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. |
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. |
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. |
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. |
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) |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
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'? |
15538 | Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis] |
Full Idea: Semantic indecision will suffice to explain the phenomenon of vagueness. [note] Provided that there exist the many precisifications for us to be undecided between. If you deny this, you will indeed have need of vague objects. | |
From: David Lewis (Many, but almost one [1993], 'Two solutions') | |
A reaction: [He mentions Van Inwagen 1990:213-83] There seem to be three solutions to vague objects: that they really are vague, that they are precise but we can't know precisely, or Lewis's view. I like Lewis's view. Do animals have any problem with vagueness? |
15537 | If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis] |
Full Idea: To deny that there are many cats on the mat (because removal of a few hairs seems to produce a new one), we must either deny that the many are cats, or else deny that the cats are many. ...I think both alternatives lead to successful solutions. | |
From: David Lewis (Many, but almost one [1993], 'The paradox') | |
A reaction: He credits the problem to Geach (and Tibbles), and says it is the same as Unger's 'problem of the many' (Idea 15536). |
15536 | We have one cloud, but many possible boundaries and aggregates for it [Lewis] |
Full Idea: Many surfaces are equally good candidates to be boundaries of a cloud; therefore many aggregates of droplets are equally good candidates to be the cloud. How is it that we have just one cloud? And yet we do. This is Unger's (1980) 'problem of the many'. | |
From: David Lewis (Many, but almost one [1993], 'The problem') | |
A reaction: This is the problem of vague objects, as opposed to the problem of vague predicates, or the problem of vague truths, or the problem of vague prepositions (like 'towards'). |
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. |
15539 | Basic to pragmatics is taking a message in a way that makes sense of it [Lewis] |
Full Idea: The cardinal principle of pragmatics is that the right way to take what is said, if at all possible, is the way that makes sense of the message. | |
From: David Lewis (Many, but almost one [1993], 'A better solution') | |
A reaction: Thus when someone misuses a word, suggesting nonsense, we gloss over it, often without even mentioning it, because the underlying sense is obvious. A good argument for the existence of propositions. Lewis doesn't mention truth. |
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. |