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Ideas for 'Dialectic of Enlightenment', 'Nominalism' and 'Intensional Logic'

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5 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 / 3. Types of Set / c. Unit (Singleton) Sets

8956	What is a singleton set, if a set is meant to be a collection of objects? [Szabó]
	Full Idea: The relationship between an object and its singleton is puzzling. Our intuitive conception of a set is a collection of objects - what are we to make of a collection of a single object?
	From: Zoltán Gendler Szabó (Nominalism [2003], 4.1)
	A reaction: The ontological problem seems to be the same as that of the empty set, and indeed the claim that a pair of entities is three things. For logicians the empty set is as real as a pet dog, but not for me.