15 ideas
| 18889 | Ostensive definitions needn't involve pointing, but must refer to something specific [Salmon,N] |
| Full Idea: So-called ostensive definitions need not literally involve ostension, e.g. pointing, but they must involve genuine reference of some sort (in this case reference to a sample of water). | |
| From: Nathan Salmon (Reference and Essence (1st edn) [1981], 4.11.2) |
| 14627 | S4, and therefore S5, are invalid for metaphysical modality [Salmon,N, by Williamson] |
| Full Idea: Salmon argues that S4 and therefore S5 are invalid for metaphysical modality. | |
| From: report of Nathan Salmon (Reference and Essence (1st edn) [1981], 238-40) by Timothy Williamson - Modal Logic within Counterfactual Logic 4 | |
| A reaction: [He gives references for Salmon, and for his own reply] Salmon's view seems to be opposed my most modern logicians (such as Ian Rumfitt). |
| 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) |
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true. | |
| From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism. |
| 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. |
| 10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
| Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them. | |
| From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry. |
| 18888 | Essentialism says some properties must be possessed, if a thing is to exist [Salmon,N] |
| Full Idea: The metaphysical doctrine of essentialism says that certain properties of things are properties that those things could not fail to have, except by not existing. | |
| From: Nathan Salmon (Reference and Essence (1st edn) [1981], 3.8.2) | |
| A reaction: A bad account of essentialism, and a long way from Aristotle. It arises from the logicians' tendency to fix objects entirely in terms of a 'flat' list of predicates (called 'properties'!), which ignore structure, constitution, history etc. |
| 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. |
| 18886 | Frege's 'sense' solves four tricky puzzles [Salmon,N] |
| Full Idea: Reference via sense solves Frege's four puzzles, of the informativeness of identity statements, the failure of substitutivity in attitude contexts, of negative existentials, and the truth-value of statements using nondenoting singular terms. | |
| From: Nathan Salmon (Reference and Essence (1st edn) [1981], 1.1.1) | |
| A reaction: These must then be compared with Kripke's three puzzles about referring via sense, and the whole debate is then spread before us. |
| 18887 | The perfect case of direct reference is a variable which has been assigned a value [Salmon,N] |
| Full Idea: The paradigm of a nondescriptional, directly referential, singular term is an individual variable. …The denotation of a variable… is semantically determined directly by the assignment of values. | |
| From: Nathan Salmon (Reference and Essence (1st edn) [1981], 1.1.2) | |
| A reaction: This cuts both ways. Maybe we are muddling ordinary reference with the simplicities of logical assignments, or maybe we make logical assignments because that is the natural way our linguistic thinking works. |
| 18891 | Nothing in the direct theory of reference blocks anti-essentialism; water structure might have been different [Salmon,N] |
| Full Idea: There seems to be nothing in the theory of direct reference to block the anti-essentialist assertion that the substance water might have been the very same entity and yet have had a different chemical structure. | |
| From: Nathan Salmon (Reference and Essence (1st edn) [1981], 6.23.1) | |
| A reaction: Indeed, water could be continuously changing its inner structure, while retaining the surface appearance that gets baptised as 'water'. We make the reasonable empirical assumption, though, that structure-change implies surface-change. |