17 ideas
| 15134 | The truthmaker principle requires some specific named thing to make the difference [Williamson] |
| Full Idea: The truthmaker principle seems compelling, because if a proposition is true, something must be different from a world in which it is false. The principle makes this specific, by treating 'something' as a quantifier binding a variable in name position. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) | |
| A reaction: See Williamson for an examination of the logical implications of this. The point is that the principle seems to require some very specific 'thing', which may be asking too much. For a start, it might be the absence of a thing. |
| 15141 | Truthmaker is incompatible with modal semantics of varying domains [Williamson] |
| Full Idea: Friends of the truthmaker principle should reject the Kripke semantics of varying domains. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3) | |
| A reaction: See other ideas from this paper to get a sense of what that is about. |
| 15140 | The converse Barcan formula will not allow contingent truths to have truthmakers [Williamson] |
| Full Idea: The converse Barcan formula does not allow any contingent truths at all to have a truthmaker. Once cannot combine the converse Barcan formula with any truthmaker principle worth having. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3) | |
| A reaction: One might reply, so much the worse for the converse Barcan formula, but Williamson doesn't think that. |
| 15131 | If metaphysical possibility is not a contingent matter, then S5 seems to suit it best [Williamson] |
| Full Idea: In S5, necessity and possibility are not themselves contingent matters. This is plausible for metaphysical modality, since metaphysical possibility, unlike practical possibility, does not depend on the contingencies of one's situation. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §1) | |
| A reaction: This is the clearest statement I have found of why S5 might be preferable for metaphysics. See Nathan Salmon for the rival view. Williamson's point sounds pretty persuasive to me. |
| 15135 | If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson] |
| Full Idea: If the domain of propositional quantification is constant across worlds, the Barcan formula and its converse hold. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) | |
| A reaction: So the issue is whether we should take metaphysics to be dealing with a constant or varying domains. Williamson seems to favour the former, but my instincts incline towards the latter. |
| 15139 | Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson] |
| Full Idea: The converse Barcan is at least plausible, since its denial says there is something that could fail to meet a condition when everything met that condition; but how could everything meet that condition if that thing did not? | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3) | |
| A reaction: Presumably the response involves a discussion of domains, since everything in a given domain might meet a condition, but something in a different domain might fail it. |
| 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. |
| 18492 | Not all quantification is either objectual or substitutional [Williamson] |
| Full Idea: We should not assume that all quantification is either objectual or substitutional. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], p.262) | |
| A reaction: [see Prior 1971:31-4] He talks of quantifying into sentence position. |
| 15136 | Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances [Williamson] |
| Full Idea: If quantification into sentence position is substitutional, then it is metaphysically neutral. A substitutionally interpreted 'existential' quantification is semantically equivalent to the disjunction (possibly infinite) of its substitution instances. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) | |
| A reaction: Is it not committed to the disjunction, just as the objectual reading commits to objects? Something must make the disjunction true. Or is it too verbal to be about reality? |
| 15138 | Not all quantification is objectual or substitutional [Williamson] |
| Full Idea: We should not assume that all quantification is objectual or substitutional. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2) |
| 15137 | If 'fact' is a noun, can we name the fact that dogs bark 'Mary'? [Williamson] |
| Full Idea: If one uses 'fact' as a noun, the question arises why one cannot name the fact that dogs bark 'Mary'. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2 n10) | |
| A reaction: What an intriguing thought! Must all nouns pass this test? 'The courage of the regiment was called Alfred'? |
| 15142 | Our ability to count objects across possibilities favours the Barcan formulas [Williamson] |
| Full Idea: Consideration of our ability to count objects across possibilities strongly favour both the Barcan formula and its converse. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §3) | |
| A reaction: I'm not sure that I can understand counting objects across possibilities. The objects themselves are possibilia, and possibilia seem to include unknowns. The unexpected is highly possible. |
| 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). |
| 19399 | Prime matter is nothing when it is at rest [Leibniz] |
| Full Idea: Primary matter is nothing if considered at rest. | |
| From: Gottfried Leibniz (Aristotle and Descartes on Matter [1671], p.90) | |
| A reaction: This goes with Leibniz's Idea 13393, that activity is the hallmark of existence. No one seems to have been able to make good sense of prime matter, and it plays little role in Aristotle's writings. |
| 15133 | A thing can't be the only necessary existent, because its singleton set would be as well [Williamson] |
| Full Idea: That there is just one necessary existent is surely false, for if x is a necessary, {x} is a distinct necessary existent. | |
| From: Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §1) | |
| A reaction: You would have to believe that sets actually 'exist' to accept this, but it is a very neat point. |