15 ideas
| 13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
| Full Idea: Quine ends up with the logic that is maximally justified by experience, ...but a large number of the core principles of logic will have to be used to select the logic that is maximally justified by experience. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Paul Boghossian - Knowledge of Logic p.233 | |
| A reaction: In order to grasp some core principles of logic, you will probably need a certain amount of experience. I take logic to be an abstracted feature of reality (unless it is extended by pure fictions). Some basic logic may be hard wired in us. |
| 9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
| Full Idea: Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand. |
| 13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
| Full Idea: Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false. | |
| From: report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5 | |
| A reaction: One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter. |
| 13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
| Full Idea: Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for. | |
| From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02 |
| 9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
| Full Idea: Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them. |
| 9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
| Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory. | |
| From: Willard Quine (Carnap and Logical Truth [1954], II) | |
| A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic. |
| 9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
| Full Idea: One's hypothesis as to there being universals is at bottom just as arbitrary or pragmatic a matter as one's adoption of a new brand of set theory or even a new system of bookkeeping. | |
| From: Willard Quine (Carnap and Logical Truth [1954], x) | |
| A reaction: This spells out clearly the strongly pragmatist vein in Quine's thinking. |
| 12295 | 3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K] |
| Full Idea: Three-dimensionalist think a thing is somehow 'stretched out' through its location at a given time though not through the period during which it exists, and it is present in its entirety at a moment when it exists though not at a position of its location. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1) | |
| A reaction: This definition is designed to set up Fine's defence of the 3-D view, by showing that various dubious asymmetries show up if you do not respect the distinctions offered by the 3-D view. |
| 12298 | Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K] |
| Full Idea: In order to have genuine motion, rather than mere variation in position, it is necessary that the object should be 'entirely present' at each moment of the change. Thus without entire presence, or existence, genuine motion will not be possible. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.6) | |
| A reaction: See Idea 4786 for a rival view of motion. Of course, who says we have to have Kit Fine's 'genuine' motion, if some sort of ersatz motion still gets you to work in the morning? |
| 12296 | 4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K] |
| Full Idea: Four-dimensionalists have thought that a material thing is as equally 'stretched out' in time as it is in space, and that there is no special way in which it is entirely present at a moment rather than at a position. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1) | |
| A reaction: Compare his definition of 3-D in Idea 12295. The 4-D is contrary to our normal way of thinking. Since I don't think the future exists, I presume that if I am a 4-D object then I have to say that I don't yet exist, and I disapprove of such talk. |
| 18882 | You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons] |
| Full Idea: Fine says it is acceptable to ask when a wedding was and where it was, and it is acceptable to ask or state where the bride was (at a certain time), but not when she was. | |
| From: report of Kit Fine (In Defence of Three-Dimensionalism [2006], p.18) by Peter Simons - Modes of Extension: comment on Fine p.18 | |
| A reaction: This is aimed at three-dimensionalists who seem to think that a bride is a prolonged event, just as a wedding is. Fine is, interestingly, invoking ordinary language. When did the wedding start and end? When was the bride's birth and death? |
| 12297 | Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K] |
| Full Idea: Even if one is a three-dimensionalist, one might affirm the existence of temporal parts, on the grounds that everything merely endures for an instant. | |
| From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.2) | |
| A reaction: This seems an important point, as belief in temporal parts is normally equated with four-dimensionalism (see Idea 12296). The idea is that a thing might be 'entirely present' at each instant, only to be replaced by a simulacrum. |
| 9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
| Full Idea: When Kant's arithmetical examples of a priori synthetic judgements were sweepingly disqualified by Frege's reduction of arithmetic to logic, attention moved to the less tendentious and logically prior question 'How is logical certainty possible?' | |
| From: Willard Quine (Carnap and Logical Truth [1954], I) | |
| A reaction: A nice summary of the story so far, from someone who should know. This still leaves the question open of whether any synthetic truths can be derived from the logical certainties which are available. |
| 9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
| Full Idea: In trying to make sense of the role of convention in a priori knowledge, the very distinction between a priori and empirical begins to waver and dissolve. | |
| From: Willard Quine (Carnap and Logical Truth [1954], VI) | |
| A reaction: This is the next stage in the argument after Wittgenstein presents the apriori as nothing more than what arises from truth tables. The rationalists react by taking us back to the original 'natural light of reason' view. Then we go round again... |
| 7825 | The politics of Leibniz was the reunification of Christianity [Stewart,M] |
| Full Idea: The politics of Leibniz may be summed up in one word: theocracy. The specific agenda motivating much of his work was to reunite the Protestant and Catholic churches | |
| From: Matthew Stewart (The Courtier and the Heretic [2007], Ch. 5) | |
| A reaction: This would be a typical project for a rationalist philosopher, who thinks that good reasoning will gradually converge on the one truth. |