16 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) |
| 18935 | Semantic theory should specify when an act of naming is successful [Sawyer] |
| Full Idea: A semantic theory of names should deliver a specification of the conditions under which a name names an individual, and hence a specification of the conditions under which a name is empty. | |
| From: Sarah Sawyer (Empty Names [2012], 1) | |
| A reaction: Naming can be private, like naming my car 'Bertrand', but never tell anyone. I like Plato's remark that names are 'tools'. Do we specify conditions for successful spanner-usage? The first step must be individuation, preparatory to naming. |
| 18945 | Millians say a name just means its object [Sawyer] |
| Full Idea: The Millian view of direct reference says that the meaning of a name is the object named. | |
| From: Sarah Sawyer (Empty Names [2012], 4) | |
| A reaction: Any theory that says meaning somehow is features of the physical world strikes me as totally misguided. Napoleon is a man, so he can't be part of a sentence. He delegates that job to words (such as 'Napoleon'). |
| 18934 | Sentences with empty names can be understood, be co-referential, and even be true [Sawyer] |
| Full Idea: Some empty names sentences can be understood, so appear to be meaningful ('Pegasus was sired by Poseidon'), ...some appear to be co-referential ('Santa Claus'/'Father Christmas'), and some appear to be straightforwardly true ('Pegasus doesn't exist'). | |
| From: Sarah Sawyer (Empty Names [2012], 1) | |
| A reaction: Hang on to this, when the logicians arrive and start telling you that your talk of empty names is vacuous, because there is no object in the 'domain' to which a predicate can be attached. Meaning, reference and truth are the issues around empty names. |
| 18938 | Frege's compositional account of truth-vaues makes 'Pegasus doesn't exist' neither true nor false [Sawyer] |
| Full Idea: In Frege's account sentences such as 'Pegasus does not exist' will be neither true nor false, since the truth-value of a sentence is its referent, and the referent of a complex expression is determined by the referent of its parts. | |
| From: Sarah Sawyer (Empty Names [2012], 2) | |
| A reaction: We can keep the idea of 'sense', which is very useful for dealing with empty names, but tweak his account of truth-values to evade this problem. I'm thinking that meaning is compositional, but truth-value isn't. |
| 18947 | Definites descriptions don't solve the empty names problem, because the properties may not exist [Sawyer] |
| Full Idea: If it were possible for a definite description to be empty - not in the sense of there being no object that satisfies it, but of there being no set of properties it refers to - the problem of empty names would not have been solved. | |
| From: Sarah Sawyer (Empty Names [2012], 5) | |
| A reaction: Swoyer is thinking of properties like 'is a unicorn', which are clearly just as vulnerable to being empty as 'the unicorn' was. It seems unlikely that 'horse', 'white' and 'horn' would be empty. |
| 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. |
| 12270 | Being is one [Melissus, by Aristotle] |
| Full Idea: Being is one. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Aristotle - Topics 104b23 | |
| A reaction: I can only really understand this in terms of physics, as the belief that ultimately there is one simple theory which explains everything. That project doesn't look terribly promising, despite the lovely simplifications of modern physics. |
| 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. |
| 3059 | There is no real motion, only the appearance of it [Melissus, by Diog. Laertius] |
| Full Idea: There is no such thing as real motion, but there only appears to be such. | |
| From: report of Melissus (fragments/reports [c.443 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 09.4.3 |
| 5100 | The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus] |
| Full Idea: There is no need for void to be the cause of all change, because it is perfectly possible for a plenum to alter qualitatively (which is something Melissus overlooked). | |
| From: comment on Melissus (fragments/reports [c.443 BCE]) by Aristotle - Physics 214a27 | |
| A reaction: In modern physics this presumably gives us fluctuations in a force field. Motion is like a cat being digested by a python. The atomist claim that emptiness is needed if anything is to move still has intuitive appeal. |
| 456 | Nothing could come out of nothing [Melissus] |
| Full Idea: If Nothing existed, in no way could anything come into being out of nothing. | |
| From: Melissus (fragments/reports [c.443 BCE], B1), quoted by (who?) - where? |