Combining Texts

All the ideas for 'Mathematics without Numbers', 'Human Nature' and 'Introduction to Zermelo's 1930 paper'

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13 ideas

1. Philosophy / D. Nature of Philosophy / 8. Humour
Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
The first-order ZF axiomatisation is highly non-categorical [Hallett,M]
Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M]
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]
16. Persons / F. Free Will / 5. Against Free Will
A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
Conceptions and apparitions are just motion in some internal substance of the head [Hobbes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
There is no absolute good, for even the goodness of God is goodness to us [Hobbes]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes]
25. Social Practice / F. Life Issues / 5. Sexual Morality
Lust involves pleasure, and also the sense of power in pleasing others [Hobbes]