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All the ideas for 'fragments/reports', 'talk' and 'Principia Mathematica'

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48 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
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
Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
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
Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
F(x) walked into a bar. The barman said.. [Sommers,W]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
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
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
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
Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
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
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
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
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 / d. Non-being
Sartre to Waitress: Coffee with no cream, please... [Sommers,W]
7. Existence / D. Theories of Reality / 4. Anti-realism
Said Plato: 'The things that we feel... [Sommers,W]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
Barman to Descartes: Would you like another drink?... [Sommers,W]
There was a young student called Fred... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
A philosopher and his wife are out for a drive... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
Dear Sir, Your astonishment's odd.... [Sommers,W]
There once was a man who said: 'God... [Sommers,W]
..But if he's a student of Berkeley... [Sommers,W]
The philosopher Berkeley once said.. [Sommers,W]
12. Knowledge Sources / B. Perception / 1. Perception
"My dog's got synaesthesia." How does he smell? ..... [Sommers,W]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
A toper who spies in the distance... [Sommers,W]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
There once was a man who said 'Damn!... [Sommers,W]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
How do behaviourists greet each other? [Sommers,W]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
'If you're aristocratic,' said Nietzsche... [Sommers,W]
24. Political Theory / D. Ideologies / 2. Anarchism
Why do anarchists drink herbal tea? [Sommers,W]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Cries the maid: 'You must marry me Hume!'... [Sommers,W]
Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
The barman called 'Time!', and Augustine said..... [Sommers,W]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
The past, present and future walked into a bar.... [Sommers,W]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]