Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Regressive Method for Premises in Mathematics' and 'Does moral phil rest on a mistake?'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason
17641 Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell]
2. Reason / A. Nature of Reason / 6. Coherence
17638 If one proposition is deduced from another, they are more certain together than alone [Russell]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
17632 Non-contradiction was learned from instances, and then found to be indubitable [Russell]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17629 Which premises are ultimate varies with context [Russell]
17630 The sources of a proof are the reasons why we believe its conclusion [Russell]
17640 Finding the axioms may be the only route to some new results [Russell]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17627 It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
17628 Arithmetic was probably inferred from relationships between physical objects [Russell]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
17637 The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
17639 Believing a whole science is more than believing each of its propositions [Russell]
14. Science / C. Induction / 2. Aims of Induction
17631 Induction is inferring premises from consequences [Russell]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
9261 The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
9262 The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
9260 Virtues won't generate an obligation, so it isn't a basis for morality [Prichard]
23. Ethics / D. Deontological Ethics / 2. Duty
9259 We feel obligations to overcome our own failings, and these are not relations to other people [Prichard]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
9258 If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
17633 The law of gravity has many consequences beyond its grounding observations [Russell]