Combining Texts

All the ideas for 'fragments/reports', 'Senses of Essence' and 'The Philosophy of Mathematics'

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16 ideas

2. Reason / D. Definition / 6. Definition by Essence
The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
Logical concepts rest on certain inferences, not on facts about implications [Fine,K]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
The property of Property Abstraction says any suitable condition must imply a property [Fine,K]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
A logical truth is true in virtue of the nature of the logical concepts [Fine,K]
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Can the essence of an object circularly involve itself, or involve another object? [Fine,K]
9. Objects / D. Essence of Objects / 3. Individual Essences
Being a man is a consequence of his essence, not constitutive of it [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
If there are alternative definitions, then we have three possibilities for essence [Fine,K]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]