Combining Texts

All the ideas for 'Introduction - Ontology', 'On Euclidean Geometry' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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15 ideas

5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The truth of an axiom must be independently recognisable [Frege]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
Real numbers are ratios of quantities, such as lengths or masses [Frege]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright]
Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
My Basic Law V is a law of pure logic [Frege]
7. Existence / C. Structure of Existence / 3. Levels of Reality
Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan]
9. Objects / F. Identity among Objects / 6. Identity between Objects
'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
Functionalism has three linked levels: physical, functional, and mental [Lycan]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
Frege took the study of concepts to be part of logic [Frege, by Shapiro]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
People are trying to explain biological teleology in naturalistic causal terms [Lycan]