45 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
18486 | We might define truth as arising from the truth-maker relation [MacBride] |
Full Idea: We might define truth using the truth-maker relation, albeit in a roundabout way, according to the pattern of saying 'S is true' is equivalent to 'there is something which makes S true'. | |
From: Fraser MacBride (Truthmakers [2013], 3.3) | |
A reaction: [MacBride gives it more algebraically, but I prefer English!] You would need to explain 'truth-making' without reference to truth. Horwich objects, reasonably, that ordinary people grasp 'truth' much more clearly than 'truth-making'. Bad idea, I think. |
18484 | Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride] |
Full Idea: For Martin the fatal error of phenomenalists was their inability to supply credible truth-makers for truths about unobserved objects; the same error afflicted Ryle's behaviourism, ...and Prior's Presentism (for past-tensed and future-tensed truths). | |
From: Fraser MacBride (Truthmakers [2013], 3.1) | |
A reaction: This seems to be the original motivation for the modern rise of the truthmaker idea. Personally I find 'Napoleon won at Austerlitz' is a perfectly good past-tensed truthmaker which is compatible with presentism. Truth-making is an excellent challenge. |
18466 | If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride] |
Full Idea: If a truthmaker entails its truth, this threatens to over-generate truth-makers for necessary truths - at least if the entailment is classical. It's a feature of this notion that anything whatsoever entails a given necessary truth. | |
From: Fraser MacBride (Truthmakers [2013], 1.1) | |
A reaction: This is a good reason to think that the truth-making relation does not consist of logical entailment. |
18473 | 'Maximalism' says every truth has an actual truthmaker [MacBride] |
Full Idea: The principle of 'maximalism' is that for every truth, then there must be something in the world that makes it true. | |
From: Fraser MacBride (Truthmakers [2013], 2.1) | |
A reaction: That seems to mean that no truths can be uttered about anything which is not in the world. If I say 'pigs might have flown', that isn't about the modal profile of actual pigs, it is about what might have resulted from that profile. |
18481 | Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride] |
Full Idea: If maximalism is intellectual heir to Russell's logical atomism, then 'optimalism' (the denial that universal and negative statements need truth-makers) is heir to Wittgenstein's version, where only atomic propositions represent states of affairs. | |
From: Fraser MacBride (Truthmakers [2013], 2.2) | |
A reaction: Wittgenstein's idea is that you can use the logical connectives to construct all the other universal and negative facts. 'Optimalism' restricts truthmaking to atomic statements. |
18483 | The main idea of truth-making is that what a proposition is about is what matters [MacBride] |
Full Idea: According the Lewis, the kernel of truth in truth-making is the idea that propositions have a subject matter. They are about things, so whether they are true or false depends on how those things stand. | |
From: Fraser MacBride (Truthmakers [2013], 2.4.1) | |
A reaction: [Lewis 'Things Qua Truth-makers' 2003] That sounds like the first step in the story, rather than the 'kernel' of the truth-making approach. |
18477 | There aren't enough positive states out there to support all the negative truths [MacBride] |
Full Idea: It's not obvious that there are enough positive states out there to underwrite all the negative truths. Even though it may be true that this liquid is odourless this needn't be because there's something further about it that excludes its being odourless. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
A reaction: What is the ontological status of all these hypothetical truths? What is the truthmaker for 'a trillion trillion negative truths exist'? What is the status of 'this is not not-red'? |
18479 | There are different types of truthmakers for different types of negative truth [MacBride] |
Full Idea: We recognise that what makes it true that there is no oil in this engine is different from what makes it true that there are no dodos left. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
A reaction: This looks like a local particular negation up against a universal negation. I'm not sure there is a big difference between 'my dodo's gone missing' (like my oil), and 'all the dodos have gone permanently missing'. |
18482 | Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride] |
Full Idea: Optimalists say that negative truths are 'true by default' (having the opposite truth value of p), and universal truths are too. Universal truths are equivalent to negative existential truths, which are true by default. | |
From: Fraser MacBride (Truthmakers [2013], 2.2) | |
A reaction: The background idea is Wittgenstein's, that if p is false, then not-p is true by default, without anyone having to assert the negation. This strikes me as a very promising approach to truthmaking. See Simons 2008. |
18485 | Even idealists could accept truthmakers, as mind-dependent [MacBride] |
Full Idea: Even an idealist could accept that there are truth-makers whilst thinking of them as mind-dependent entities. | |
From: Fraser MacBride (Truthmakers [2013], 3.1) | |
A reaction: This undercuts anyone (me, perhaps?) who was hoping to prop up their robust realism with an angry demand to be shown the truthmakers. |
18474 | Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride] |
Full Idea: If the sentence 'This sentence has no truth-maker' has a truth-maker, then it must be true. But then what it says must be the case, so it has no truth-maker. Hence by reductio the sentence has no truth-maker. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.1) | |
A reaction: [Argument proposed by Peter Milne 2005] Rodriguez-Pereyra replies that the sentence is meaningless, so that it can't possibly be true. The Liar sentence is also said to be meaningless. The argument opposes Maximalism. |
18490 | Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride] |
Full Idea: Maybe the truth-maker panegyrists have misconstrued the logical form of 'makes true'. They have taken it to be a verb like 'x hits y', when really it is akin to the connective '→' or 'because'. | |
From: Fraser MacBride (Truthmakers [2013], 3.7) | |
A reaction: [He cites Melia 2005] This isn't any sort of refutation of truth-making, but an offer of how to think of the phenomenon if you reject the big principle. I like truth-making, but resist the 'makes' that brings unthought propositions into existence. |
18493 | Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride] |
Full Idea: When supporters of truth-making talk of 'something' which makes a sentence true, they make the assumption that it is an objectual quantifier in name position. | |
From: Fraser MacBride (Truthmakers [2013], 3.8) | |
A reaction: We might say, more concisely, that they are 'reifying' the something. This makes it sound as if Armstrong and Bigelow have made a mistake, but that are simply asserting that this particular quantification is indeed objectual. |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
Full Idea: I once wrote that there are three linguistic devices that make it possible for us to frame undecidable statements: quantification over infinity totalities, as expressed by word such as 'never'; the subjunctive conditional form; and the past tense. | |
From: Michael Dummett (Truth and the Past [2001], 4) | |
A reaction: Dummett now repudiates the third one. Statements containing vague concepts also appear to be undecidable. Personally I have no problems with deciding (to a fair extent) about 'never x', and 'if x were true', and 'it was x'. |
18489 | Connectives link sentences without linking their meanings [MacBride] |
Full Idea: The 'connectives' are expressions that link sentences but without expressing a relation that holds between the states of affairs, facts or tropes that these sentences denote. | |
From: Fraser MacBride (Truthmakers [2013], 3.7) | |
A reaction: MacBride notes that these contrast with ordinary verbs, which do express meaningful relations. |
18476 | 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride] |
Full Idea: Statements of the form 'a is F' aren't invariably positive ('a is dead'), and nor are statements of the form 'a isn't F' ('a isn't blind') always negative. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.4) | |
A reaction: The point is that the negation may be implicit in the predicate. There are many ways to affirm or deny something, other than by use of the standard syntax. |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
Full Idea: There is surely no number n such that "n grains of sand do not make a heap, although n+1 grains of sand do" is true. | |
From: Michael Dummett (Truth and the Past [2001], 4) | |
A reaction: It might be argued that there is such a number, but no human being is capable of determing it. Might God know the value of n? On the whole Dummett's view seems the most plausible. |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
A reaction: See Idea 10572. |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
Full Idea: The intuitionist account of the meaning of mathematical statements does not employ the notion of a statement's being true, but only that of something's being a proof of the statement. | |
From: Michael Dummett (Truth and the Past [2001], 2) | |
A reaction: I remain unconvinced that anyone could give an account of proof that didn't discreetly employ the notion of truth. What are we to make of "we suspect this is true, but no one knows how to prove it?" (e.g. Goldbach's Conjecture). |
18480 | Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride] |
Full Idea: 'To be is to be a truth-maker' has been proposed as a replacement the standard conception of ontological commitment, that to be is to be the value of a variable. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.4.2) | |
A reaction: [He cites Ross Cameron 2008] Unconvincing. What does it mean to say that some remote unexperienced bit of the universe 'makes truths'? How many truths? Where do these truths reside when they aren't doing anything useful? |
8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
Full Idea: The idea of 'Cambridge Change' is like saying 'the landscape changes as you travel east'. | |
From: Michael Dummett (Truth and the Past [2001], 5) | |
A reaction: The phrase was coined in Oxford. It is a useful label with which realists can insult solipsists, idealists and other riff-raff. Four Dimensionalists seem to see time in this way. Events sit there, and we travel past them. But there are indexical events. |
18471 | Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride] |
Full Idea: The concept of 'grounding' appears to cry out for treatment as a family resemblance concept, a concept whose instances have no more in common than different games do. | |
From: Fraser MacBride (Truthmakers [2013], 1.6) | |
A reaction: I like the word 'determinations', though MacBride's point my also apply to that. I take causation to be one species of determination, and truth-making to be another. They form a real family, with no adoptees. |
18472 | Which has priority - 'grounding' or 'truth-making'? [MacBride] |
Full Idea: Some philosophers define 'grounding' in terms of 'truth-making', rather than the other way around. | |
From: Fraser MacBride (Truthmakers [2013], 1.6) | |
A reaction: [Cameron exemplifies the first, and Schaffer the second] I would have thought that grounding was in the world, but truth-making required the introduction of propositions about the world by minds, so grounding is prior. Schaffer is right. |
18475 | Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride] |
Full Idea: The logical atomism of Russell admitted some logically complex facts but not others - in contrast to Wittgenstein's version which admitted only atomic facts. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.3) | |
A reaction: For truthmakers, it looks as if the Wittgenstein version might do a better job (e.g. with negative truths). I quite like the Russell approach, where complex facts underwrite the logical connectives. Disjunctive, negative, conjunctive, hypothetical facts. |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
Full Idea: In distinguishing between what can establish a statement about the past as true and what it is that that statement says, we are repudiating antirealism about the past. | |
From: Michael Dummett (Truth and the Past [2001], 3) | |
A reaction: This is a late shift of ground from the champion of antirealism. If Dummett's whole position is based on a 'justificationist' theory of meaning, he must surely have a different theory of meaning now for statements about the past? |
18478 | Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride] |
Full Idea: It is almost universally acknowledged that Wittgenstein's plan to show all necessity is logical necessity ended in failure - indeed foundered upon the very problem of explaining colour incompatibilities. | |
From: Fraser MacBride (Truthmakers [2013], 2.1.4.1) | |
A reaction: I'm not sure whether you can 'show' that colour incompatibility is some sort of necessity, though intuitively it seems so. I'm thinking that 'necessity' is a unitary concept, with a wide variety of sources generating it. |
8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
Full Idea: The existence of a universe from which sentience was permanently absent is an unintelligible fantasy. What exists is what can be known to exist. What is true is what can be known to be true. Reality is what can be experienced and known. | |
From: Michael Dummett (Truth and the Past [2001], 5) | |
A reaction: This strikes me as nonsense. The fact that we cannot think about a universe without introducing a viewpoint does not mean that we cannot 'intellectually imagine' its existence devoid of viewpoints. Nothing could ever experience a star's interior. |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
A reaction: The point is that no particular object is now required to make the abstraction. |
8193 | Verification is not an individual but a collective activity [Dummett] |
Full Idea: Verification is not an individual but a collective activity. | |
From: Michael Dummett (Truth and the Past [2001], 3) | |
A reaction: This generates problems. Are deceased members of the community included? (Yes, says Dummett). If someone speaks to angels (Blake!), do they get included? Is a majority necessary? What of weird loners? Etc. |
8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
Full Idea: To demonstrate the necessity of a truth-conditional theory of meaning, a proponent of such a theory must argue that use cannot be described without appeal to the conditions for the truth of statements. | |
From: Michael Dummett (Truth and the Past [2001], 1) | |
A reaction: Unlike Dummett, I find that argument rather appealing. How do you decide the possible or appropriate use for a piece of language, if you don't already know what it means. Basing it all on social conventions means it could be meaningless ritual. |
8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
Full Idea: It is not enough for the truth-condition theorist to argue that we need the concept of truth: he must show that we should have the same conception of truth that he has. | |
From: Michael Dummett (Truth and the Past [2001], 2) | |
A reaction: Davidson invites us to accept Tarski's account of truth. It invites the question of what the theory would be like with a very robust correspondence account of truth, or a flabby rather subjective coherence view, or the worst sort of pragmatic view. |
8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
Full Idea: Maybe both the past and the future are real, determined by our current temporal perspective. Past is then events capable of having a causal influence upon events near us, and future is events we can affect, but from which we receive no information. | |
From: Michael Dummett (Truth and the Past [2001], 5) | |
A reaction: This is the Four-Dimensional view, which is opposed to Presentism. Might immediate unease is that it gives encouragement to fortune-tellers, whom I have always dismissed with 'You can't see the future, because it doesn't exist'. |
8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |
Full Idea: The idea that only the present is real cannot be sustained. St Augustine pointed out that the present has no duration; it is a mere boundary between past and future, and dependent on them. It also denies truth-value to statements about past or future. | |
From: Michael Dummett (Truth and the Past [2001], 5) | |
A reaction: To defend Presentism, I suspect that one must focus entirely on the activities of consciousness and short-term memory. All truths, of past or future, must refer totally to such mental events. But what could an event be if there is no enduring time? |