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All the ideas for 'Frege philosophy of mathematics', 'Essence and Modality' and 'Paradox without Self-Reference'

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49 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
My account shows how the concept works, rather than giving an analysis [Fine,K]
2. Reason / D. Definition / 4. Real Definition
Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K]
2. Reason / D. Definition / 6. Definition by Essence
Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K]
2. Reason / D. Definition / 7. Contextual Definition
A contextual definition permits the elimination of the expression by a substitution [Dummett]
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 / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen]
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 / C. Structure of Existence / 4. Ontological Dependence
An object is dependent if its essence prevents it from existing without some other object [Fine,K]
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 / D. Essence of Objects / 2. Types of Essence
Essences are either taken as real definitions, or as necessary properties [Fine,K]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Simple modal essentialism refers to necessary properties of an object [Fine,K]
Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Metaphysical necessity is a special case of essence, not vice versa [Fine,K]
Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe]
The nature of singleton Socrates has him as a member, but not vice versa [Fine,K]
It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami]
9. Objects / D. Essence of Objects / 9. Essence and Properties
Essential properties are part of an object's 'definition' [Fine,K, by Rami]
9. Objects / E. Objects over Time / 12. Origin as Essential
If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K]
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 / C. Sources of Modality / 1. Sources of Necessity
The subject of a proposition need not be the source of its necessity [Fine,K]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
Conceptual necessities rest on the nature of all concepts [Fine,K]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K]
Metaphysical necessities are true in virtue of the nature of all objects [Fine,K]
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 / E. Analyticity / 2. Analytic Truths
Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K]
The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K]
27. Natural Reality / C. Space / 3. Points in Space
Why should the limit of measurement be points, not intervals? [Dummett]