Combining Texts

All the ideas for 'Summa', 'Ecce Homo' and 'Grundgesetze der Arithmetik 1 (Basic Laws)'

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19 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
A warlike philosopher challenges problems to single combat [Nietzsche]
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]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
Prime matter is free of all forms, but has the potential for all forms [Eustachius]
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]
22. Metaethics / B. Value / 2. Values / i. Self-interest
The distinction between egoistic and non-egoistic acts is absurd [Nietzsche]
22. Metaethics / C. The Good / 1. Goodness / i. Moral luck
A bad result distorts one's judgement about the virtue of what one has done [Nietzsche]
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
The overcoming of pity I count among the noble virtues [Nietzsche]
23. Ethics / F. Existentialism / 6. Authentic Self
To become what you are you must have no self-awareness [Nietzsche]
23. Ethics / F. Existentialism / 8. Eternal Recurrence
Eternal recurrence is the highest attainable affirmation [Nietzsche]
25. Social Practice / E. Policies / 5. Education / c. Teaching
One repays a teacher badly if one remains only a pupil [Nietzsche]
28. God / C. Attitudes to God / 5. Atheism
I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche]