18 ideas
| 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) |
| 11970 | Logicians like their entities to exhibit a maximum degree of purity [Kaplan] |
| Full Idea: Logicians like their entities to exhibit a maximum degree of purity. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.97) | |
| A reaction: An important observation, which explains why the modern obsession with logic has often led us down the metaphysical primrose path to ontological hell. |
| 11989 | For Russell, expressions dependent on contingent circumstances must be eliminated [Kaplan] |
| Full Idea: It is a tenet of Russell's theory that all expressions, and especially definite descriptions, whose denotation is dependent upon contingent circumstances must be eliminated. | |
| From: David Kaplan (How to Russell a Frege-Church [1975], II) |
| 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) |
| 11969 | Models nicely separate particulars from their clothing, and logicians often accept that metaphysically [Kaplan] |
| Full Idea: The use of models is so natural to logicians ...that they sometimes take seriously what are only artefacts of the model, and adopt a bare particular metaphysics. Why? Because the model so nicely separates the bare particular from its clothing. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.97) | |
| A reaction: See also Idea 11970. I think this observation is correct, and incredibly important. We need to keep quite separate the notion of identity in conceptual space from our notion of identity in the actual world. The first is bare, the second fat. |
| 11971 | The simplest solution to transworld identification is to adopt bare particulars [Kaplan] |
| Full Idea: If we adopt the bare particular metaphysical view, we have a simple solution to the transworld identification problem: we identify by bare particulars. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.98) | |
| A reaction: See Ideas 11969 and 11970 on this idea. The problem with bare particulars is that they can change their properties utterly, so that Aristotle in the actual world can be a poached egg in some possible world. We need essences. |
| 11973 | Unusual people may have no counterparts, or several [Kaplan] |
| Full Idea: An extremely vivid person might have no counterparts, and Da Vinci seems to me to have more than one essence. Bertrand Russell is clearly the counterpart of at least three distinct persons in some more plausible world. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.100) | |
| A reaction: Lewis prefers the notion that there is at most one counterpart, the 'closest' entity is some world. I think he also claims there is at least one counterpart. I like Kaplan's relaxed attitude to these things, which has more explanatory power. |
| 11972 | Essence is a transworld heir line, rather than a collection of properties [Kaplan] |
| Full Idea: I prefer to think of essence as a transworld heir line, rather than as the more familiar collection of properties, because the latter too much suggests the idea of a fixed and final essential description. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.100) | |
| A reaction: He is sympathetic to the counterpart idea, and close to Lewis's view of essences, as the intersection of counterparts. I like his rebellion against fixed and final descriptions, but am a bit doubtful about his basic idea. Causation should be involved. |
| 11990 | 'Haecceitism' says that sameness or difference of individuals is independent of appearances [Kaplan] |
| Full Idea: The doctrine that we can ask whether this is the same individual in another possible world, and that a common 'thisness' may underlie extreme dissimilarity, or distinct thisnesses may underlie great resemblance, I call 'Haecceitism'. | |
| From: David Kaplan (How to Russell a Frege-Church [1975], IV) | |
| A reaction: Penelope Mackie emphasises that this doctrine, that each thing is somehow individuated, is not the same as believing in actual haecceities, specific properties which achieve the individuating. |
| 9668 | 'Haecceitism' is common thisness under dissimilarity, or distinct thisnesses under resemblance [Kaplan] |
| Full Idea: That a common 'thisness' may underlie extreme dissimilarity or distinct thisnesses may underlie great resemblance I call 'haecceitism'. (I prefer the pronunciation Hex'-ee-i-tis-m). | |
| From: David Kaplan (How to Russell a Frege-Church [1975], IV) | |
| A reaction: [odd pronunciation, if 'haec' is pronounced haeek] The view seems to be very unpopular (e.g. with Lewis, Bird and Mumford). But there is an intuitive sense of whether or not two things are identical when they seem dissimilar. |
| 11991 | If quantification into modal contexts is legitimate, that seems to imply some form of haecceitism [Kaplan] |
| Full Idea: If one regards the usual form of quantification into modal and other intensional contexts - modality de re - as legitimate (without special explanations), then one seems committed to some form of haecceitism. | |
| From: David Kaplan (How to Russell a Frege-Church [1975], IV) | |
| A reaction: That is, modal reference requires fixed identities, irrespective of possible changes in properties. Why could one not refer to objects just as bundles of properties, with some sort of rules about when it ceased to be that particular bundle (keep 60%?)? |
| 11967 | Sentences might have the same sense when logically equivalent - or never have the same sense [Kaplan] |
| Full Idea: Among the proposals for conditions under which two sentences have the same ordinary sense, the most liberal (Carnap and Church) is that they be logically equivalent, and the most restrictive (Benson Mates) is that they never have the same sense. | |
| From: David Kaplan (Transworld Heir Lines [1967], p.89) | |
| A reaction: Personally I would move the discussion to the level of the propositions being expressed before I attempted a solution. |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |
| Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does. | |
| From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1 | |
| A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox. |
| 14894 | Indexicals have a 'character' (the standing meaning), and a 'content' (truth-conditions for one context) [Kaplan, by Macià/Garcia-Carpentiro] |
| Full Idea: Kaplan distinguished two different semantic features of indexical expressions: a 'character' that captures the standing meaning of the expression, and a 'content' that consists of their truth-conditional contribution in particular contexts. | |
| From: report of David Kaplan (Demonstratives [1989]) by Macià/Garcia-Carpentiro - Introduction to 'Two-Dimensional Semantics' 1 | |
| A reaction: This seems so clearly right that there isn't much to dispute. You can't understand the word 'I' or 'now' if you don't understand both its general purpose, and what it is doing in a particular utterance. But will this generalise to other semantics? |
| 14700 | 'Content' gives the standard modal profile, and 'character' gives rules for a context [Kaplan, by Schroeter] |
| Full Idea: Kaplan sees two aspects of meaning, the 'content', reflecting a thing's modal profile, which is modelled by standard possible worlds semantics, and 'character', giving rules for different contexts. Proper names have constant character; indexicals vary. | |
| From: report of David Kaplan (Demonstratives [1989]) by Laura Schroeter - Two-Dimensional Semantics 1.1.1 | |
| A reaction: This gives rise to 2-D matrices for representing meaning, and the possible worlds are used twice, for evaluating meaning and then for evaluating context of use. I've always been struck by the two-dimensional semantics of passwords. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |