13 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. |
| 12899 | The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis] |
| Full Idea: I allow knowledge without belief, as in the case of the timid student who knows the answer but has no confidence that he has it right, and so does not believe what he knows. | |
| From: David Lewis (Elusive Knowledge [1996], p.429) | |
| A reaction: [He cites Woozley 1953 for the timid student] I don't accept this example (since my views on knowledge are rather traditional, I find). Why would the student give that answer if they didn't believe it? Sustained timid correctness never happens. |
| 12897 | To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis] |
| Full Idea: If you claim that S knows that P, and yet grant that S cannot eliminate a certain possibility of not-P, it certainly seems as if you have granted that S does not after all know that P. To speak of fallible knowledge just sounds contradictory. | |
| From: David Lewis (Elusive Knowledge [1996], p.419) | |
| A reaction: Starting from this point, fallibilism seems to be a rather bold move. The only sensible response seems to be to relax the requirement that not-P must be eliminable. Best: in one epistemic context P, in another not-P. |
| 12898 | Justification is neither sufficient nor necessary for knowledge [Lewis] |
| Full Idea: I don't agree that the mark of knowledge is justification, first because justification isn't sufficient - your true opinion that you will lose the lottery isn't knowledge, whatever the odds; and also not necessary - for what supports perception or memory? | |
| From: David Lewis (Elusive Knowledge [1996]) | |
| A reaction: I don't think I agree. The point about the lottery is that an overwhelming reason will never get you to knowing that you won't win. But good reasons are coherent, not statistical. If perceptions are dubious, justification must be available. |
| 12895 | Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S] |
| Full Idea: The context-sensitivity of 'knows' is a function of contextual restrictions on the domain of quantification. | |
| From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended p.68 | |
| A reaction: I think the shifting 'domain of quantification' is one of the most interesting features of ordinary talk. Or, more plainly. 'what are you actually talking about?' is the key question in any fruitful dialogue. Sophisticated speakers tacitly shift domain. |
| 19562 | We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S] |
| Full Idea: S knows P if S's evidence eliminates every alternative. But the nature of the alternatives depends on context. So for Lewis, the context sensitivity of 'knows' is a function of contextual restrictions ln the domain of quantification. | |
| From: report of David Lewis (Elusive Knowledge [1996]) by Stewart Cohen - Contextualism Defended (and reply) 1 | |
| A reaction: A typical modern attempt to 'regiment' a loose term like 'context'. That said, I like the idea. I'm struck by how the domain varies during a conversation (as in 'what we are talking about'). Domains standardly contain 'objects', though. |
| 21125 | Liberals must respect family freedom - but families are the great oppressors of women [Nussbaum] |
| Full Idea: A liberal society should give people considerable latitude to form families as they choose. …On the other hand the family …is one of the most notorious homes of sex hierarchy, denial of sexual opportunity, and sex-based violence and humiliation. | |
| From: Martha Nussbaum (Rawls and Feminism [2003], 03), quoted by Andrew Shorten - Contemporary Political Theory | |
| A reaction: The question of how the state might intervene in the family rarely seems to turn up in standard political theory. This idea shows why that is a mistake. |