Combining Texts

All the ideas for 'Laches', 'Defining 'Intrinsic' (with Rae Langton)' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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15 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / D. Definition / 1. Definitions
Interdefinition is useless by itself, but if we grasp one separately, we have them both [Lewis]
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 / B. Properties / 4. Intrinsic Properties
We must avoid circularity between what is intrinsic and what is natural [Lewis, by Cameron]
A property is 'intrinsic' iff it can never differ between duplicates [Lewis]
Ellipsoidal stars seem to have an intrinsic property which depends on other objects [Lewis]
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]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]