20 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 |
| 1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
| Full Idea: Although it is impossible to make contact in a finite time with things that are infinite in quantity, it is possible to do so with things that are infinitely divisible, since the time itself is also infinite in this way. | |
| From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A25) by Aristotle - Physics 233a21 |
| 5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
| Full Idea: Zeno's so-called 'Achilles' claims that the slowest runner will never be caught by the fastest runner, because the one behind has first to reach the point from which the one in front started, and so the slower one is bound always to be in front. | |
| From: report of Zeno (Elea) (fragments/reports [c.450 BCE]) by Aristotle - Physics 239b14 | |
| A reaction: The point is that the slower runner will always have moved on when the faster runner catches up with the starting point. We must understand how humble the early Greeks felt when they confronted arguments like this. It was like a divine revelation. |
| 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. |
| 1512 | Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea] |
| Full Idea: Zeno is wrong in arguing that the tiniest fragment of millet makes a sound; there is no reason why the fragment should be able to move in any amount of time the air which the whole bushel moved as it fell. | |
| From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A29) by Aristotle - Physics 250a16 |
| 1508 | Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea] |
| Full Idea: Zeno's third argument claims that a moving arrow is still. Here the conclusion depends on assuming that time is composed of nows; if this assumption is not granted, the argument fails. | |
| From: comment on Zeno (Elea) (fragments/reports [c.450 BCE], A27?) by Aristotle - Physics 239b5 |
| 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. |
| 15645 | Nominal essence are the observable properties of things [Eagle] |
| Full Idea: It is clear the nominal essences really are the properties of the things which have them: they are (a subset of) the observable properties of the things. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: I think this is wrong. The surface characteristics are all that is available to us, so our classifications must be based on those, but it is on the ideas of them, not their intrinsic natures. That is empiricsm! What makes the properties 'essential'? |
| 15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
| Full Idea: If the kinds there are depend not on the essences of the objects but on their observed distinguishing particulars, ...then for any kind that we think there is, it is possible that there are many underlying essences which are observably indistinguishable. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: Eagle is commenting on Locke's reliance on nominal essences. This seems to be the genuine problem with jadeite and nephrite (both taken to be 'jade'), or with 'fool's gold'. This isn't an objection to Locke; it just explains the role of science. |
| 15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
| Full Idea: Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], IV) | |
| A reaction: This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about. |
| 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... |
| 454 | If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea] |
| Full Idea: It things are many, they can't be more or less than they are, so they must be finite, but also there must be endless things between each thing, so they must be infinite. | |
| From: Zeno (Elea) (fragments/reports [c.450 BCE], B3), quoted by Simplicius - On Aristotle's 'Physics' 140.29 |
| 15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |
| Full Idea: The natural thought is to think that real kinds are given only by classification on the basis of essential properties: properties that make an object the kind of thing that it is. | |
| From: Antony Eagle (Locke on Essences and Kinds [2005], II) | |
| A reaction: Circularity alert! Circularity alert! Essence gives a thing its kind - and hence we can see what the kind is? Test for a trivial property! Eagle is not unaware of these issues. Does he mean 'necessary' rather than 'essential'? |
| 455 | That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea] |
| Full Idea: That which moves, moves neither in the place in which it is, nor in that in which it is not. | |
| From: Zeno (Elea) (fragments/reports [c.450 BCE], B4), quoted by (who?) - where? |
| 1511 | If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius] |
| Full Idea: If there is a place it will be in something, because everything that exists is in something. But what is in something is in a place. Therefore the place will be in a place, and so on ad infinitum. Therefore, there is no such thing as place. | |
| From: report of Zeno (Elea) (fragments/reports [c.450 BCE], B3) by Simplicius - On Aristotle's 'Physics' 9.562.3 |