Combining Philosophers

All the ideas for Paul Bernays, Brian R. Martin and Rod Girle

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32 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]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10304 Very few things in set theory remain valid in intuitionist mathematics [Bernays]
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 / H. Proof Systems / 5. Tableau Proof
7790 If an argument is invalid, a truth tree will indicate a counter-example [Girle]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10303 Restricted Platonism is just an ideal projection of a domain of thought [Bernays]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10306 Mathematical abstraction just goes in a different direction from logic [Bernays]
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]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
21202 The strong force has a considerably greater range than the weak force [Martin,BR]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
21211 If an expected reaction does not occur, that implies a conservation law [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
21209 Electron emit and reabsorb photons, which create and reabsorb virtual electrons and positrons [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
21201 A 'field' is just a region to which points can be assigned in space and time [Martin,BR]
21212 The Higgs field, unlike others, has a nozero value in a state without particles [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
21205 Many physicists believe particles have further structure, if only we could see it [Martin,BR]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
21203 Uncertainty allows very brief violations of energy conservation - even shorter with higher energies [Martin,BR]
21207 The Exclusion Principle says no two fermions occupy the same state, with the same numbers [Martin,BR]
27. Natural Reality / B. Modern Physics / 4. Standard Model / b. Standard model
21204 The standard model combines theories of strong interaction, and electromagnetic and weak interaction [Martin,BR]
27. Natural Reality / B. Modern Physics / 4. Standard Model / c. Particle properties
21208 Eletrons don't literally 'spin', because they are point-like [Martin,BR]
21210 Virtual particles surround any charged particle [Martin,BR]
21206 The properties of a particle are determined by its quantum numbers and its mass [Martin,BR]
27. Natural Reality / B. Modern Physics / 5. Unified Models / b. String theory
21213 String theory only has one free parameter (tension) - unlike the standard model with 19 [Martin,BR]
27. Natural Reality / F. Chemistry / 2. Modern Elements
21200 An 'element' is what cannot be decomposed by chemistry [Martin,BR]