Combining Texts

All the ideas for 'Grundgesetze der Arithmetik 1 (Basic Laws)', 'Knowledge by Acquaintance and Description-1' and 'Letter on Freedom'

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12 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
For every event it is possible for an omniscient being to give a reason for its occurrence [Leibniz]
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 / 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]
8. Modes of Existence / D. Universals / 2. Need for Universals
We know a universal in 'yellow differs from blue' or 'yellow resembles blue less than green does' [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
My 'acquaintance' with sense-data is nothing like my knowing New York [Williams,M on Russell]
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]