19 ideas
11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
Full Idea: We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it bit by bit, plank by plank. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
A reaction: This is an interesting commitment to Strawson's 'revisionary' metaphysics, rather than its duller cousin 'descriptive' metaphysics. Good for Quine. Remember, though, Davidson's 'On the Very Idea of Conceptual Scheme'. |
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
Full Idea: My Proceduralism offers axiom-free foundations for mathematics. Axioms give way to the stipulation of procedures. We obtain a form of logicism, but with a procedural twist, and with a logic which is ontologically neutral, and no assumption of objects. | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1) | |
A reaction: [See Ideas 9222 and 9223 for his Proceduralism] Sounds like philosophical heaven. We get to take charge of mathematics, without the embarrassment of declaring ourselves to be platonists. Someone, not me, should evaluate this. |
9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
Full Idea: I call my new approach to mathematics 'proceduralism'. It agrees with Hilbert and Poincaré that the objects and truths are postulations, but takes them to be imperatival rather than indicative in form; not propositions, but procedures for construction. | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], Intro) | |
A reaction: I'm not sure how an object or a truth can be a procedure, any more than a house can be a procedure. If a procedure doesn't have a product then it is an idle way to pass the time. The view seems to be related to fictionalism. |
9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
Full Idea: My Proceduralism has one simple rule (introduce an object), and four complex rules: Composition (combining two procedures), Conditionality (if A, do B), Universality (do a procedure for every x), and Iteration (rule to keep doing B). | |
From: Kit Fine (Our Knowledge of Mathematical Objects [2005], 1) | |
A reaction: It sounds like a highly artificial and private game which Fine has invented, but he claims that this is the sort of thing that practising mathematicians have always done. |
11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
Full Idea: A river is a process through time, and the river stages are its momentary parts. Identification of the river bathed in once with the river bathed in again is just what determines our subject matter to be a river process as opposed to a river stage. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1) | |
A reaction: So if we take a thing which has stages, but instead of talking about the stages we talk about a single thing that endures through them, then we are talking about a process. Sounds very good to me. |
11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
Full Idea: 'Red' is surely not going to be opposed to 'Cayster' [name of a river], as abstract to concrete, merely because of discontinuity in geometrical shape? | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
A reaction: I've been slow to grasp the truth of this. However, Quine assumes that 'red' is concrete because 'Cayster' is, but it is perfectly arguable that 'Cayster' is an abstraction, despite all that water. |
11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
Full Idea: The use of general terms does not commit us to admitting a corresponding abstract entity into our ontology, but an abstract singular term, including the law of putting equals for equals, flatly commits us to an abstract entity named by the term. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4) | |
A reaction: Does this mean that in 'for the sake of the children', I have to believe in 'sakes' if I can find a synonym which will substitute for it? |
11096 | Discourse generally departmentalizes itself to some degree [Quine] |
Full Idea: Discourse generally departmentalizes itself to some degree. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
A reaction: I pick this out because I think it is important. There is a continually shifting domain in any conversation ('what we are talking about'), and speech cannot be understand if the shifting domain or department has not been grasped. |
11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
Full Idea: No more need be demanded of 'is square' than that our listener learn when to expect us to apply it to an object and when not; there is no need for the phrase itself to be the name in turn of a separate object of any kind. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4) |
11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
Full Idea: Why not view 'red' as naming a single concrete object extended in space and time? ..To say a drop is red is to say that the one object, the drop, is a spatio-temporal part of the other, red, as a waterfall is part of a river. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) |
11097 | Red is the largest red thing in the universe [Quine] |
Full Idea: Red is the largest red thing in the universe - the scattered total thing whose parts are all the red things. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 3) |
17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
Full Idea: The concept of identity is central in specifying spatio-temporally broad objects by ostension. Without identity, n acts of ostension merely specify up to n objects. ..But when we affirm identity of object between ostensions, they refer to the same object. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1) | |
A reaction: Quine says that there is an induction involved. On the whole, Quine seems to give a better account of identity than Geach or Wiggins can offer. |
11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
Full Idea: We might propound the maxim of the 'identification of indiscernibles': Objects indistinguishable from one another within the terms of a given discourse should be construed as identical for that discourse. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
A reaction: This increasingly strikes me as the correct way to discuss such things. Identity is largely contextual, and two things can be viewed as type-identical for practical purposes (e.g. teaspoons), but distinguished if it is necessary. |
11104 | Concepts are language [Quine] |
Full Idea: Concepts are language. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
A reaction: Hm. This seems to mean that animals and pre-linguistic children have no concepts. I just don't believe that. |
11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |
Full Idea: Applying the operator '-ness' or 'class of' to abstract general terms, we get second-level abstract singular terms. | |
From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
A reaction: This is the derivation of abstract concepts by naming classes, rather than by deriving equivalence classes. Any theory which doesn't allow multi-level abstraction is self-evidently hopeless. Quine says Frege and Russell get numbers this way. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |