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All the ideas for 'Frege philosophy of mathematics', 'The Principles of Human Knowledge' and 'The Emperor's New 'Knows''

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63 ideas

2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
An idea can only be like another idea [Berkeley]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
In classical logic, logical truths are valid formulas; in higher-order logics they are purely logical [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
A prime number is one which is measured by a unit alone [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units
A number is a multitude composed of units [Dummett]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
We understand 'there are as many nuts as apples' as easily by pairing them as by counting them [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The identity of a number may be fixed by something outside structure - by counting [Dummett]
Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Set theory isn't part of logic, and why reduce to something more complex? [Dummett]
7. Existence / A. Nature of Existence / 4. Abstract Existence
Abstract ideas are impossible [Berkeley]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
The distinction of concrete/abstract, or actual/non-actual, is a scale, not a dichotomy [Dummett]
7. Existence / D. Theories of Reality / 2. Realism
Realism is just the application of two-valued semantics to sentences [Dummett]
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 / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
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 / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
The existence of abstract objects is a pseudo-problem [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Abstract objects nowadays are those which are objective but not actual [Dummett]
It is absurd to deny the Equator, on the grounds that it lacks causal powers [Dummett]
'We've crossed the Equator' has truth-conditions, so accept the Equator - and it's an object [Dummett]
9. Objects / A. Existence of Objects / 2. Abstract Objects / d. Problems with abstracta
Abstract objects need the context principle, since they can't be encountered directly [Dummett]
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 / 2. Defining Identity
Content is replaceable if identical, so replaceability can't define identity [Dummett, by Dummett]
Frege introduced criteria for identity, but thought defining identity was circular [Dummett]
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]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
How could 'S knows he has hands' not have a fixed content? [Bach]
If contextualism is right, knowledge sentences are baffling out of their context [Bach]
Sceptics aren't changing the meaning of 'know', but claiming knowing is tougher than we think [Bach]
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 / D. Concepts / 4. Structure of Concepts / i. Conceptual priority
Maybe a concept is 'prior' to another if it can be defined without the second concept [Dummett]
An argument for conceptual priority is greater simplicity in explanation [Dummett]
18. Thought / E. Abstraction / 1. Abstract Thought
Abstract terms are acceptable as long as we know how they function linguistically [Dummett]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
There is no reason why abstraction by equivalence classes should be called 'logical' [Dummett, by Tait]
We arrive at the concept 'suicide' by comparing 'Cato killed Cato' with 'Brutus killed Brutus' [Dummett]
18. Thought / E. Abstraction / 8. Abstractionism Critique
To abstract from spoons (to get the same number as the forks), the spoons must be indistinguishable too [Dummett]
19. Language / A. Nature of Meaning / 2. Meaning as Mental
Language is presumably for communication, and names stand for ideas [Berkeley]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / D. Propositions / 4. Mental Propositions
I can't really go wrong if I stick to wordless thought [Berkeley]
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 / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]
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]