Combining Texts

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

expand these ideas     |    start again     |     specify just one area for these texts


16 ideas

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
One geometry cannot be more true than another [Poincaré]
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]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
If we succeed in speaking the truth, we cannot know we have done it [Xenophanes]
13. Knowledge Criteria / E. Relativism / 1. Relativism
If God had not created honey, men would say figs are sweeter [Xenophanes]
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 / e. The One
The basic Eleatic belief was that all things are one [Xenophanes, by Plato]
28. God / A. Divine Nature / 2. Divine Nature
Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius]
28. God / C. Attitudes to God / 5. Atheism
Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes]
Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes]