Combining Texts

All the ideas for 'fragments/reports', 'Introduction to Zermelo's 1930 paper' and 'On the Ultimate Origination of Things'

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13 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom involves the desire to achieve perfection [Leibniz]
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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette]
There must be a straining towards existence in the essence of all possible things [Leibniz]
Because something does exist, there must be a drive in possible things towards existence [Leibniz]
10. Modality / A. Necessity / 7. Natural Necessity
The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz]
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The principle of determination in things obtains the greatest effect with the least effort [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]