Combining Texts

All the ideas for 'Inexpressible Properties and Propositions', 'Grundgesetze der Arithmetik 1 (Basic Laws)' and 'The Ages of the World'

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14 ideas

3. Truth / H. Deflationary Truth / 3. Minimalist Truth
Instances of minimal truth miss out propositions inexpressible in current English [Hofweber]
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]
Quantification can't all be substitutional; some reference is obviously to objects [Hofweber]
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 / 1. Nature of Properties
Since properties have properties, there can be a typed or a type-free theory of them [Hofweber]
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]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]