61 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| Full Idea: We are able to reason about inconsistent beliefs, stories, and theories in useful and important ways | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 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. |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| Full Idea: In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation. | |
| From: Edwin D. Mares (Negation [2014], 5.5) | |
| A reaction: How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome. |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| Full Idea: Intuitionist logic appears most attractive in the form of a natural deduction system. | |
| From: Edwin D. Mares (Negation [2014], 5.5) |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| Full Idea: One reason for wanting a three-valued logic is to act as a basis of a theory of presupposition. | |
| From: Edwin D. Mares (Negation [2014], 3.1) | |
| A reaction: [He cites Strawson 1950] The point is that you can get a result when the presupposition does not apply, as in talk of the 'present King of France'. |
| 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? |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| Full Idea: The problem with material implication, and classical logic more generally, is that it considers only the truth value of formulas in deciding whether to make an implication stand between them. It ignores everything else. | |
| From: Edwin D. Mares (Negation [2014], 7.1) | |
| A reaction: The obvious problem case is conditionals, and relevance is an obvious extra principle that comes to mind. |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| Full Idea: Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction. | |
| From: Edwin D. Mares (Negation [2014], 2.2) | |
| A reaction: Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool. |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| Full Idea: On its standard reading, excluded middle tells us that bivalence holds. To reject excluded middle, we must reject either non-contradiction, or ¬(A∧B) ↔ (¬A∨¬B) [De Morgan 3], or the principle of double negation. All have been tried. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| Full Idea: If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false. | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: Mates's point is to show that passively taking the normal account of negation for granted has important implications. |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| Full Idea: In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning). | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: [compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating. |
| 1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
| Full Idea: We look to bound variables in connection with ontology not in order to know what there is, but in order to know what a given remark or doctrine, ours or someone else's, says there is. | |
| From: Willard Quine (On What There Is [1948], p.15) |
| 8455 | Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein] |
| Full Idea: Quine says that names need not be part of one's canonical notation; in fact, whatever scientific purposes are accomplished by names can be carried out just as well by the devices of quantification, variables and predicates. | |
| From: report of Willard Quine (On What There Is [1948]) by Alex Orenstein - W.V. Quine Ch.2 | |
| A reaction: This is part of Quine's analysis of where the ontological commitment of a language is to be found. Kripke's notion that a name baptises an item comes as a challenge to this view. |
| 8456 | Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein] |
| Full Idea: Quine extended Russell's theory for defining away definite descriptions, so that he could also define away names. | |
| From: report of Willard Quine (On What There Is [1948]) by Alex Orenstein - W.V. Quine Ch.2 | |
| A reaction: Quine also gets rid of universals and properties, so his ontology is squeezed from both the semantic and the metaphysical directions. Quine seems to be the key figure in modern ontology. If you want to expand it (E.J. Lowe), justify yourself to Quine. |
| 1611 | Names can be converted to descriptions, and Russell showed how to eliminate those [Quine] |
| Full Idea: I have shown that names can be converted to descriptions, and Russell has shown that descriptions can be eliminated. | |
| From: Willard Quine (On What There Is [1948], p.12) |
| 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. |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| Full Idea: Many-valued logics do not have reasonable natural deduction systems. | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| Full Idea: Situation semantics for logics consider not what is true in worlds, but what information is contained in situations. | |
| From: Edwin D. Mares (Negation [2014], 6.2) | |
| A reaction: Since many theoretical physicists seem to think that 'information' might be the most basic concept of a natural ontology, this proposal is obviously rather appealing. Barwise and Perry are the authors of the theory. |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| Full Idea: The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 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. |
| 1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
| Full Idea: The logicism of Frege, Russell, Whitehead, Church and Carnap condones the use of bound variables or reference to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
| Full Idea: The formalism of Hilbert keeps classical maths as a play of insignificant notations. Agreement is found among the rules which, unlike the notations, are quite significant and intelligible. | |
| From: Willard Quine (On What There Is [1948], p.15) |
| 1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
| Full Idea: The intuitionism of Poincaré, Brouwer, Weyl and others holds that classes are invented, and accepts reference to abstract entities only if they are constructed from pre-specified ingredients. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| Full Idea: For the intuitionist, talk of mathematical objects is rather misleading. For them, there really isn't anything that we should call the natural numbers, but instead there is counting. What intuitionists study are processes, such as counting and collecting. | |
| From: Edwin D. Mares (Negation [2014], 5.1) | |
| A reaction: That is the first time I have seen mathematical intuitionism described in a way that made it seem attractive. One might compare it to a metaphysics based on processes. Apparently intuitionists struggle with infinite sets and real numbers. |
| 1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
| Full Idea: Conceptualism holds that there are universals but they are mind-made. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 10241 | For Quine, there is only one way to exist [Quine, by Shapiro] |
| Full Idea: Quine takes 'existence' to be univocal, with a single ontology for his entire 'web of belief'. | |
| From: report of Willard Quine (On What There Is [1948]) by Stewart Shapiro - Philosophy of Mathematics 4.9 | |
| A reaction: Thus, there can be no 'different way of existing' (such as 'subsisting') for abstract objects such as those of mathematics. I presume that Quine's low-key physicalism is behind this. |
| 4064 | The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane] |
| Full Idea: According to Quine's conception of existence, the idea of a thing and the idea of existence are two sides of the same coin. | |
| From: report of Willard Quine (On What There Is [1948]) by Tim Crane - Elements of Mind 1.5 | |
| A reaction: I suspect that Quine's ontology is too dependent on language, but this thought seems profoundly right |
| 19277 | Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale] |
| Full Idea: It is because Quine holds constant singular terms to be always eliminable by an extension of Russell's theory of definite descriptions that he takes the bound variables of first-order quantification to be the sole means by which we refer to objects. | |
| From: report of Willard Quine (On What There Is [1948]) by Bob Hale - Necessary Beings 01.2 | |
| A reaction: Hale defends a Fregean commitment to existence based on the reference of singular terms in true statements. I think they're both wrong. If you want to know what I am committed to, ask me. Don't infer it from my use of English, or logic. |
| 12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
| Full Idea: Quine's approach to ontology asks the wrong question, a scientific rather than philosophical question, and answers it in the wrong way, by appealing to philosophical considerations in addition to ordinary scientific considerations. | |
| From: comment on Willard Quine (On What There Is [1948]) by Kit Fine - The Question of Ontology p.161 | |
| A reaction: He goes on to call Quine's procedure 'cockeyed'. Presumably Quine would reply with bafflement that scientific and philosophical questions could be considered as quite different from one another. |
| 8496 | What actually exists does not, of course, depend on language [Quine] |
| Full Idea: Ontological controversy tends into controversy over language, but we must not jump to the conclusion that what there is depends on words. | |
| From: Willard Quine (On What There Is [1948], p.16) | |
| A reaction: An important corrective to my constant whinge against philosophers who treat ontology as if it were semantics, of whom Quine is the central villain. Quine was actually quite a sensible chap. |
| 1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
| Full Idea: To be assumed as an entity is to be reckoned as the value of a variable. This amounts roughly to saying that to be is to be in the range of reference of a pronoun. | |
| From: Willard Quine (On What There Is [1948], p.13) | |
| A reaction: Cf. Idea 7784. |
| 8459 | Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein] |
| Full Idea: In fiction, 'Once upon a time there was an F who...' obviously does not make an ontological commitment, so Quine says the question of which ontology we accept must be dealt with in terms of the role an ontology plays in a scientific worldview. | |
| From: report of Willard Quine (On What There Is [1948]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: This seems to invite questions about the ontology of people who don't espouse a scientific worldview. If your understanding of the outside world and of the past is created for you by storytellers, you won't be a Quinean. |
| 8497 | An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine] |
| Full Idea: Our acceptance of ontology is similar in principle to our acceptance of a scientific theory; we adopt the simplest conceptual scheme into which the disordered fragments of raw experience can be fitted and arranged. | |
| From: Willard Quine (On What There Is [1948], p.16) | |
| A reaction: Quine (who says he likes 'desert landscapes') is the modern hero for anyone who loves Ockham's Razor, and seeks extreme simplicity. And yet he finds himself committed to the existence of sets to achieve this. |
| 16261 | If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine] |
| Full Idea: If Quine restricts himself to first-order predicate calculus, then the ontological implications concern the subjects of predicates. The nature of predicates, and what must be true for the predication, have disappeared from the radar screen. | |
| From: comment on Willard Quine (On What There Is [1948]) by Tim Maudlin - The Metaphysics within Physics 3.1 | |
| A reaction: Quine's response, I presume, is that the predicates can all be covered extensionally (red is a list of the red objects), and so a simpler logic will do the whole job. I agree with Maudlin though. |
| 7698 | If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine] |
| Full Idea: To apply Quine's criterion that to be is to be the value of a quantifier-bound variable, we must already know the values of bound variables, which is to say that we must already be in possession of a preferred existence domain. | |
| From: comment on Willard Quine (On What There Is [1948], Ch.6) by Dale Jacquette - Ontology | |
| A reaction: [A comment on Idea 1610]. Very nice to accuse Quine, of all people, of circularity, given his attack on analytic-synthetic with the same strategy! The values will need to be known extra-lingistically, to avoid more circularity. |
| 1612 | Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine] |
| Full Idea: The three medieval views on universals (realism, conceptualism and nominalism) reappear in the philosophy of maths as logicism, intuitionism and formalism. | |
| From: Willard Quine (On What There Is [1948], p.14) |
| 15402 | There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine] |
| Full Idea: There is not any entity whatever, individual or otherwise, which is named by the word 'redness'. ...That the houses and roses and sunsets are all of them red may be taken as ultimate and irreducible. | |
| From: Willard Quine (On What There Is [1948], p.10) | |
| A reaction: This seems to invite the 'ostrich' charge (Armstrong), that there is something left over that needs explaining. If the reds are ultimate and irreducible, that seems to imply that they have no relationship at all to one another. |
| 4443 | Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong] |
| Full Idea: Quine has attempted to bypass the problem of universals by arguing for the ontological innocence of predicates, since it is the application conditions of predicates which furnish the Realists with much of their case. | |
| From: report of Willard Quine (On What There Is [1948]) by David M. Armstrong - Universals p.503 | |
| A reaction: Presumably this would be a claim that predicates appear to commit us to properties, but that properties are not natural features, and can be reduced to something else. Tricky.. |
| 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. |
| 8498 | Treating scattered sensations as single objects simplifies our understanding of experience [Quine] |
| Full Idea: By bringing together scattered sense events and treating them as perceptions of one object, we reduce the complexity of our stream of experience to a manageable conceptual simplicity. | |
| From: Willard Quine (On What There Is [1948], p.17) | |
| A reaction: If, however, our consideration of tricky cases, such as vague objects, or fast-changing objects, or spatially coinciding objects made it all seem too complex, then Quine's argument would be grounds for abandoning objects. See Merricks. |
| 8856 | Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo] |
| Full Idea: Fifty years ago, Quine convinced everyone who cared that the argument for abstract objects, if there were going to be one, would have to be a posteriori in nature; an argument that numbers, for example, are indispensable entities for 'total science'. | |
| From: report of Willard Quine (On What There Is [1948], §1) by Stephen Yablo - Apriority and Existence | |
| A reaction: This sets the scene for the modern debate on the a priori. The claim that abstractions are indispensable for a factual account of the physical world strikes me as highly implausible. |
| 12443 | Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine] |
| Full Idea: Is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselve and distinct from one another. | |
| From: Willard Quine (On What There Is [1948], p.4) | |
| A reaction: Can he seriously mean that we are not allowed to talk about possible objects? If I design a house, it is presumably identical to the house I am designing, and distinct from houses I'm not designing. |
| 18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
| Full Idea: There is no likelihood that each sentence about physical objects can actually be translated, however deviously and complexly, into the phenomenalistic language. | |
| From: Willard Quine (On What There Is [1948], p.18), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
| Full Idea: This essay offered a verificationist account of language without the logical positivist error of supposing that verification could be reduced to a mere sequence of sense-experiences. | |
| From: comment on Willard Quine (On What There Is [1948]) by Daniel C. Dennett - works | |
| A reaction: This is because of Quine's holistic view of theory, so that sentences are not tested individually, where sense-data might be needed as support, but as whole teams which need to be simple, coherent etc. |
| 1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
| Full Idea: The useful ways in which ordinary people talk about meanings boil down to two: the having of meanings, which is significance, and sameness of meaning, or synonymy. | |
| From: Willard Quine (On What There Is [1948], p.11) | |
| A reaction: If the Fregean criterion for precise existence is participation in an identity relation, then synonymy does indeed pinpoint what we mean by 'meaning. |
| 1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
| Full Idea: Some philosophers construe meaningfulness as the having (in some sense of 'having') of some abstract entity which he calls a meaning, whereas I do not. | |
| From: Willard Quine (On What There Is [1948], p.11) | |
| A reaction: To call a meaning an 'entity' is to put a spin on it that makes it very implausible. Introspection shows us a gap between grasping a word and grasping its meaning. |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| Full Idea: In 'situation semantics' individuals, properties, facts, and events are treated as abstractions from situations. | |
| From: Edwin D. Mares (Negation [2014], 6.1) | |
| A reaction: [Barwise and Perry 1983 are cited] Since I take the process of abstraction to be basic to thought, I am delighted to learn that someone has developed a formal theory based on it. I am immediately sympathetic to situation semantics. |
| 19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
| Full Idea: Quine relates predicates to the things of which they can be predicated ...and hence predicates are 'true of' each and every thing of which the predicate can be truly predicated. | |
| From: report of Willard Quine (On What There Is [1948]) by Donald Davidson - Truth and Predication 5 | |
| A reaction: Davidson comments that the virtue of Quine's view is negative, in avoiding a regress in the explanation of predication. I'm not sure about true 'of' as an extra sort of truth, but I like dropping predicates from ontology, and sticking to truths. |