Combining Texts

All the ideas for 'Mathematics without Numbers', 'talk' and 'Interview with Philippa Foot'

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13 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
Observing irrelevant items supports both 'all x are y' and 'all x are non-y', revealing its absurdity [Schofield,J]
18. Thought / A. Modes of Thought / 5. Rationality / b. Human rationality
Full rationality must include morality [Foot]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
Practical reason is goodness in choosing actions [Foot]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
It is an odd Humean view to think a reason to act must always involve caring [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
Human defects are just like plant or animal defects [Foot]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
Concepts such as function, welfare, flourishing and interests only apply to living things [Foot]
Humans need courage like a plant needs roots [Foot]
22. Metaethics / B. Value / 1. Nature of Value / b. Fact and value
There is no fact-value gap in 'owls should see in the dark' [Foot]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
Principles are not ultimate, but arise from the necessities of human life [Foot]
22. Metaethics / B. Value / 2. Values / a. Normativity
If you demonstrate the reason to act, there is no further question of 'why should I?' [Foot]