Combining Texts

All the ideas for 'Intensional Logic', 'On the General Idea of Proof Theory' and 'The Poetics'

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

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)
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 / B. Logical Consequence / 1. Logical Consequence
13827 Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz]
     Full Idea: Defining logical consequence in the way Tarski does is a rather meagre result, treating an argument as a black box, observing input and output, while disregarding inner structure. We should define logical consequence on the basis of valid arguments.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §2)
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 / J. Model Theory in Logic / 1. Logical Models
13826 Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz]
     Full Idea: In model theory, which has dominated the last decades, one concentrates on logically valid sentences, and what follows logically from what, but one disregards questions concerning how we know these things.
     From: Dag Prawitz (On the General Idea of Proof Theory [1974], §1)
10. Modality / B. Possibility / 1. Possibility
22518 The actual must be possible, because it occurred [Aristotle]
     Full Idea: Actual events are evidently possible, otherwise they would not have occurred.
     From: Aristotle (The Poetics [c.347 BCE], 1451b18)
     A reaction: [quoted online by Peter Adamson] Seems like common sense, but it's important to have Aristotle assert it.
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.
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
16566 Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle]
     Full Idea: Poetry is something more philosophic and of graver import than history, since its statements are rather of universals, whereas those of history are singulars.
     From: Aristotle (The Poetics [c.347 BCE], 1451b05)
     A reaction: Hm. Characters in great novels achieve universality by being representated very particularly. Great depth of mind seems required to be a poet, but less so for a historian (though there is, I presume, no upward limit on the possible level of thought).