14 ideas
| 15545 | Armstrong's analysis seeks truthmakers rather than definitions [Lewis] |
| Full Idea: I suggest that Armstrong has an unfamiliar notion of analysis, as not primarily a quest for definitions, but as a quest for truth-makers. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'The demand') | |
| A reaction: This is not a dichotomy, I think, but a shift of emphasis. A definition will probably refer to truthmakers; a decent account of truthmakers would approximate a definition. |
| 15546 | Predications aren't true because of what exists, but of how it exists [Lewis] |
| Full Idea: Predications seem, for the most part, to be true not because of whether things are, but because of how things are. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'The demand') | |
| A reaction: This simple point shows that you get into a tangle if you insist that truthmakers just consist of what exists. Lewis says Armstrong offers states of affairs as truthmakers for predications. |
| 15548 | Say 'truth is supervenient on being', but construe 'being' broadly [Lewis] |
| Full Idea: I want to say that 'truth is supervenient on being', but as an Ostrich about universals I want to construe 'being' broadly. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'Truth') | |
| A reaction: [His slogan is borrowed from Bigelow 1988:132-,158-9] This seems much more promising that the more precise and restricted notion of truthmakers, as resting on the existence of particular things. Presentism is the big test case. |
| 14399 | Presentism says only the present exists, so there is nothing for tensed truths to supervene on [Lewis] |
| Full Idea: Presentism says that although there is nothing outside the present, yet there are past-tensed and future-tensed truths that do not supervene on the present, and hence do not supervene on being. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], p.207) | |
| A reaction: Since I rather like both presentism and truth supervening on being, this observation comes as rather a devastating blow. I thought philosophy would be quite easy, but it's turning out to be rather tricky. Could tensed truths supervene on the present? |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 15543 | How do things combine to make states of affairs? Constituents can repeat, and fail to combine [Lewis] |
| Full Idea: To me it is mysterious how a state of affairs is made out of its particular and universal constituents. Different states of affairs may have the very same constituents, and the existence of constituents by no means entails the existence of the states. | |
| From: David Lewis (Armstrong on combinatorial possibility [1992], 'What is there') | |
| A reaction: He is rejecting the structure of states of affairs as wholes made of parts. But then mereology was never going to explain the structure of the world. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |