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All the ideas for 'Frege philosophy of mathematics', '11: Book of Kings 1' and 'Penguin Dictionary of Philosophy'

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58 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
Linguistic philosophy approaches problems by attending to actual linguistic usage [Mautner]
1. Philosophy / F. Analytic Philosophy / 7. Limitations of Analysis
Analytic philosophy studies the unimportant, and sharpens tools instead of using them [Mautner]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
The 'hermeneutic circle' says parts and wholes are interdependent, and so cannot be interpreted [Mautner]
2. Reason / D. Definition / 4. Real Definition
'Real' definitions give the essential properties of things under a concept [Mautner]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
'Contextual definitions' replace whole statements, not just expressions [Mautner]
2. Reason / D. Definition / 9. Recursive Definition
Recursive definition defines each instance from a previous instance [Mautner]
2. Reason / D. Definition / 10. Stipulative Definition
A stipulative definition lays down that an expression is to have a certain meaning [Mautner]
2. Reason / D. Definition / 11. Ostensive Definition
Ostensive definitions point to an object which an expression denotes [Mautner]
2. Reason / F. Fallacies / 5. Fallacy of Composition
The fallacy of composition is the assumption that what is true of the parts is true of the whole [Mautner]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic is based on the notion that there can be membership of a set to some degree [Mautner]
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]
5. Theory of Logic / B. Logical Consequence / 6. Entailment
Entailment is logical requirement; it may be not(p and not-q), but that has problems [Mautner]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
Strict implication says false propositions imply everything, and everything implies true propositions [Mautner]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner]
A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
Vagueness seems to be inconsistent with the view that every proposition is true or false [Mautner]
5. Theory of Logic / G. Quantification / 1. Quantification
Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner]
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 / 3. Nature of Numbers / n. Pi
He made a molten sea, which was ten cubits across, and thirty cubits round the edge [Anon (Kings)]
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 / 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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
Nominalism assumes unmediated mental contact with objects [Dummett]
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 / 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]
10. Modality / B. Possibility / 9. Counterfactuals
Counterfactuals presuppose a belief (or a fact) that the condition is false [Mautner]
Counterfactuals are not true, they are merely valid [Mautner]
Counterfactuals are true if in every world close to actual where p is the case, q is also the case [Mautner]
Counterfactuals say 'If it had been, or were, p, then it would be q' [Mautner]
Maybe counterfactuals are only true if they contain valid inference from premisses [Mautner]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Essentialism is often identified with belief in 'de re' necessary truths [Mautner]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
Fallibilism is the view that all knowledge-claims are provisional [Mautner]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
'Sense-data' arrived in 1910, but it denotes ideas in Locke, Berkeley and Hume [Mautner]
14. Science / C. Induction / 5. Paradoxes of Induction / a. Grue problem
Observing lots of green x can confirm 'all x are green' or 'all x are grue', where 'grue' is arbitrary [Mautner, by PG]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
'All x are y' is equivalent to 'all non-y are non-x', so observing paper is white confirms 'ravens are black' [Mautner, by PG]
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 / C. Assigning Meanings / 5. Fregean Semantics
Fregean semantics assumes a domain articulated into individual objects [Dummett]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
The references of indexicals ('there', 'now', 'I') depend on the circumstances of utterance [Mautner]
20. Action / C. Motives for Action / 5. Action Dilemmas / b. Double Effect
Double effect is the distinction between what is foreseen and what is intended [Mautner]
Double effect acts need goodness, unintended evil, good not caused by evil, and outweighing [Mautner]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
'Essentialism' is opposed to existentialism, and claims there is a human nature [Mautner]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]