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| 8996 | If if time is money then if time is not money then time is money then if if if time is not money... |
| Full Idea: If if time is money then if time is not money then time is money then if if if time is not money then time is money then time is money then if time is money then time is money. | |||
| From: Willard Quine (Truth by Convention [1935], p.95) | |||
| A reaction: Quine offers this with no hint of a smile. I reproduce it for the benefit of people who hate analytic philosophy, and get tired of continental philosophy being attacked for its obscurity. |
| 8995 | Definition by words is determinate but relative; fixing contexts could make it absolute |
| Full Idea: A definition endows a word with complete determinacy of meaning relative to other words. But we could determine the meaning of a new word absolutely by specifying contexts which are to be true and contexts which are to be false. | |||
| From: Willard Quine (Truth by Convention [1935], p.89) | |||
| A reaction: This is the beginning of Quine's distinction between the interior of 'the web' and its edges. The attack on the analytic/synthetic distinction will break down the boundary between the two. Surprising to find 'absolute' anywhere in Quine. |
| 10064 | Quine quickly dismisses If-thenism |
| Full Idea: Quine quickly dismisses If-thenism. | |||
| From: report of Willard Quine (Truth by Convention [1935], p.327) by Alan Musgrave - Logicism Revisited §5 | |||
| A reaction: [Musgrave quotes a long chunk of Quine which is hard to compress!] Effectively, he says If-thenism is cheating, or begs the question, by eliminating whole sections of perfectly good mathematics, because they cannot be derived from axioms. |
| 20296 | Logic needs general conventions, but that needs logic to apply them to individual cases |
| Full Idea: Quine argues that logic could not be established by conventions, since the logical truths, being infinite in number, must be given by general conventions rather than singly; and logic is needed in the meta-theory, to apply to individual cases. | |||
| From: report of Willard Quine (Truth by Convention [1935]) by Georges Rey - The Analytic/Synthetic Distinction 3.4 | |||
| A reaction: A helpful insight into Quine's claim. If only someone would print these one sentence summaries at the top of classic papers, we would all get far more out of them at first reading. Assuming Rey is right! |
| 8998 | Claims that logic and mathematics are conventional are either empty, uninteresting, or false |
| Full Idea: If logic and mathematics being true by convention says the primitives can be conventionally described, that works for anything, and is empty; if the conventions are only for those fields, that's uninteresting; if a general practice, that is false. | |||
| From: Willard Quine (Truth by Convention [1935], p.102) | |||
| A reaction: This is Quine's famous denial of the traditional platonist view, and the new Wittgensteinian conventional view, preparing the ground for a more naturalistic and empirical view. I feel more sympathy with Quine than with the other two. |
| 8999 | Logic isn't conventional, because logic is needed to infer logic from conventions |
| Full Idea: If logic is to proceed mediately from conventions, logic is needed for inferring logic from the conventions. Conventions for adopting logical primitives can only be communicated by free use of those very idioms. | |||
| From: Willard Quine (Truth by Convention [1935], p.104) | |||
| A reaction: A common pattern of modern argument, which always seems to imply that nothing can ever get off the ground. I suspect that there are far more benign circles in the world of thought than most philosophers imagine. |
| 9000 | If a convention cannot be communicated until after its adoption, what is its role? |
| Full Idea: When a convention is incapable of being communicated until after its adoption, its role is not clear. | |||
| From: Willard Quine (Truth by Convention [1935], p.106) | |||
| A reaction: Quine is discussing the basis of logic, but the point applies to morality - that if there is said to be a convention at work, the concepts of morality must already exist to get the conventional framework off the ground. What is it that comes first? |
| 8994 | If analytic geometry identifies figures with arithmetical relations, logicism can include geometry |
| Full Idea: Geometry can be brought into line with logicism simply by identifying figures with arithmetical relations with which they are correlated thought analytic geometry. | |||
| From: Willard Quine (Truth by Convention [1935], p.87) | |||
| A reaction: Geometry was effectively reduced to arithmetic by Descartes and Fermat, so this seems right. You wonder, though, whether something isn't missing if you treat geometry as a set of equations. There is more on the screen than what's in the software. |
| 8997 | There are four different possible conventional accounts of geometry |
| Full Idea: We can construe geometry by 1) identifying it with algebra, which is then defined on the basis of logic; 2) treating it as hypothetical statements; 3) defining it contextually; or 4) making it true by fiat, without making it part of logic. | |||
| From: Willard Quine (Truth by Convention [1935], p.99) | |||
| A reaction: [Very compressed] I'm not sure how different 3 is from 2. These are all ways to treat geometry conventionally. You could be more traditional, and say that it is a description of actual space, but the multitude of modern geometries seems against this. |
| 8993 | If mathematics follows from definitions, then it is conventional, and part of logic |
| Full Idea: To claim that mathematical truths are conventional in the sense of following logically from definitions is the claim that mathematics is a part of logic. | |||
| From: Willard Quine (Truth by Convention [1935], p.79) | |||
| A reaction: Quine is about to attack logic as convention, so he is endorsing the logicist programme (despite his awareness of Gödel), but resisting the full Wittgenstein conventionalist picture. |