12 ideas
| 5831 | The new view is that "water" is a name, and has no definition [Schwartz,SP] |
| Full Idea: Perhaps the modern view is best expressed as saying that "water" has no definition at all, at least in the traditional sense, and is a proper name of a specific substance. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: This assumes that proper names have no definitions, though I am not clear how we can grasp the name 'Aristotle' without some association of properties (human, for example) to go with it. We need a definition of 'definition'. |
| 14970 | Normal system K has five axioms and rules [Cresswell] |
| Full Idea: Normal propositional modal logics derive from the minimal system K: wffs of PC are axioms; □(p⊃q)⊃(□p⊃□q); uniform substitution; modus ponens; necessitation (α→□α). | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1) |
| 14971 | D is valid on every serial frame, but not where there are dead ends [Cresswell] |
| Full Idea: If a frame contains any dead end or blind world, then D is not valid on that frame, ...but D is valid on every serial frame. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.1) |
| 14972 | S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell] |
| Full Idea: In S4 there are exactly 14 distinct modalities, and any modality may be reduced to one containing no more than three modal operators in sequence. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: The significance of this may be unclear, but it illustrates one of the rewards of using formal systems to think about modal problems. There is at least an appearance of precision, even if it is only conditional precision. |
| 14973 | In S5 all the long complex modalities reduce to just three, and their negations [Cresswell] |
| Full Idea: S5 contains the four main reduction laws, so the first of any pair of operators may be deleted. Hence all but the last modal operator may be deleted. This leaves six modalities: p, ◊p, □p, and their negations. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) |
| 14976 | Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell] |
| Full Idea: If one wants the quantifiers in each world to range only over the things that exist in that world, and one doesn't believe that the same things exist in every world, one would probably not want the Barcan formula. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.2) | |
| A reaction: I haven't quite got this, but it sounds to me like I should reject the Barcan formula (but Idea 9449!). I like a metaphysics to rest on the actual world (with modal properties). I assume different things could have existed, but don't. |
| 5829 | We refer to Thales successfully by name, even if all descriptions of him are false [Schwartz,SP] |
| Full Idea: We can refer to Thales by using the name "Thales" even though perhaps the only description we can supply is false of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: It is not clear what we would be referring to if all of our descriptions (even 'Greek philosopher') were false. If an archaeologist finds just a scrap of stone with a name written on it, that is hardly a sufficient basis for successful reference. |
| 5830 | The traditional theory of names says some of the descriptions must be correct [Schwartz,SP] |
| Full Idea: The traditional theory of proper names entails that at least some combination of the things ordinarily believed of Aristotle are necessarily true of him. | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §III) | |
| A reaction: Searle endorses this traditional theory. Kripke and co. tried to dismiss it, but you can't. If all descriptions of Aristotle turned out to be false (it was actually the name of a Persian statue), our modern references would have been unsuccessful. |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| Full Idea: A relation is 'Euclidean' if aRb and aRc imply bRc. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.1.2) | |
| A reaction: If a thing has a relation to two separate things, then those two things will also have that relation between them. If I am in the same family as Jim and as Jill, then Jim and Jill are in the same family. |
| 14975 | A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell] |
| Full Idea: A de dicto necessary truth says that something is φ, that this proposition is a necessary truth, i.e. that in every accessible world something (but not necessarily the same thing in each world) is φ. | |
| From: Max J. Cresswell (Modal Logic [2001], 7.2.1) | |
| A reaction: At last, a really clear and illuminating account of this term! The question is then invited of what is the truthmaker for a de dicto truth, assuming that the objects themselves are truthmakers for de re truths. |
| 15432 | Structural universals might serve as possible worlds [Forrest, by Lewis] |
| Full Idea: Forrest proposed that structural universals should serve as ersatz possible worlds. | |
| From: report of Peter Forrest (Ways Worlds Could Be [1986]) by David Lewis - Against Structural Universals 'Intro' | |
| A reaction: I prefer powers to property universals. Perhaps a possible world is a maximal set of co-existing dispositions? |
| 5826 | The intension of "lemon" is the conjunction of properties associated with it [Schwartz,SP] |
| Full Idea: The conjunction of properties associated with a term such as "lemon" is often called the intension of the term "lemon". | |
| From: Stephen P. Schwartz (Intro to Naming,Necessity and Natural Kinds [1977], §II) | |
| A reaction: The extension of "lemon" is the set of all lemons. At last, a clear explanation of the word 'intension'! The debate becomes clear - over whether the terms of a language are used in reference to ideas of properties (and substances?), or to external items. |