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All the ideas for 'Frege's Theory of Numbers', 'On What There Is' and 'The Analytic/Synthetic Distinction'

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39 ideas

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
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)
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
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.
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.
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
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)
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
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)
6. Mathematics / C. Sources of Mathematics / 7. Formalism
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)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
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)
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
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)
7. Existence / A. Nature of Existence / 2. Types of Existence
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.
7. Existence / A. Nature of Existence / 3. Being / g. Particular being
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
7. Existence / A. Nature of Existence / 6. Criterion for Existence
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.
7. Existence / D. Theories of Reality / 1. Ontologies
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.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
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.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
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.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
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.
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.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
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.
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.
8. Modes of Existence / D. Universals / 1. Universals
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)
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
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.
8. Modes of Existence / E. Nominalism / 3. Predicate Nominalism
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..
9. Objects / A. Existence of Objects / 1. Physical Objects
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.
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
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.
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
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.
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
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
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey]
     Full Idea: Where Kant and others had traditionally assumed that the a priori concerned beliefs 'justifiable independently of experience', Quine and others of the time came to regard it as beliefs 'unrevisable in the light of experience'.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 3.7)
     A reaction: That throws a rather striking light on Quine's project. Of course, if the a priori is also necessary, then it has to be unrevisable. But is a bachelor necessarily an unmarried man? It is not necessary that 'bachelor' has a fixed meaning.
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
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.
19. Language / A. Nature of Meaning / 8. Synonymy
Externalist synonymy is there being a correct link to the same external phenomena [Rey]
     Full Idea: Externalists are typically committed to counting expressions as 'synonymous' if they happen to be linked in the right way to the same external phenomena, even if a thinker couldn't realise that they are by reflection alone.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.2)
     A reaction: [He cites Fodor] Externalists always try to link to concrete things in the world, but most of our talk is full of generalities, abstractions and fiction which don't link directly to anything.
19. Language / A. Nature of Meaning / 10. Denial of Meanings
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.
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.
19. Language / C. Assigning Meanings / 3. Predicates
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.
19. Language / E. Analyticity / 1. Analytic Propositions
'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey]
     Full Idea: If Bob is married to Sue, then Sue is married to Bob. If x bigger than y, and y bigger than z, x is bigger than z. The symmetry of 'marriage' or transitivity of 'bigger than' are not obviously 'contained in' the corresponding thoughts.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 1.2)
     A reaction: [Also 'if something is red, then it is coloured'] This is a Fregean criticism of Kant. It is not so much that Kant was wrong, as that the concept of analyticity is seen to have a much wider application than Kant realised. Especially in mathematics.
Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey]
     Full Idea: Rejecting 'a married bachelor' as contradictory would seem to have no justification other than the claim that 'All bachelors are unmarried is analytic, and so cannot serve to justify or explain that claim.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 1.2)
     A reaction: Rey is discussing Frege's objection to Kant (who tried to prove the necessity of analytic judgements, on the basis of the denial being a contradiction).
Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey]
     Full Idea: What's peculiar about the analytic is that denying it seem unintelligible. Far from unrevisability explaining analyticity, it seems to be analyticitiy that explains unrevisability; we only balk at denying unmarried bachelors because that's what it means!
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 3.7)
     A reaction: This is a criticism of Quine, who attacked analyticity when it is understood as unrevisability. Obviously we could revise the concept of 'bachelor', if our marriage customs changed a lot. Rey seems right here.
The meaning properties of a term are those which explain how the term is typically used [Rey]
     Full Idea: It may be that the meaning properties of a term are the ones that play a basic explanatory role with regard to the use of the term generally, the ones in virtue ultimately of which a term is used with that meaning.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.3)
     A reaction: [He cites Devitt 1996, 2002, and Horwich 1998, 2005) I spring to philosophical life whenever I see the word 'explanatory', because that is the point of the whole game. They are pointing to the essence of the concept (which is explanatory, say I).
An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey]
     Full Idea: The existence of a separate language faculty may be an odd but psychologically real fact about us, and it may thereby supply a real basis for commitments about not only what is or is not grammatical, but about what is a matter of natural language meaning.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.4)
     A reaction: This is the Chomskyan view of analytic sentences. An example from Chomsky (1977:142) is the semantic relationships of persuade, intend and believe. It's hard to see how the secret faculty on its own could do the job. Consensus is needed.
Research throws doubts on the claimed intuitions which support analyticity [Rey]
     Full Idea: The movement of 'experimental philosophy' has pointed to evidence of considerable malleability of subject's 'intuitions' with regard to the standard kinds of thought experiments on which defenses of analytic claims typically rely.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.4)
     A reaction: See Cappelen's interesting attack on the idea that philosophy relies on intuitions, and hence his attack on experimental philosophy. Our consensus on ordinary English usage hardly qualifies as somewhat vague 'intuitions'.
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey]
     Full Idea: How in the end are we going to distinguish claims or the analytic as 'rational insight', 'primitive compulsion', inferential practice or folk belief from merely some deeply held empirical conviction, indeed, from mere dogma.
     From: Georges Rey (The Analytic/Synthetic Distinction [2013], 4.1)
     A reaction: This is Rey's summary of the persisting Quinean challenge to analytic truths, in the face of a set of replies, summarised by the various phrases here. So do we reject a dogma of empiricism, by asserting dogmatic empiricism?