7 ideas
| 18241 | Sufficient reason is implied by contradiction, of an insufficient possible which exists [Wolff, by Korsgaard] |
| Full Idea: Wolff believed that the principle of sufficient reason could be derived from the principle of contradiction, for there would be a contradiction in the insufficiently determined existence of a merely possible thing. | |
| From: report of Christian Wolff (works [1730]) by Christine M. Korsgaard - Intro to Ethics, Politics, Religion in Kant 'A child' | |
| A reaction: Sounds as if he might be begging to question. You would only protest against the insufficient determination of something if you already believed in the principle of sufficient reason. Nice try. |
| 17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
| Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
| 17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
| Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
| A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
| 17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
| Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
| Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
| From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
| 8338 | A phenomenalist about objects has to be a regularity theorist about causation [Strawson,G] |
| Full Idea: If you are a phenomenalist about objects, then there is an important sense in which you ought to be a Regularity theorist about what causation is, in such objects. | |
| From: Galen Strawson (The Secret Connexion [1989], App C) | |
| A reaction: Strawson is denying that Hume is a phenomenalist. One might go a little further, and say that a phenomenalist should abandon the idea of causation (as Russell did). |
| 18242 | Confucius shows that ethics can rest on reason, rather than on revelation [Wolff, by Korsgaard] |
| Full Idea: Wolff claimed that the moral philosophy of Confucius shows that ethics is accessible to natural reason and independent of revelation. | |
| From: report of Christian Wolff (works [1730]) by Christine M. Korsgaard - Intro to Ethics, Politics, Religion in Kant 'A child' | |
| A reaction: Wolff was banished for proposing this idea. |