Combining Texts

All the ideas for 'Explanation in Mathematics', 'Function and Concept' and 'Essence and Modality'

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35 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]
4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
Relations are functions with two arguments [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
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]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
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]
Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu]
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]
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 / 3. Ontology of Concepts / c. Fregean concepts
Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
A concept is a function whose value is always a truth-value [Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
19. Language / B. Reference / 5. Speaker's Reference
I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
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]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
The Ontological Argument fallaciously treats existence as a first-level concept [Frege]