14 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. |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist. | |
| From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11 | |
| A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance? |
| 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. |
| 14804 | Is chance just unknown laws? But the laws operate the same, whatever chance occurs [Peirce] |
| Full Idea: Chance is the name for some law that is unknown to us? If you say 'each die moves under the influence of precise mechanical laws', it seems to me it is not these laws which made the tie turn up sixes, for the laws act the same when other throws come up. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.333) |
| 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... |
| 14805 | Is there any such thing as death among the lower organisms? [Peirce] |
| Full Idea: Among some of the lower organisms, it is a moot point with biologists whether there be anything which ought to be called death. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.334) | |
| A reaction: The point, presumably, is that one phase of an organisms moves into another, and the 'individuals' are not distinct enough for their 'death' to be a significant transition. A nicely mind-expanding thought. |
| 14806 | If the world is just mechanical, its whole specification has no more explanation than mere chance [Peirce] |
| Full Idea: The mechanical philosopher leaves the whole specification of the world utterly unaccounted for, which is pretty nearly as bad as to baldly attribute it to chance. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.337) | |
| A reaction: If now complete is even remotely available, then that doesn't seem to matter too much, but if there is one message modern physics teaches philosophy, it is that we should not give up on trying to answer the deeper questions. |
| 14803 | The more precise the observations, the less reliable appear to be the laws of nature [Peirce] |
| Full Idea: Try to verify any law of nature, and you will find that the more precise your observations, the more certain they will be to show irregular departures from the law. | |
| From: Charles Sanders Peirce (The Doctrine of Necessity Examined [1892], p.331) | |
| A reaction: This nicely encapsulates modern doubts about whether the so-called 'laws' of nature actually capture what is going on in the real world. |