Combining Texts

All the ideas for 'fragments/reports', 'Principia Mathematica' and 'The Principles of Human Knowledge'

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60 ideas

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
An idea can only be like another idea [Berkeley]
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]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Abstract ideas are impossible [Berkeley]
7. Existence / D. Theories of Reality / 4. Anti-realism
Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron]
8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals
Universals do not have single meaning, but attach to many different particulars [Berkeley]
No one will think of abstractions if they only have particular ideas [Berkeley]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Universals do not have any intrinsic properties, but only relations to particulars [Berkeley]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
Material substance is just general existence which can have properties [Berkeley]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley]
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 / C. Knowing Reality / 2. Phenomenalism
Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
The only substance is spirit, or that which perceives [Berkeley]
The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley]
When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley]
12. Knowledge Sources / B. Perception / 2. Qualities in Perception / e. Primary/secondary critique
No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley]
Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley]
Figure and extension seem just as dependent on the observer as heat and cold [Berkeley]
12. Knowledge Sources / B. Perception / 3. Representation
Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley]
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 / 4. Other Minds / a. Other minds
Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
If animals have ideas, and are not machines, they must have some reason [Berkeley]
15. Nature of Minds / B. Features of Minds / 4. Intentionality / b. Intentionality theories
Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
The mind creates abstract ideas by considering qualities separated from their objects [Berkeley]
I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley]
16. Persons / D. Continuity of the Self / 7. Self and Thinking
Ideas are perceived by the mind, soul or self [Berkeley]
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 / A. Nature of Meaning / 2. Meaning as Mental
Language is presumably for communication, and names stand for ideas [Berkeley]
19. Language / D. Propositions / 3. Concrete Propositions
Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
19. Language / D. Propositions / 4. Mental Propositions
I can't really go wrong if I stick to wordless thought [Berkeley]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / a. Early Modern matter
No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
The laws of nature are mental regularities which we learn by experience [Berkeley]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
All motion is relative, so a single body cannot move [Berkeley]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
I cannot imagine time apart from the flow of ideas in my mind [Berkeley]
29. Religion / D. Religious Issues / 3. Problem of Evil / a. Problem of Evil
Particular evils are really good when linked to the whole system of beings [Berkeley]