Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Alan Musgrave and Rod Girle

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24 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
7786 Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle]
7798 There are three axiom schemas for propositional logic [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
7787 Possible worlds logics use true-in-a-world rather than true [Girle]
7788 Modal logic has four basic modal negation equivalences [Girle]
7796 Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle]
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 / C. Ontology of Logic / 3. If-Thenism
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
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]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058 No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
10063 Formalism is a bulwark of logical positivism [Musgrave]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
12887 A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
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]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]