14 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'. |
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 15785 | Our commitments are to an 'ontology', but also to an 'ideology', or conceptual system [Hintikka] |
| Full Idea: We must distinguish between what we are committed to existing in the actual world or a possible world ('ontology'), and what we are committed to as a part of our ways of dealing with the world conceptually, as a part of our conceptual system ('ideology'). | |
| From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02 | |
| A reaction: I think this is the most illuminating idea I have read on the subject of ontological commitment. I'm fighting for the idea that what we think is true should be kept separate from what we think exists. Ideology is a nice addition to the mix. |
| 15786 | Commitment to possible worlds is part of our ideology, not part of our ontology [Hintikka] |
| Full Idea: Quantification over members of one particular world is a measure of ideology, quantification that crosses possible worlds is often a measure of ideology. | |
| From: Jaakko Hintikka (Semantics for Propositional Attitudes [1969], p.95), quoted by William Lycan - The Trouble with Possible Worlds 02 | |
| A reaction: I like this. See Idea 15785 for the underlying distinction. It leaves the question open of what we might mean by 'ideological commitment'. |
| 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. |