14 ideas
| 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) |
| 18431 | Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards] |
| Full Idea: Simons's 'nuclear' option blends features of the substratum and bundle theories. First we have tropes collected by virtue of their internal relations, forming the essential kernel or nucleus. This nucleus then bears the non-essential tropes. | |
| From: report of Peter Simons (Particulars in Particular Clothing [1994], p.567) by Douglas Edwards - Properties 3.5 | |
| A reaction: [compression of Edwards's summary] This strikes me as being a remarkably good theory. I am not sure of the ontological status of properties, such that they can (unaided) combine to make part of an object. What binds the non-essentials? |
| 14348 | An 'antidote' allows a manifestation to begin, but then blocks it [Corry] |
| Full Idea: An 'antidote' (or 'mask') to a disposition (unlike a 'finkish' one) leaves the disposition intact, but interferes with the causal chain between the disposition and its manifestation so that the manifestation doesn't come about. | |
| From: Richard Corry (Dispositional Essentialism Grounds Laws of Nature? [2010], 2) | |
| A reaction: [He cites Bird 1997] Thus the disposition of the poison at least begins to manifest, but its disposition to kill is blocked. So what was the disposition of the poison? |
| 14347 | A 'finkish' disposition is one that is lost immediately after the appropriate stimulus [Corry] |
| Full Idea: An object's disposition is said to be 'finkish' if the object loses the disposition after the occurrence of the appropriate stimulus, but before the manifestation has had time to come about. | |
| From: Richard Corry (Dispositional Essentialism Grounds Laws of Nature? [2010], 2) | |
| A reaction: [He cites Lewis 1997] An example would be some sort of safety device which only cuts in if the disposition seems about to operate (e.g. turns off electricity). It seems to block analyses of dispositions simply in terms of their outcomes. |
| 14350 | If a disposition is never instantiated, it shouldn't be part of our theory of nature [Corry] |
| Full Idea: If we have no good reason to believe that a disposition is instantiated, then the disposition should play no role in our theorizing about the world. | |
| From: Richard Corry (Dispositional Essentialism Grounds Laws of Nature? [2010], 3) | |
| A reaction: It is part of our theory that a substantial lump of uranium will explode, but also that a galaxy-sized lump of uranium would explode. Surely we are committed to the latter, even though it never happens? |
| 14351 | Maybe an experiment unmasks an essential disposition, and reveals its regularities [Corry] |
| Full Idea: The dispositional essentialist can argue that what happens in laboratory conditions is that, by controlling external influences, we effectively 'unmask' the relevant dispositions, and thus observe the regularities to which those dispositions give rise. | |
| From: Richard Corry (Dispositional Essentialism Grounds Laws of Nature? [2010], 5) | |
| A reaction: That seems to me to be exactly right, though Corry dislikes it, and even suggests that dispositional essentialist might not like it. |
| 14346 | Dispositional essentialism says fundamental laws of nature are strict, not ceteris paribus [Corry] |
| Full Idea: Dispositional essentialism implies that the fundamental laws of nature must be strict, not ceteris paribus. | |
| From: Richard Corry (Dispositional Essentialism Grounds Laws of Nature? [2010], 1) | |
| A reaction: I am not keen on the 'laws' of nature, but since essentialism seems to make them necessary, you can't get stricter than that. |