Combining Philosophers

All the ideas for Melvin Fitting, Stephen Wolfram and Anil Gupta

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25 ideas

2. Reason / D. Definition / 1. Definitions
Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta]
Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta]
2. Reason / D. Definition / 2. Aims of Definition
A definition needs to apply to the same object across possible worlds [Gupta]
The 'revision theory' says that definitions are rules for improving output [Gupta]
2. Reason / D. Definition / 3. Types of Definition
Traditional definitions are general identities, which are sentential and reductive [Gupta]
Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta]
A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta]
2. Reason / D. Definition / 4. Real Definition
Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta]
2. Reason / D. Definition / 6. Definition by Essence
If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta]
2. Reason / D. Definition / 10. Stipulative Definition
Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta]
2. Reason / D. Definition / 11. Ostensive Definition
Ostensive definitions look simple, but are complex and barely explicable [Gupta]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta]
3. Truth / F. Semantic Truth / 2. Semantic Truth
A weakened classical language can contain its own truth predicate [Gupta]
4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
If terms change their designations in different states, they are functions from states to objects [Fitting]
Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Classical logic is deliberately extensional, in order to model mathematics [Fitting]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
λ-abstraction disambiguates the scope of modal operators [Fitting]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
The Liar reappears, even if one insists on propositions instead of sentences [Gupta]
Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
At one level maths and nature are very similar, suggesting some deeper origin [Wolfram]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Definite descriptions pick out different objects in different possible worlds [Fitting]
27. Natural Reality / C. Space / 4. Substantival Space
Space and its contents seem to be one stuff - so space is the only existing thing [Wolfram]