Combining Texts

All the ideas for 'works', 'On Interpretation' and 'Principia Mathematica'

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47 ideas

2. Reason / B. Laws of Thought / 4. Contraries
1708 In "Callias is just/not just/unjust", which of these are contraries? [Aristotle]
3. Truth / B. Truthmakers / 10. Making Future Truths
1703 It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
1704 Statements are true according to how things actually are [Aristotle]
4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
22272 Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle]
9405 Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9542 The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9728 Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
9729 Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9730 Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9731 Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9732 Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9733 Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21720 Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10044 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
18208 We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
8204 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
9359 Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
21593 In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
1701 A prayer is a sentence which is neither true nor false [Aristotle]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036 In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248 A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152 Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
10025 Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
10037 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093 The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
8691 The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10305 In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
8684 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8746 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
1706 Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle]
7. Existence / A. Nature of Existence / 5. Reason for Existence
1707 Maybe necessity and non-necessity are the first principles of ontology [Aristotle]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12033 An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
21725 The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
23474 A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
23455 The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
23480 The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
18275 Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
2337 For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam]
19. Language / D. Propositions / 3. Concrete Propositions
23453 Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
19. Language / D. Propositions / 4. Mental Propositions
13763 Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle]
19. Language / F. Communication / 3. Denial
1705 It doesn't have to be the case that in opposed views one is true and the other false [Aristotle]
27. Natural Reality / D. Time / 1. Nature of Time / g. Growing block
1702 Things may be necessary once they occur, but not be unconditionally necessary [Aristotle]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
16713 Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
6610 I believe because it is absurd [Tertullian]