Combining Texts

All the ideas for 'fragments/reports', 'The Structure of Science' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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15 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
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]
7. Existence / C. Structure of Existence / 2. Reduction
Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
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 / 6. Early Matter Theories / c. Ultimate substances
Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]