17 ideas
| 4742 | Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong] |
| Full Idea: In Armstrong's version of the correspondence theory, the truth-making relation is not one-one, but one-many or many-one. Thus 'p or q' has two truth makers, p and q. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.129), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Interesting. Armstrong deals in universals. He also cites many swans as truth-makers for 'there is a least one black swan'. Not correspondence as we know it, Jim. |
| 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. |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 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. |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| Full Idea: Armstrong has difficulty explaining how laws entail regularities. There is no real modality in the basic components of the world, but he wants to support counterfactuals. His official position is a kind of fictionalism. | |
| From: comment on David M. Armstrong (A World of States of Affairs [1997], 49-51) by Alexander Bird - Nature's Metaphysics 4.4.4 | |
| A reaction: Armstrong seems to be up against the basic problems that laws won't explain anything if they are merely regularities (assuming they are not decrees of a supernatural force). |
| 15550 | Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis] |
| Full Idea: Armstrong has a distinctive conception of (fundamental) properties as contingently existing beings with multiple locations in space and time. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by David Lewis - A world of truthmakers? p.220 | |
| A reaction: Armstrong tries to get a naturalistically founded platonism (which he claims is Aristotelian), but the idea that one thing can be multiply located strikes me as daft (especially if the number of its locations increases or decreases). |
| 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. |
| 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. |
| 4743 | The truth-maker for a truth must necessitate that truth [Armstrong] |
| Full Idea: The truth-maker for a truth must necessitate that truth. | |
| From: David M. Armstrong (A World of States of Affairs [1997], p.115), quoted by Pascal Engel - Truth Ch.1 | |
| A reaction: Armstrong's 'truth-make principle'. It seems to be a necessity which is neither natural nor analytic, making it metaphysically necessary. Or is it part of the definition of truth? |
| 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... |
| 4798 | In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos] |
| Full Idea: In recent writings, Armstrong makes a direct identification of necessitation with causation. | |
| From: report of David M. Armstrong (A World of States of Affairs [1997]) by Stathis Psillos - Causation and Explanation §6.3.3 | |
| A reaction: Obviously logical necessity is not causal, but as a proposal for simplifying accounts of necessity in nature, this is wonderfully simple and appealing. Is his proposal an elevation of causation, or a degradation of necessity? |