Combining Texts

All the ideas for 'works', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'Outline of a System of the Philosophy of Nature'

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14 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]
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 / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
For Schelling the Absolute spirit manifests as nature in which self-consciousness evolves [Schelling, by Lewis,PB]
Metaphysics aims at the Absolute, which goes beyond subjective and objective viewpoints [Schelling, by Pinkard]
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 / 1. Nature
Schelling sought a union between the productivities of nature and of the mind [Schelling, by Bowie]
Schelling made organisms central to nature, because mere mechanism could never produce them [Schelling, by Pinkard]