12 ideas
8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
5044 | Reality must be made of basic unities, which will be animated, substantial points [Leibniz] |
8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |
5045 | No machine or mere organised matter could have a unified self [Leibniz] |
5046 | The soul does know bodies, although they do not influence one another [Leibniz] |
5043 | To regard animals as mere machines may be possible, but seems improbable [Leibniz] |