Combining Texts

All the ideas for 'works', 'The Methods of Ethics (7th edn)' and 'Maths as a Science of Patterns'

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14 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
There are too many mathematical objects for them all to be mental or physical [Resnik]
Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
16. Persons / F. Free Will / 2. Sources of Free Will
If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick]
23. Ethics / A. Egoism / 1. Ethical Egoism
Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick]
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf]
29. Religion / B. Monotheistic Religion / 4. Christianity / d. Heresy
Philosophers are the forefathers of heretics [Tertullian]
29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism
I believe because it is absurd [Tertullian]