21 ideas
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
Full Idea: The common feature of every designating term is that designation may change from state to state - thus it can be formalized by a function from states to objects. | |
From: Melvin Fitting (Intensional Logic [2007], 3) | |
A reaction: Specifying the objects sounds OK, but specifying states sounds rather tough. |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
Full Idea: To first order modal logic (with quantification over objects) we can add a second kind of quantification, over intensions. An intensional object, or individual concept, will be modelled by a function from states to objects. | |
From: Melvin Fitting (Intensional Logic [2007], 3.3) |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
Full Idea: Awareness logic enriched Hintikka's epistemic models with an awareness function, mapping each state to the set of formulas we are aware of at that state. This reflects some bound on the resources we can bring to bear. | |
From: Melvin Fitting (Intensional Logic [2007], 3.6.1) | |
A reaction: [He cites Fagin and Halpern 1988 for this] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
Full Idea: In justification logics, the logics of knowledge are extended by making reasons explicit. A logic of proof terms was created, with a semantics. In this, mathematical truths are known for explicit reasons, and these provide a measure of complexity. | |
From: Melvin Fitting (Intensional Logic [2007], 3.6.1) |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
From: Melvin Fitting (Intensional Logic [2007], §1) |
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) |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
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. |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
Full Idea: Definite descriptions pick out different objects in different possible worlds quite naturally. | |
From: Melvin Fitting (Intensional Logic [2007], 3.4) | |
A reaction: A definite description can pick out the same object in another possible world, or a very similar one, or an object which has almost nothing in common with the others. |
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 Macią/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 Macią/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. |