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. |
| 16698 | Days exist, and yet they seem to be made up of parts which don't exist [Burley] |
| Full Idea: I grant that a successive being is composed out of non-beings, as is clear of a day, which is composed of non-entities. Some part of this day is past and some future, and yet this day is. | |
| From: Walter Burley (Commentary on 'Physics' [1325], III text 11,f.65rb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3 | |
| A reaction: The dilemma of Aristotle over time infected the scholastic attempt to give an account of successive entities. A day is a wonderfully elusive entity for a metaphysician. |
| 16690 | Unlike permanent things, successive things cannot exist all at once [Burley] |
| Full Idea: This is the difference between permanent and successive things: that a permanent thing exists all at once, or at least can exist all at once, whereas it is incompatible with a successive thing to exist all at once. | |
| From: Walter Burley (Commentary on 'Physics' [1325], III txt 11,f.65rb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.1 | |
| A reaction: Permanent things sound like what are now called 'three-dimensional' objects, but scholastic 'entia successiva' are not the same as spacetime 'worms' or collections of temporal stages. |
| 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. |
| 16719 | The primary qualities are mixed to cause secondary qualities [Burley] |
| Full Idea: Secondary qualities are caused by a mixture of primary qualities. | |
| From: Walter Burley (De formis [1330], pars post p.65), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 21.2 | |
| A reaction: Like paint. He probably has in mind hot, cold, wet and dry as the primary qualities. |
| 8840 | There are five possible responses to the problem of infinite regress in justification [Cleve] |
| Full Idea: Sceptics respond to the regress problem by denying knowledge; Foundationalists accept justifications without reasons; Positists say reasons terminate is mere posits; Coherentists say mutual support is justification; Infinitists accept the regress. | |
| From: James Van Cleve (Why coherence is not enough [2005], I) | |
| A reaction: A nice map of the territory. The doubts of Scepticism are not strong enough for anyone to embrace the view; Foundationalist destroy knowledge (?), as do Positists; Infinitism is a version of Coherentism - which is the winner. |
| 8841 | Modern foundationalists say basic beliefs are fallible, and coherence is relevant [Cleve] |
| Full Idea: Contemporary foundationalists are seldom of the strong Cartesian variety: they do not insist that basic beliefs be absolutely certain. They also tend to allow that coherence can enhance justification. | |
| From: James Van Cleve (Why coherence is not enough [2005], III) | |
| A reaction: It strikes me that they have got onto a slippery slope. How certain are the basic beliefs? How do you evaluate their certainty? Could incoherence in their implications undermine them? Skyscrapers need perfect foundations. |