21 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'. |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |