Combining Texts

All the ideas for 'fragments/reports', 'Interview with Philippa Foot' and 'Mathematics without Foundations'

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17 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
We understand some statements about all sets [Putnam]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
Science requires more than consistency of mathematics [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
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]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
Archelaus said life began in a primeval slime [Archelaus, by Schofield]