or false. | |
| From: Donald Davidson (Truth and Predication [2005], 7) |
| 9585 | Since every definition is an equation, one cannot define equality itself [Frege] |
| Full Idea: Since every definition is an equation, one cannot define equality itself. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This seems a particularly nice instance of the general rule that 'you have to start somewhere'. It is a nice test case for the nature of meaning to ask 'what do you understand when you understand equality?', given that you can't define it. |
| 19140 | 'Satisfaction' is a generalised form of reference [Davidson] |
| Full Idea: We can think of 'satisfaction' as a generalised form of reference. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Just the sort of simple point we novices need from the great minds, to help us see what is going on. One day someone is going to explain Tarski's account of truth in plain English, but probably not in my lifetime. |
| 17446 | Counting rests on one-one correspondence, of numerals to objects [Frege] |
| Full Idea: Counting rests itself on a one-one correlation, namely of numerals 1 to n and the objects. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]), quoted by Richard G. Heck - Cardinality, Counting and Equinumerosity 3 | |
| A reaction: Parsons observes that counting will establish a one-one correspondence, but that doesn't make it the aim of counting, and so Frege hasn't answered Husserl properly. Which of the two is conceptually prior? How do you decide. |
| 9582 | Husserl rests sameness of number on one-one correlation, forgetting the correlation with numbers themselves [Frege] |
| Full Idea: When Husserl says that sameness of number can be shown by one-one correlation, he forgets that this counting itself rests on a univocal one-one correlation, namely that between the numerals 1 to n and the objects of the set. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is the platonist talking. Neo-logicism is attempting to build numbers just from the one-one correlation of objects. |
| 9586 | In a number-statement, something is predicated of a concept [Frege] |
| Full Idea: In a number-statement, something is predicated of a concept. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.328) | |
| A reaction: A succinct statement of Frege's theory of numbers. By my lights that would make numbers at least second-order abstractions. |
| 9580 | Our concepts recognise existing relations, they don't change them [Frege] |
| Full Idea: The bringing of an object under a concept is merely the recognition of a relation which previously already obtained, [but in the abstractionist view] objects are essentially changed by the process, so that objects brought under a concept become similar. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege's view would have to account for occasional misapplications of concepts, like taking a dolphin to be a fish, or falsely thinking there is someone in the cellar. |
| 9589 | Numbers are not real like the sea, but (crucially) they are still objective [Frege] |
| Full Idea: The sea is something real and a number is not; but this does not prevent it from being something objective; and that is the important thing. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.337) | |
| A reaction: This seems a qualification of Frege's platonism. It is why people start talking about abstract items which 'subsist', instead of 'exist'. It shows Frege's motivation in all this, which is to secure logic and maths from the vagaries of psychology. |
| 9577 | The naïve view of number is that it is like a heap of things, or maybe a property of a heap [Frege] |
| Full Idea: The most naïve opinion of number is that it is something like a heap in which things are contained. The next most naïve view is the conception of number as the property of a heap, cleansing the objects of their particulars. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.323) | |
| A reaction: A hundred toothbrushes and a hundred sponges can be seen to contain the same number (by one-to-one mapping), without actually knowing what that number is. There is something numerical in the heap, even if the number is absent. |
| 9578 | If objects are just presentation, we get increasing abstraction by ignoring their properties [Frege] |
| Full Idea: If an object is just presentation, we can pay less attention to a property and it disappears. By letting one characteristic after another disappear, we obtain concepts that are increasingly more abstract. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: Frege despises this view. Note there is scope in the despised view for degrees or levels of abstraction, defined in terms of number of properties ignored. Part of Frege's criticism is realist. He retains the object, while Husserl imagines it different. |
| 19173 | Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help [Davidson] |
| Full Idea: 'Theaetetus is a member of the set of seated objects' doesn't mention the predicate 'sits', but has a new predicate 'is a member of', with no given semantic role. We are back with Plato's problem with the predicate 'instantiates'. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Plato's problem is the 'third man' problem - a regress in the explanation. In other words, if we are trying to explain predication, treating predicates as sets gets us nowhere. Just as I always thought. But you have to want explanations. |
| 19142 | Probability can be constrained by axioms, but that leaves open its truth nature [Davidson] |
| Full Idea: Kolmogorov's axiomatisation of probability puts clear constraints on the concept of probability, but leaves open whether probability is further characterised as relative frequency, degree of belief, or something else. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Davidson cites this to show the limitations of axiomatic approaches to any topic (e.g. sets, truth, arithmetic). The item in question must be treated as a 'primitive'. This always has the feeling of second-best. |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
| From: James Van Cleve (Why coherence is not enough [2005], I) | |
| A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
| From: James Van Cleve (Why coherence is not enough [2005], III) | |
| A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |
| 19169 | Predicates are a source of generality in sentences [Davidson] |
| Full Idea: Predicates introduce generality into sentences. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: Not sure about this. Most words introduce generality. 'From' is a very general word about direction. 'Dogs bark' is as generally about dogs as it is generally about barking. |
| 9581 | Many people have the same thought, which is the component, not the private presentation [Frege] |
| Full Idea: The same thought can be grasped by many people. The components of a thought, and even more so the things themselves, must be distinguished from the presentations which in the soul accompany the grasping of a thought. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.325) | |
| A reaction: This is the basic realisation, also found in Russell, of how so much confusion has crept into philosophy, in Berkeley, for example. Frege starts down the road which leads to the externalist view of content. |
| 9579 | Disregarding properties of two cats still leaves different objects, but what is now the difference? [Frege] |
| Full Idea: If from a black cat and a white cat we disregard colour, then posture, then location, ..we finally derive something which is completely without restrictions on content; but what is derived from the objects does differ, although it is not easy to say how. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.324) | |
| A reaction: This is a key objection to abstractionism for Frege - we are counting two cats, not two substrata of essential catness, or whatever. But what makes a cat countable? (Key question!) It isn't its colour, or posture or location. |
| 9587 | How do you find the right level of inattention; you eliminate too many or too few characteristics [Frege] |
| Full Idea: Inattention is a very strong lye which must not be too concentrated, or it dissolves everything (such as the connection between the objects), but must not be too weak, to produce sufficient change. Personally I cannot find the proper dilution. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.330) | |
| A reaction: We may sympathise with the lack of precision here (frustrating for a logician), but it is not difficult to say of a baseball defence 'just concentrate on the relations, and ignore the individuals who implement it'. You retain basic baseball skills. |
| 9588 | Number-abstraction somehow makes things identical without changing them! [Frege] |
| Full Idea: Number-abstraction simply has the wonderful and very fruitful property of making things absolutely the same as one another without altering them. Something like this is possible only in the psychological wash-tub. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.332) | |
| A reaction: Frege can be awfully sarcastic. I don't really see his difficulty. For mathematics we only need to know what is countable about an object - we don't need to know how many hairs there are on the cat, only that it has identity. |
| 9583 | Psychological logicians are concerned with sense of words, but mathematicians study the reference [Frege] |
| Full Idea: The psychological logicians are concerned with the sense of the words and with the presentations, which they do not distinguish from the sense; but the mathematicians are concerned with the matter itself, with the reference of the words. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.326) | |
| A reaction: This is helpful for showing the point of his sense/reference distinction; it is part of his campaign against psychologism, by showing that there is a non-psychological component to language - the reference, where it meets the public world. |
| 9584 | Identity baffles psychologists, since A and B must be presented differently to identify them [Frege] |
| Full Idea: The relation of sameness remains puzzling to a psychological logician. They cannot say 'A is the same as B', because that requires distinguishing A from B, so that these would have to be different presentations. | |
| From: Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894], p.327) | |
| A reaction: This is why Frege needed the concept of reference, so that identity could be outside the mind (as in Hesperus = Phosophorus). Think about an electron; now think about a different electron. |
| 19149 | If we reject corresponding 'facts', we should also give up the linked idea of 'representations' [Davidson] |
| Full Idea: If we give up facts that make entities true, we ought to give up representations at the same time, for the legitimacy of each depends on the legitimacy of the other. | |
| From: Donald Davidson (Truth and Predication [2005], 2) | |
| A reaction: Not sure about this, because I'm not sure I know what he means by 'representations'. Surely every sentence is 'about' something? Is that just the references within the sentence, but not the sentence as a whole? |
| 19163 | You only understand an order if you know what it is to obey it [Davidson] |
| Full Idea: We understand an imperative if and only if we know under what conditions what it orders or commands is obeyed. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: How could this be wrong? 'Do you understand the order?' 'Yes sir!' 'Well do it then!' 'Do what sir?' |
| 19152 | Utterances have the truth conditions intended by the speaker [Davidson] |
| Full Idea: An utterance has certain truth conditions only if the speaker intends it to be interpreted as having those truth conditions. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: This seems to be a concession to the rather sensible things that Grice said about meaning. What about malapropisms? Surely there the speaker does not understand the truth conditions of her own utterance? Truth conditions are in the head? |
| 19162 | Meaning involves use, but a sentence has many uses, while meaning stays fixed [Davidson] |
| Full Idea: Meaning depends on use, but it is not easy to say how, for uses to which we may put the utterance of a sentence are endless while its meaning remains fixed. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: Quite so. The password is 'Swordfish' (or 'Sweet marjoram', if you prefer). |
| 19131 | We recognise sentences at once as linguistic units; we then figure out their parts [Davidson] |
| Full Idea: Our interest in the parts of sentences is derivative; we recognise at once that sentences are effective linguistic units, while we must figure out or decide what constitutes the meaningful words and particles. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: It depends on whether linguistic priority goes to complete thoughts that require expression, or to naming and ostensive definition to relate to elements of the environment. I find it hard to have a strong view on this one. Just So stories? |
| 19156 | Modern predicates have 'places', and are sentences with singular terms deleted from the places [Davidson] |
| Full Idea: The notion of 'places' in a predicate is the key to the modern concept of a predicate. Any expression obtained from a sentence by deleting one or more singular terms from the sentence counts as a predicate. | |
| From: Donald Davidson (Truth and Predication [2005], 4) |
| 19176 | The concept of truth can explain predication [Davidson] |
| Full Idea: My strategy is to show how our grasp of the concept of truth can explain predication. | |
| From: Donald Davidson (Truth and Predication [2005], 7) | |
| A reaction: His account of the concept of truth centres on Tarski's theory, but he clearly thinks more is needed than the bare bones offered by Tarski. The point, I think, is that predication is what makes a sentence 'truth-apt'. |
| 19133 | If you assign semantics to sentence parts, the sentence fails to compose a whole [Davidson] |
| Full Idea: The puzzle is that once plausible assignments of semantic roles have been made to parts of sentences, the parts do not seem to compose a united whole. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: It's not clear to me that a sentence does compose a 'whole', given that you can often add or remove bits from sentences, sometimes without changing the meaning. We often, in speech, assemble sentences before we have thought of their full meaning. |
| 19132 | Top-down semantic analysis must begin with truth, as it is obvious, and explains linguistic usage [Davidson] |
| Full Idea: Truth is the essential semantic concept with which to begin a top-down analysis of sentences, since truth, or lack of it, is the most obvious semantic property of sentences, and provides the clearest explanation of judging and conveying information. | |
| From: Donald Davidson (Truth and Predication [2005], Intro) | |
| A reaction: [a bit compressed] Presumably this goes with giving sentences semantic priority. The alternative approach is compositional, and is likely to give reference of terms priority over truth of the sentence. But accurate reference is a sort of truth. |
| 19158 | 'Humanity belongs to Socrates' is about humanity, so it's a different proposition from 'Socrates is human' [Davidson] |
| Full Idea: The sentence 'Humanity belongs to Socrates' is about the concept of humanity, unlike the "equivalent" 'Socrates is human', so they express different propositions. | |
| From: Donald Davidson (Truth and Predication [2005], 5) | |
| A reaction: [compressed] I like this a lot, because it shows why we should focus on propositions rather than on sentences, or even utterances. And asking what the sentence is 'about' focuses us on the underlying proposition or thought. |
| 19154 | The principle of charity says an interpreter must assume the logical constants [Davidson] |
| Full Idea: The principle of charity says that it is unavoidable that the pattern of sentences to which a speaker assents reflects the semantics of the logical constants. | |
| From: Donald Davidson (Truth and Predication [2005], 3) | |
| A reaction: That is not all the principle says, of course. Davidson seems to assume classical logic here, with a bivalent semantics. I wonder if all speakers use 'false' in the normal way, as well as 'true'? Do all languages even contain 'true'? |
| 19161 | We indicate use of a metaphor by its obvious falseness, or trivial truth [Davidson] |
| Full Idea: The sentences that contain metaphors are typically obviously false or trivially true, because these are typically indications that something is intended as a metaphor. | |
| From: Donald Davidson (Truth and Predication [2005], 6) | |
| A reaction: A nice point which sounds correct. Metaphors are famous being false, but the 'obvious' falseness signals the metaphor. If a metaphor is only obscurely false, that makes it difficult to read. |