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All the ideas for 'Intensional Logic', 'Unity of Science as a Working Hypothesis' and 'works'

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11 ideas

4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
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)
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
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]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
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)
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
     Full Idea: Von Neumann defines each number as the set of all smaller numbers.
     From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
     Full Idea: Von Neumann suggested that functions be pressed into service to replace sets.
     From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
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)
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
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.
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
     Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers.
     From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm'
     A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started.
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
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.
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
20653 Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]
     Full Idea: There are six 'reductive levels' in science: social groups, (multicellular) living things, cells, molecules, atoms, and elementary particles.
     From: report of H.Putnam/P.Oppenheim (Unity of Science as a Working Hypothesis [1958]) by Peter Watson - Convergence 10 'Intro'
     A reaction: I have the impression that fields are seen as more fundamental that elementary particles. What is the status of the 'laws' that are supposed to govern these things? What is the status of space and time within this picture?