Combining Philosophers

All the ideas for Charles Parsons, Ion and Rod Girle

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24 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
7798 There are three axiom schemas for propositional logic [Girle]
7786 Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
7799 Proposition logic has definitions for its three operators: or, and, and identical [Girle]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
7797 Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
7794 There are seven modalities in S4, each with its negation [Girle]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
7793 ◊p → □◊p is the hallmark of S5 [Girle]
7795 S5 has just six modalities, and all strings can be reduced to those [Girle]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9470 Modal logic is not an extensional language [Parsons,C]
7787 Possible worlds logics use true-in-a-world rather than true [Girle]
7796 Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle]
7788 Modal logic has four basic modal negation equivalences [Girle]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
7789 Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
5. Theory of Logic / H. Proof Systems / 5. Tableau Proof
7790 If an argument is invalid, a truth tree will indicate a counter-example [Girle]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
10. Modality / A. Necessity / 3. Types of Necessity
7800 Analytic truths are divided into logically and conceptually necessary [Girle]
10. Modality / B. Possibility / 1. Possibility
7801 Possibilities can be logical, theoretical, physical, economic or human [Girle]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
7792 A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
467 A virtue is a combination of intelligence, strength and luck [Ion]