Combining Philosophers

All the ideas for Michael Burke, B Russell/AN Whitehead and Thomas Reid

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50 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 / 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]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
Persistence conditions cannot contradict, so there must be a 'dominant sortal' [Burke,M, by Hawley]
The 'dominant' of two coinciding sortals is the one that entails the widest range of properties [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
'The rock' either refers to an object, or to a collection of parts, or to some stuff [Burke,M, by Wasserman]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
Tib goes out of existence when the tail is lost, because Tib was never the 'cat' [Burke,M, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Maybe the clay becomes a different lump when it becomes a statue [Burke,M, by Koslicki]
Sculpting a lump of clay destroys one object, and replaces it with another one [Burke,M, by Wasserman]
Burke says when two object coincide, one of them is destroyed in the process [Burke,M, by Hawley]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Two entities can coincide as one, but only one of them (the dominant sortal) fixes persistence conditions [Burke,M, by Sider]
9. Objects / E. Objects over Time / 1. Objects over Time
Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid]
9. Objects / E. Objects over Time / 13. No Identity over Time
We treat slowly changing things as identical for the sake of economy in language [Reid]
9. Objects / F. Identity among Objects / 1. Concept of Identity
Real identity admits of no degrees [Reid]
Identity is familiar to common sense, but very hard to define [Reid]
Identity can only be affirmed of things which have a continued existence [Reid]
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]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar]
12. Knowledge Sources / B. Perception / 1. Perception
Sensation is not committed to any external object, but perception is [Reid]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H]
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]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
A person is a unity, and doesn't come in degrees [Reid]
16. Persons / A. Concept of a Person / 2. Persons as Responsible
Personal identity is the basis of all rights, obligations and responsibility [Reid]
16. Persons / A. Concept of a Person / 3. Persons as Reasoners
I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
Memory reveals my past identity - but so does testimony of other witnesses [Reid]
Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid]
If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid]
If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid]
If consciousness is personal identity, it is continually changing [Reid]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
Thoughts change continually, but the self doesn't [Reid]
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]
Only the act of judging completes the meaning of a statement [Russell/Whitehead]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
Reid said that agent causation is a unique type of causation [Reid, by Stout,R]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane]