20 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. |
| 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) |
| 10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
| Full Idea: I can start with a triangle, and rise by degrees to all straight-lined figures and to extension itself. The lower degree will include the higher degree. Since the higher degree is less determinate, it can represent more things. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] This attempts to explain the generalising ability of abstraction cited in Idea 10501. If you take a complex object and eliminate features one by one, it can only 'represent' more particulars; it could hardly represent fewer. |
| 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. |
| 18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
| Full Idea: We can have knowledge of what is outside us only through the mediation of ideas in us. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], p.63), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 1 'Conc' |
| 16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
| Full Idea: The form is what renders a thing such and distinguishes it from others, whether it is a being really distinct from the matter, according to the Schools, or whether it is only the arrangement of the parts. By this form one must explain its properties. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], III.18 p240), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 27.6 | |
| A reaction: If we ask 'what explains the properties of this thing' it is hard to avoid coming up with something that might be called the 'form'. Note that they allow either substantial or corpuscularian forms. It is hard to disagree with the idea. |
| 10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
| Full Idea: The mind cannot perfectly understand things that are even slightly composite unless it considers them a part at a time. ...This is generally called knowing by abstraction. (..the human body, for example). | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: This adds the interesting thought that the mind is forced to abstract, rather than abstraction being a luxury extra feature. Knowledge through analysis is knowledge by abstraction. Also a nice linking of abstraction to epistemology. |
| 10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
| Full Idea: If I draw an equilateral triangle on a piece of paper, ..I shall have an idea of only a single triangle. But if I ignore all the particular circumstances and focus on the three equal lines, I will be able to represent all equilateral triangles. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: [compressed] They observed that we grasp composites through their parts, and now that we can grasp generalisations through particulars, both achieved by the psychological act of abstraction, thus showing its epistemological power. |
| 10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
| Full Idea: Geometers by no means assume that there are lines without width or surfaces without depth. They only think it is possible to consider the length without paying attention to the width. We can measure the length of a path without its width. | |
| From: Arnauld / Nicole (Logic (Port-Royal Art of Thinking) [1662], I.5) | |
| A reaction: A nice example which makes the point indubitable. The modern 'rigorous' account of abstraction that starts with Frege seems to require more than one object, in order to derive abstractions like direction or number. Path widths are not comparatives. |
| 541 | Virtue comes more from habit than character [Critias] |
| Full Idea: More men are good through habit than through character. | |
| From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41 |
| 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. |
| 542 | Fear of the gods was invented to discourage secret sin [Critias] |
| Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret. | |
| From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54 |