15 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. |
| 21642 | If quantification is all substitutional, there is no ontology [Quine] |
| Full Idea: Ontology is meaningless for a theory whose only quantification is substitutionally construed. | |
| From: Willard Quine (Ontological Relativity [1968], p.64), quoted by Thomas Hofweber - Ontology and the Ambitions of Metaphysics 03.5.1 n18 | |
| A reaction: Hofweber views it as none the worse for that, since clearly lots of quantification has no ontological commitment at all. But he says it is rightly called 'a nominalists attempt at a free lunch'. |
| 1633 | Absolute ontological questions are meaningless, because the answers are circular definitions [Quine] |
| Full Idea: What makes ontological questions meaningless when taken absolutely is not universality but circularity. A question of the form "What is an F?" can only be answered with "An F is a G", which makes sense relative to the uncritical acceptance of G. | |
| From: Willard Quine (Ontological Relativity [1968], p.53) |
| 18964 | Ontology is relative to both a background theory and a translation manual [Quine] |
| Full Idea: Ontology is doubly relative. Specifying the universe of a theory makes sense only relative to some background theory, and only relative to some choice of a manual of translation of one theory into another. | |
| From: Willard Quine (Ontological Relativity [1968], p.54) | |
| A reaction: People tend to forget about the double nature of Quine's notion of ontological commitment, and usually only talk about the commitment of the theory being employed. Why is the philosophical community not devoting itself to the study of tranlation manuals? |
| 18965 | We know what things are by distinguishing them, so identity is part of ontology [Quine] |
| Full Idea: We cannot know what something is without knowing how it is marked off from other things. Identity is thus of a piece with ontology. | |
| From: Willard Quine (Ontological Relativity [1968], p.55) | |
| A reaction: Actually it is failure of identity which seems to raise questions of individuation. If I say 'this apple is [pause] identical to this apple', I don't see how that helps me to individuate apples. |
| 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. |
| 21516 | We want certainty in order achieve secure results for action [Dewey] |
| Full Idea: The ultimate ground of the quest for cognitive certainty is the need for security in the results for action. | |
| From: John Dewey (The Quest for Certainty [1929], p.39), quoted by Erik J. Olsson - Against Coherence 10.5 | |
| A reaction: Just what a pragmatist should say. This may be true within an evolutionary account of human nature, but seems unlikely when doing a sudoku. The 'ground' of the quest may not be the same as its 'source'. |
| 1634 | Two things are relative - the background theory, and translating the object theory into the background theory [Quine] |
| Full Idea: Relativity has two components: to the choice of a background theory, and to the choice of how to translate the object theory into the background theory. | |
| From: Willard Quine (Ontological Relativity [1968], p.67) |
| 8470 | Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein] |
| Full Idea: For Quine, we cannot sensibly ask which is the real number five, the Frege-Russell set or the Von Neumann one. There is no arithmetical or empirical way of deciding between the two. Reference is inscrutable. | |
| From: report of Willard Quine (Ontological Relativity [1968]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: To generalise from a problem of reference in the highly abstract world of arithmetic, and say that all reference is inscrutable, strikes me as implausible. |
| 18963 | Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine] |
| Full Idea: The indeterminacy between 'rabbit', 'rabbit stage' and the rest depended only on a correlative indeterminacy of translation of the English apparatus of individuation - pronouns, plurals, identity, numerals and so on. | |
| From: Willard Quine (Ontological Relativity [1968], p.35) | |
| A reaction: This spells out the problem a little better than in 'Word and Object'. I just don't believe these problems are intractable. Quine is like a child endlessly asking 'why?'. |