11 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) |
| 20618 | Persons must be conscious, reasoning, motivated, communicative, self-aware [Warren, by Tuckness/Wolf] |
| Full Idea: Suggested characteristics of personhood: consciousness (esp. of pain); reasoning and problem solving; self-motivated activity; varied communication on many topics; self-concepts and self-awareness. | |
| From: report of Mary Anne Warren (On the Moral and Legal State of Abortion [1973], p.55) by Tuckness,A/Wolf,C - This is Political Philosophy 8 'Standing' | |
| A reaction: [a 'famous' article] A number of non-human animals come very close to passing these tests. I suspect the complex communication is only in there to disqualify them from getting the full certificate. (But she wrote on animal rights). |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| Full Idea: Pherecydes of Syros said that the principle and element of all things is earth. | |
| From: report of Pherecydes (fragments/reports [c.600 BCE]) by Sextus Empiricus - Against the Physicists (two books) I.360 | |
| A reaction: Sextus is giving the history, and mentions it before saying that Thales thought it was water. Earth seems a sensible starting point, and I am guessing that Thales was trying to think a bit more deeply than Pherecydes about it. |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |
| Full Idea: As far as the literature tells us, Pherecydes of Syros was the first who pronounced the souls of men to be eternal. | |
| From: report of Pherecydes (fragments/reports [c.600 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xvi.38 | |
| A reaction: Presumably before that it was the physical person who arrived in the Underworld. The Hindu tradition seems to require the soul to be very long-lived, if not eternal. Why did Pherecydes come up with this idea? |