12 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. |
| 20660 | At one level maths and nature are very similar, suggesting some deeper origin [Wolfram] |
| Full Idea: At some rather abstract level one can immediately recognise one basic similarity between nature and mathematics ...this suggests that the overall similarity between mathematics and nature must have a deeper origin. | |
| From: Stephen Wolfram (A New Kind of Science [2002], p.772), quoted by Peter Watson - Convergence 17 'Philosophy' | |
| A reaction: Personally I think mathematics has been derived by abstracting from the patterns in nature, and then further extrapolating from those abstractions. So the puzzle in nature is not the correspondence with mathematics, but the patterns. |
| 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. |
| 9073 | Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J] |
| Full Idea: The procedure of abstraction will not allow us to distinguish the ambiguity between 'mole' as an animal and as an artefact. The stages of abstraction will only end up with 'physical object', and this will then count as the definition. | |
| From: Jonathan Barnes (Commentary on 'Posterior Analytics [1993], n to 97b7) | |
| A reaction: This is a problem if you adhere to a rather precise account of the steps of abstraction, with every stage explicit (and probably expressed in terms of sets), but I suspect that the real tangle of semi-conscious abstraction avoids this problem. |
| 9074 | Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J] |
| Full Idea: Abstractions cannot account for those general terms whose instances do not have any set of features in common. The word 'game' is not ambiguous, but not all games have one thing in common; they are united by looser 'family resemblance'. | |
| From: Jonathan Barnes (Commentary on 'Posterior Analytics [1993], n to 97b7) | |
| A reaction: (This point comes from Wittgenstein, Idea 4141) English-speakers can't agree on borderline cases (avoiding cracks in pavements). Life is just a game. The objection would be refuted by discussion of higher-level abstractions to make connections. |
| 9072 | Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J] |
| Full Idea: If we create abstractions by collection of attributes common to groups of entities, we will collect far too many attributes, and wrongly put them into the definition (such as 'having hairless palms' when identifying 'men'). | |
| From: Jonathan Barnes (Commentary on 'Posterior Analytics [1993], n to 97b7) | |
| A reaction: [compressed] Defining 'man' is a hugely complex business (see Idea 1763!), unlike defining 'hair' or 'red'. Some attributes will strike perceivers immediately, but absence of an attribute is not actually 'perceived' at all. |
| 20659 | Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram] |
| Full Idea: It seems plausible that both space and its contents should somehow be made of the same stuff - so that in a sense space becomes the only thing in the universe. | |
| From: Stephen Wolfram (A New Kind of Science [2002], p.474), quoted by Peter Watson - Convergence 17 'Philosophy' | |
| A reaction: I presume the concept of a 'field' is what makes this idea possible. |