11 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) |
| 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. |
| 10197 | An immanent universal is wholly present in more than one place [Zimmerman,DW] |
| Full Idea: An immanent universal will routinely be 'at some distance from itself', in the sense that it is wholly present in more than one place. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306) | |
| A reaction: This is the Aristotelian view, which sounds distinctly implausible in this formulation. Though I suppose redness is wholly present in a tomato, in the way that fourness is wholly present in the Horsemen of the Apocalypse. How many rednesses are there? |
| 10198 | If only two indiscernible electrons exist, future differences must still be possible [Zimmerman,DW] |
| Full Idea: If nothing existed except two electrons, which are indiscernible, it remains possible that differences will emerge later. Even if this universe has eternal symmetry, such differences are still logically, metaphysically, physically and causally possible. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.306) | |
| A reaction: The question then is whether the two electrons have hidden properties that make differences possible. Zimmerman assumes that 'laws' of an indeterministic kind will do the job. I doubt that. Can differences be discerned after the event? |
| 10199 | Discernible differences at different times may just be in counterparts [Zimmerman,DW] |
| Full Idea: Possible differences which may later become discernible could be treated as differences in a counterpart, which is similar to, but not identical with, the original object. | |
| From: Dean W. Zimmerman (Distinct Indiscernibles and the Bundle Theory [1997], p.307) | |
| A reaction: [compressed] This is a reply to Idea 10198, which implies that two things could never be indiscernible over time, because of their different possibilities. One must then decide issues about rigid designation and counterparts. |
| 15793 | We can take 'ways things might have been' as irreducible elements in our ontology [Stalnaker, by Lycan] |
| Full Idea: Stalnaker suggests talking 'ways things might have been' as sui generis elements of our ontology - actual abstract entities in their own right, not to be reduced to more familiar items. | |
| From: report of Robert C. Stalnaker (Possible Worlds [1976]) by William Lycan - The Trouble with Possible Worlds 09 | |
| A reaction: This seems to rest on an ontology of 'states of affairs', favoured by Armstrong, and implied in the Tractatus. How big is a state of affairs? How manys states of affairs can be co-present? |
| 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. |