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. |
| 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. |
| 8836 | Must all justification be inferential? [Ginet] |
| Full Idea: The infinitist view of justification holds that every justification must be inferential: no other kind of justification is possible. | |
| From: Carl Ginet (Infinitism not solution to regress problem [2005], p.141) | |
| A reaction: This is the key question in discussing whether justification is foundational. I'm not sure whether 'inference' is the best word when something is evidence for something else. I am inclined to think that only propositions can be reasons. |
| 8837 | Inference cannot originate justification, it can only transfer it from premises to conclusion [Ginet] |
| Full Idea: Inference cannot originate justification, it can only transfer it from premises to conclusion. And so it cannot be that, if there actually occurs justification, it is all inferential. | |
| From: Carl Ginet (Infinitism not solution to regress problem [2005], p.148) | |
| A reaction: The idea that justification must have an 'origin' seems to beg the question. I take Klein's inifinitism to be a version of coherence, where the accumulation of good reasons adds up to justification. It is not purely inferential. |
| 22137 | Observation can force rejection of some part of the initial set of claims [Duhem, by Boulter] |
| Full Idea: Logic and observation alone do not force a scientist to reject a scientific claim if experimental observations so not turn out as expected. The scientist must reject something of the initial set of claims, but that is a matter of choice. | |
| From: report of Pierre Duhem (The Aim and Structure of Physical Theory [1906]) by Stephen Boulter - Why Medieval Philosophy Matters 2 | |
| A reaction: This is a key point against any simplified Popperian notion of falsification. Tiny observations can't kill huge well supported theories. |
| 18197 | Experiments only test groups of hypotheses, and can't show which one is wrong [Duhem] |
| Full Idea: The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses; when the experiment is in disagreement with his predictions ...it does not designate which one should be changed. | |
| From: Pierre Duhem (The Aim and Structure of Physical Theory [1906], p.187), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
| A reaction: This is the idea frequently invoked by Quine, in support of his holistic view of scientific knowledge (along with Neurath's Boat). |