Combining Texts

All the ideas for 'Intensional Logic', 'Hat-Tricks and Heaps' and 'works'

unexpand these ideas     |    start again     |     specify just one area for these texts

9 ideas

1. Philosophy / B. History of Ideas / 5. Later European Thought
7822 A neo-Stoic movement began in the late sixteenth century [Lipsius, by Grayling]
     Full Idea: A neo-Stoic movement began at the end of the sixteenth century, under the inspiration of the Dutch scholar Justus Lipsius.
     From: report of Justus Lipsius (works [1584]) by A.C. Grayling - What is Good? Ch.5
     A reaction: I would take this to be just as much a movement against Christianity as the interest in the less theistic Epicurus. They wanted the virtues of Christianity without the theological trappings.
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)
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.
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
9117 The smallest heap has four objects: three on the bottom, one on the top [Hart,WD, by Sorensen]
     Full Idea: Hart argues that the smallest heap consists of four objects: three on the bottom, one on the top.
     From: report of William D. Hart (Hat-Tricks and Heaps [1992]) by Roy Sorensen - Vagueness and Contradiction Intro
     A reaction: If the objects were rough bolders, you could get away with two on the bottom. He's wrong. No one would accept as a 'heap' four minute grains barely visible to the naked eye. No one would describe such a group of items in a supermarket as a heap.
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.