17 ideas
| 8368 | A correct definition is what can be substituted without loss of meaning [Ducasse] |
| Full Idea: A definition of a word is correct if the definition can be substituted for the word being defined in an assertion without in the least changing the meaning which the assertion is felt to have. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §1) | |
| A reaction: This sounds good, but a very bland and uninformative rephrasing would fit this account, without offering anything very helpful. The word 'this' could be substituted for a lot of object words. A 'blade' is 'a thing always attached to a knife handle'. |
| 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) |
| 8886 | Being a true justified belief is not a sufficient condition for knowledge [Gettier] |
| Full Idea: The claim that someone knows a proposition if it is true, it is believed, and the person is justified in their belief is false, in that the conditions do not state a sufficient condition for the claim. | |
| From: Edmund L. Gettier (Is Justified True Belief Knowledge? [1963], p.145) | |
| A reaction: This is the beginning of the famous Gettier Problem, which has motivated most epistemology for the last forty years. Gettier implies that justification is necessary, even if it is not sufficient. He gives two counterexamples. |
| 8367 | Causation is defined in terms of a single sequence, and constant conjunction is no part of it [Ducasse] |
| Full Idea: The correct definition of the causal relation is to be framed in terms of one single case of sequence, and constancy of conjunction is therefore no part of it. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], Intro) | |
| A reaction: This is the thesis of Ducasse's paper. I immediately warm to it. I take constant conjunction to be a consequence and symptom of causation, not its nature. There is a classic ontology/epistemology confusion to be avoided here. |
| 8372 | We see what is in common between causes to assign names to them, not to perceive them [Ducasse] |
| Full Idea: The part of a generalization concerning what is common to one individual concrete event and the causes of certain other events of the same kind is involved in the mere assigning of a name to the cause and its effect, but not in the perceiving them. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §5) | |
| A reaction: A nice point, that we should keep distinct the recognition of a cause, and the assigning of a general name to it. Ducasse is claiming that we can directly perceive singular causation. |
| 8369 | Causes are either sufficient, or necessary, or necessitated, or contingent upon [Ducasse] |
| Full Idea: There are four causal connections: an event is sufficient for another if it is its cause; an event is necessary for another if it is a condition for it; it is necessitated by another if it is an effect; it is contingent upon another if it is a resultant. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §2) | |
| A reaction: An event could be a condition for another without being necessary. He seems to have missed the indispensable aspect of a necessary condition. |
| 8373 | When a brick and a canary-song hit a window, we ignore the canary if we are interested in the breakage [Ducasse] |
| Full Idea: If a brick and the song of a canary strike a window, which breaks....we can truly say that the song of the canary had nothing to do with it, that is, in so far as what occurred is viewed merely as a case of breakage of window. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §5) | |
| A reaction: This is the germ of Davidson's view, that causation is entirely dependent on the mode of description, rather than being an actual feature of reality. If one was interested in the sound of the breakage, the canary would become relevant. |
| 8370 | A cause is a change which occurs close to the effect and just before it [Ducasse] |
| Full Idea: The cause of the particular change K was such particular change C as alone occurred in the immediate environment of K immediately before. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §3) | |
| A reaction: The obvious immediately difficulty would be overdetermination, as when it rains while I am watering my garden. The other problem would coincidence, as when I clap my hands just before a bomb goes off. |
| 8371 | Recurrence is only relevant to the meaning of law, not to the meaning of cause [Ducasse] |
| Full Idea: The supposition of recurrence is wholly irrelevant to the meaning of cause: that supposition is relevant only to the meaning of law. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §4) | |
| A reaction: This sounds plausible, especially if our notion of laws of nature is built up from a series of caused events. But we could just have an ontology of 'similar events', out of which we build laws, and 'causation' could drop out (á la Russell). |
| 8374 | We are interested in generalising about causes and effects purely for practical purposes [Ducasse] |
| Full Idea: We are interested in causes and effects primarily for practical purposes, which needs generalizations; so the interest of concrete individual facts of causation is chiefly an indirect one, as raw material for generalizations. | |
| From: Curt Ducasse (Nature and Observability of Causal Relations [1926], §6) | |
| A reaction: A nice explanation of why, if causation is fundamentally about single instances, people seem so interested in generalisations and laws. We want to predict, and we want to explain, and we want to intervene. |