Combining Philosophers

All the ideas for Eubulides, Frank P. Ramsey and M Fitting/R Mendelsohn

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70 ideas

3. Truth / H. Deflationary Truth / 1. Redundant Truth
3750 "It is true that x" means no more than x [Ramsey]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9738 Each line of a truth table is a model [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML
9727 Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn]
9726 We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
9737 The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
13136 The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
13141 Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn]
13138 Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn]
13142 Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
13145 D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
13146 B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
13147 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
13148 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
9740 If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
9739 If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
13137 Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn]
13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
13139 Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn]
13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
13149 S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
9742 The system K has no accessibility conditions [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13114 □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
9744 The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / e. System K4
9746 The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
9745 The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
9747 The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9404 Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13112 In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn]
13111 Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13113 F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13728 The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
13729 The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13430 Infinity: there is an infinity of distinguishable individuals [Ramsey]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
13428 Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
9725 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
5. Theory of Logic / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
13334 Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
6409 The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13426 Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
13425 Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]
8. Modes of Existence / D. Universals / 1. Universals
8495 The distinction between particulars and universals is a mistake made because of language [Ramsey]
8493 We could make universals collections of particulars, or particulars collections of their qualities [Ramsey]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
8494 Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
13766 'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
10993 Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read]
10. Modality / B. Possibility / 8. Conditionals / e. Supposition conditionals
14279 Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13725 □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn]
13731 Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
13726 Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3212 Beliefs are maps by which we steer [Ramsey]
11. Knowledge Aims / A. Knowledge / 4. Belief / d. Cause of beliefs
22328 I just confront the evidence, and let it act on me [Ramsey]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
22325 A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey]
19724 Belief is knowledge if it is true, certain, and obtained by a reliable process [Ramsey]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
6894 Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey]
14. Science / C. Induction / 6. Bayes's Theorem
19143 Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
18818 Sentence meaning is given by the actions to which it would lead [Ramsey]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
9418 All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey]
9420 Causal laws result from the simplest axioms of a complete deductive system [Ramsey]