15 ideas
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
| From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
| From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 7306 | If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A] |
| Full Idea: If having a reference were the only semantic property in terms of which we could explain the functioning of names, we would be in trouble with respect to names that simply have no bearer. | |
| From: Alexander Miller (Philosophy of Language [1998], 2.1.1) | |
| A reaction: (Miller is discussing Frege) 'Odysseus' is given as an example. Instead of switching to a bundle of descriptions, we could say that we just imagine an object which is stamped with the name. Names always try to refer. |
| 7322 | Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A] |
| Full Idea: We should distinguish 'constitutive scepticism' (about the existence of certain sorts of facts) from the traditional 'epistemological scepticism' (which concedes that the sort of fact in question exists, but questions our right to claim knowledge of it). | |
| From: Alexander Miller (Philosophy of Language [1998], 4.7) | |
| A reaction: I would be inclined to call the first type 'ontological scepticism'. Miller is discussing Quine's scepticism about meaning. Atheists fall into the first group, and agnostics into the second. An important, and nicely simple, distinction. |
| 7325 | Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A] |
| Full Idea: Dispositional facts are facts about what we will do, not about what we ought to do, and as such cannot capture the normativity of meaning. | |
| From: Alexander Miller (Philosophy of Language [1998], 6.2) | |
| A reaction: Miller is discussing language, but this raises a nice question for all behaviourist accounts of mental events. Perhaps there is a disposition to behave in a guilty way if you do something you think you shouldn't do. (Er, isn't 'guilt' a mental event?) |
| 7324 | Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A] |
| Full Idea: Grice wants to explain linguistic meaning in terms of the content of propositional attitudes, Dummett has championed the view that propositional attitudes must be explained by linguistic meaning, while Davidson says they must be explained together. | |
| From: Alexander Miller (Philosophy of Language [1998], 6.1) | |
| A reaction: A useful map. My intuition says propositional attitudes come first, for evolutionary reasons. We are animals first, and speakers second. Thought precedes language. A highly social animal flourishes if it can communicate. |
| 7323 | If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A] |
| Full Idea: On a deflationary concept of truth, for a sentence to possess truth-conditions it is sufficient that it be disciplined by norms of correct usage, and that it possess the syntax distinctive of declarative sentences. | |
| From: Alexander Miller (Philosophy of Language [1998], 5.3) | |
| A reaction: Idea 6337 gives the basic deflationary claim. He mentions Boghossian as source of this point. So much the worse for the deflationary concept of truth, say I. What are the truth-conditions of "Truth rotates"? |
| 7315 | 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A] |
| Full Idea: The syntactic notion of contradiction (p and not-p) is well understood, but is no help in explaining analyticity, since "Jones is a married bachelor" is not of that syntactic form. | |
| From: Alexander Miller (Philosophy of Language [1998], 4.2) | |
| A reaction: This point is based on Quine. This means we cannot define analytic sentences as those whose denial is a contradiction, even though that seems to be true of them. Both the Kantian and the modern logical versions of analyticity are in trouble. |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
| 7328 | The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A] |
| Full Idea: Properly construed, the principle of charity is a holistic constraint applying, not to individual beliefs, but rather to systems of belief: we must interpret a speaker so that most of the beliefs in his system are, by our lights, true. | |
| From: Alexander Miller (Philosophy of Language [1998], 8.7) | |
| A reaction: This is a lot more plausible than applying the principle to individual sentences, particularly if you are in the company of habitual ironists or constitutional liars. |
| 7329 | Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A] |
| Full Idea: A more sophisticated version of the principle of charity holds that we interpret speakers not as necessarily having beliefs that are true by our own lights, but as having beliefs that are intelligible by our own lights. | |
| From: Alexander Miller (Philosophy of Language [1998], 8.7) | |
| A reaction: Consider Idea 4161 in the light of this. Presumably this means that we treat them as having a coherent set of beliefs, even if they seem to us to fail to correspond to reality. I prefer the stronger version that there has to be some proper truth in there. |
| 7333 | The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A] |
| Full Idea: The main problem faced by non-cognitivism is known as the Frege-Geach problem: if I say "If murder is wrong, then getting your brother to murder people is wrong", that is an unasserted context, and I don't necessarily express disapproval of murder. | |
| From: Alexander Miller (Philosophy of Language [1998], 9.2) | |
| A reaction: The emotivist or non-cognitivist might mount a defence by saying there is some second-order or deep-buried emotion involved. Could a robot without feelings even understand what humans meant when they said "It is morally wrong"? |