45 ideas
| 14415 | A ground must be about its truth, and not just necessitate it [Merricks] |
| Full Idea: A ground does not merely necessitate its truth. A ground is also what its truth is appropriately about. | |
| From: Trenton Merricks (Truth and Ontology [2007], 7.II) |
| 14408 | Truthmaker needs truths to be 'about' something, and that is often unclear [Merricks] |
| Full Idea: It is not always obvious what (if anything) a truth is about, in the sense of 'about' relevant to Truthmaker and truth-supervenient-on-being. Prior says 'Queen Anne is dead' is not about Queen Anne, and may be about the Earth. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.III) | |
| A reaction: A very nice and rather subtle objection to the Truthmaker thesis. Specifying the truthmaker for a given truth looks like a doddle in simple cases, but clearly it can become extremely elusive in other cases. |
| 14395 | If a ball changes from red to white, Truthmaker says some thing must make the change true [Merricks] |
| Full Idea: If a single ball goes from being red to being white, Truthmaker implies that something exists which makes it true that the second thing follows the first. | |
| From: Trenton Merricks (Truth and Ontology [2007], 3.V) |
| 14398 | Truthmaker says if an entity is removed, some nonexistence truthmaker must replace it [Merricks] |
| Full Idea: Truthmaker makes it impossible simply to remove an entity. One must always replace it with something else; namely, a truthmaker for the claim that that entity does not exist. | |
| From: Trenton Merricks (Truth and Ontology [2007], 4.I-3) | |
| A reaction: This is a particularly strong and persuasive argument from Merricks against the truthmaker view. Clearly the truthmaker for non-existence can't be there when it exists, and the destruction bringing the negative truthmaker into existence sounds odd. |
| 14403 | If Truthmaker says each truth is made by the existence of something, the theory had de re modality at is core [Merricks] |
| Full Idea: Truthmaker says that, for each truth, there is something that, by its mere existence, makes that truth true, …so Truthmaker has de re modality at its core. | |
| From: Trenton Merricks (Truth and Ontology [2007], 5.III) | |
| A reaction: I have no problem with de re modality, so this doesn't bother me. Merricks brings out nicely the baggage which you must carry if you are a Truthmaker. |
| 14397 | Truthmaker demands not just a predication, but an existing state of affairs with essential ingredients [Merricks] |
| Full Idea: The claim 'that Fido is brown' seems to demand only a brown Fido, but Truthmaker demands more. It demands both that a state of affairs along the lines of 'Fido's being brown' exists, and also that this state has its constituents essentially. | |
| From: Trenton Merricks (Truth and Ontology [2007], 4.I) | |
| A reaction: One would need to reread Merricks to get this clear, but my instinct is that the two scenarios are not very different. 'A brown Fido' would require Fido to be necessarily brown to do the job. |
| 14396 | If 'truth supervenes on being', worlds with the same entities, properties and relations have the same truths [Merricks] |
| Full Idea: 'Truth supervenes on being' says that any two possible worlds alike with respect to what entities exist and which properties (and relations) each of those entities exemplifies are thereby alike with respect to what is true. | |
| From: Trenton Merricks (Truth and Ontology [2007], 4) | |
| A reaction: Merricks says this view is found in early Wittgenstein, as well as in David Lewis. He suggests that this is a weaker and more plausible thesis than the full commitment to truthmakers. It still allows some truths to lack truthmakers. Sounds plausible. |
| 14400 | If truth supervenes on being, that won't explain why truth depends on being [Merricks] |
| Full Idea: If 'truth supervenes on being' aims to articulate the idea that truth depends on being, it must say more than that truth supervenes on being. | |
| From: Trenton Merricks (Truth and Ontology [2007], 4.VI) | |
| A reaction: This is a perennial problem with supervenience accounts, such as the supervenience of beauty on the object, or of mind on brain. |
| 14394 | It is implausible that claims about non-existence are about existing things [Merricks] |
| Full Idea: It is implausible that a claim asserting that a thing fails to exist is made true by - and so is appropriately about - some other, existing thing. | |
| From: Trenton Merricks (Truth and Ontology [2007], 3.V) |
| 14390 | Truthmaker isn't the correspondence theory, because it offers no analysis of truth [Merricks] |
| Full Idea: Because Truthmaker offers no analysis of being true, Truthmaker is not the correspondence theory of truth. | |
| From: Trenton Merricks (Truth and Ontology [2007], 1.IV) | |
| A reaction: I'm not convinced that the correspondence theory offers an 'analysis' of truth. It doesn't seem to do much more than offer a word which suggests an analogy with some relation in the world. |
| 14412 | Speculations about non-existent things are not about existent things, so Truthmaker is false [Merricks] |
| Full Idea: That 'there might have been a dozen more fundamental particles' is true, but not appropriately about any existing entities or their properties. Since Truthmaker says that all truths are about existing entities, it must be false. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.VI) | |
| A reaction: Since I don't necessarily agree that 'there might have been a dozen more fundamental particles' (see Scientific Essentialism), and I take the disagreement to have some basis, I doubt this idea. What stops 'there could be circular squares' from being true? |
| 14414 | I am a truthmaker for 'that a human exists', but is it about me? [Merricks] |
| Full Idea: I am a truthmaker for 'that a human exists', but it is not obvious that that proposition is thus about me. | |
| From: Trenton Merricks (Truth and Ontology [2007], 7.I) | |
| A reaction: This is part of the general rather good objection that it is often unclear what a truth is 'about' (Idea 14408). The original Gettier examples about justification illustrate this problem. They make things true, in a surprising way. |
| 14418 | Being true is not a relation, it is a primitive monadic property [Merricks] |
| Full Idea: Being true is not a relation. …Being true is a monadic property. …Being true is a primitive property. | |
| From: Trenton Merricks (Truth and Ontology [2007], 8.IV) | |
| A reaction: Even after reading Merricks on this, I am not sure I understand it. If a single sentence floats in the void, it is hard to see how the 'monadic' property of truth could accrue to it. |
| 14391 | If the correspondence theory is right, then necessary truths must correspond to something [Merricks] |
| Full Idea: Suppose for the sake of argument that the correspondence theory is correct. Then it is analytic that each necessary truth, in virtue of being true, corresponds to something. | |
| From: Trenton Merricks (Truth and Ontology [2007], 2.II) | |
| A reaction: The sort of nice simple observation for which I admire Merricks. You don't have to give up on the correspondence theory at this point, but you will have to go through with some substantial metaphysics to keep it afloat. |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 14419 | Deflationism just says there is no property of being truth [Merricks] |
| Full Idea: I take 'deflationism' to be nothing other than the claim that there is no property of being true. | |
| From: Trenton Merricks (Truth and Ontology [2007], 8.V) |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 14393 | The totality state is the most plausible truthmaker for negative existential truths [Merricks] |
| Full Idea: The claim that the totality state is the sole truthmaker for negative existential truths emerges as the best position for a truthmaker theorist. | |
| From: Trenton Merricks (Truth and Ontology [2007], 3.III) |
| 14413 | Some properties seem to be primitive, but others can be analysed [Merricks] |
| Full Idea: Some properties (perhaps negative charge, or the relation of identity) admit of no analysis, and so are primitive. But others are analysable, and so not primitive | |
| From: Trenton Merricks (Truth and Ontology [2007], 7.I) |
| 14416 | An object can have a disposition when the revelant conditional is false [Merricks] |
| Full Idea: It is possible for an object to have a disposition even though the relevant conditional is false. | |
| From: Trenton Merricks (Truth and Ontology [2007], 7.III) | |
| A reaction: This is the now standard observation that finks (killing the disposition) and antidotes (blocking the effect of the disposition) can intervene, as in safety mechanisms in electrical gadgets. There may be replies available here. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 14392 | Fregeans say 'hobbits do not exist' is just 'being a hobbit' is not exemplified [Merricks] |
| Full Idea: A Fregean about existence claims would say that 'that hobbits do not exist' is nothing other than the claim that 'being a hobbit' is not exemplified. | |
| From: Trenton Merricks (Truth and Ontology [2007], 3.II) | |
| A reaction: 'My passport has ceased to exist' seems to be a bit more dramatic than a relationship with a concept. |
| 14410 | You believe you existed last year, but your segment doesn't, so they have different beliefs [Merricks] |
| Full Idea: Your belief that you existed in the year 2000 is true; the belief of a segment of you that it then existed is false; so, by the indiscernibility of identicals, there must be two beliefs here. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.IV n20) | |
| A reaction: Merricks may be begging the question here. But in the segment view there is nothing which can truly believe it existed a year ago, so therefore nothing here has continued existence, so the segments cannot be part of a single thing. |
| 14417 | Counterfactuals aren't about actuality, so they lack truthmakers or a supervenience base [Merricks] |
| Full Idea: A counterfactual is not appropriately about the way anything is, …but about how something would be, had other things differed from how they actually are. As a result, true counterfactuals have neither truthmakers nor a superveniece base. | |
| From: Trenton Merricks (Truth and Ontology [2007], 7.IV) | |
| A reaction: Might not the truthmakers for counterfactuals reside in the dispositional facts about actuality? We assess the truth of counterfactuals in degrees, so something must determine our views. |
| 14402 | If 'Fido is possibly black' depends on Fido's counterparts, then it has no actual truthmaker [Merricks] |
| Full Idea: If Fido's being possibly black reduces (in Lewis's account) to the existence of black counterparts of Fido, then 'Fido is possibly black' is actually true, but it has no actually existing truthmaker. | |
| From: Trenton Merricks (Truth and Ontology [2007], 5.I) | |
| A reaction: This problem is increasingly the target of my views about dispositions and powers. Fido is not possibly a prize-winning novelist, but is possibly dead or in good health, because of the actual nature and dispositions of Fido. |
| 22086 | The most important aspect of a human being is not reason, but passion [Kierkegaard, by Carlisle] |
| Full Idea: Kierkegaard insisted that the most important aspect of a human being is not reason, but passion. | |
| From: report of Søren Kierkegaard (works [1845]) by Clare Carlisle - Kierkegaard: a guide for the perplexed Intro | |
| A reaction: Hume comes to mind for a similar view, but in character Hume was far more rational than Kierkegaard. |
| 14406 | Presentists say that things have existed and will exist, not that they are instantaneous [Merricks] |
| Full Idea: Presentists deny that everything is instantaneous; they think that many objects not only exist, but also have existed and will exist. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.I) | |
| A reaction: The second half is because presentists are committed to the truth of tensed existence claims (despite a lack of any theory as to how they work). Does anyone hold a theory of Instantaneousism? |
| 14407 | Presentist should deny there is a present time, and just say that things 'exist' [Merricks] |
| Full Idea: I think presentists should deny that there is anything at all that is the present time, just as they should deny that there are past times or future times. They should say that existing at the present time is just 'existing'. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.I) | |
| A reaction: The whole context is needed to understand Merrick's interesting claim. If there is no present, when can events happen? |
| 14411 | Maybe only presentism allows change, by now having a property, and then lacking it [Merricks] |
| Full Idea: Maybe presentism alone allows for genuine change, by permitting the direct having of a property by something and then, later, the absolute lacking of that property by that same thing. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.IV n23) | |
| A reaction: Four-dimensionalism (perdurantism) is the view which is most often charged with not explaining change, and that tends to be associated with eternalism. Are there just two coherent packages of views here? |
| 14405 | How can a presentist explain an object's having existed? [Merricks] |
| Full Idea: I am not sure what account presentists should give of an object's having existed. | |
| From: Trenton Merricks (Truth and Ontology [2007], 6.I) | |
| A reaction: Personally I am pretty puzzled by the eternalist and growing-block accounts of an object having existed, so we are all up a gum tree here. The best bet is to pull truth and existence apart, but heaven knows what that implies. See Idea 14399. |