Combining Texts

All the ideas for 'Kant and the Critique of Pure Reason', 'The Essence of Aesthetic' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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16 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / c. Eighteenth century philosophy
Hamann, Herder and Jacobi were key opponents of the Enlightenment [Gardner]
Kant halted rationalism, and forced empiricists to worry about foundations [Gardner]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Only Kant and Hegel have united nature, morals, politics, aesthetics and religion [Gardner]
2. Reason / E. Argument / 2. Transcendental Argument
Transcendental proofs derive necessities from possibilities (e.g. possibility of experiencing objects) [Gardner]
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 / 2. Geometry
Modern geoemtry is either 'pure' (and formal), or 'applied' (and a posteriori) [Gardner]
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 / 6. Fundamentals / c. Monads
Leibnizian monads qualify as Kantian noumena [Gardner]
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]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
The experience of expression and communication are intermingled in art [Croce]