43 ideas
8927 | Philosophy moves essentially in the element of universality [Hegel] |
21776 | Philosophy aims to reveal the necessity and rationality of the categories of nature and spirit [Hegel, by Houlgate] |
8935 | Without philosophy, science is barren and futile [Hegel] |
22082 | Truth does not appear by asserting reasons and then counter-reasons [Hegel] |
22035 | The structure of reason is a social and historical achievement [Hegel, by Pinkard] |
8932 | Truth does not come from giving reasons for and against propositions [Hegel] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
7077 | The true is the whole [Hegel] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
15611 | I develop philosophical science from the simplest appearance of immediate consciousness [Hegel, by Hegel] |
8928 | The Absolute is not supposed to be comprehended, but felt and intuited [Hegel] |
8929 | In the Absolute everything is the same [Hegel] |
21774 | Genuine idealism is seeing the ideal structure of the world [Hegel, by Houlgate] |
8934 | Being is Thought [Hegel] |
21773 | Experience is immediacy, unity, forces, self-awareness, reason, culture, absolute being [Hegel, by Houlgate] |
22033 | Hegel tried to avoid Kant's dualism of neutral intuitions and imposed concepts [Hegel, by Pinkard] |
21771 | Consciousness derives its criterion of knowledge from direct knowledge of its own being [Hegel] |
20741 | Consciousness is shaped dialectically, by opposing forces and concepts [Hegel, by Aho] |
21770 | Consciousness is both of objects, and of itself [Hegel] |
5647 | Hegel claims knowledge of self presupposes desire, and hence objects [Hegel, by Scruton] |
5648 | For Hegel knowledge of self presupposes objects, and also a public and moral social world [Hegel, by Scruton] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
8930 | The in-itself must become for-itself, which requires self-consciousness [Hegel] |
8936 | Human nature only really exists in an achieved community of minds [Hegel] |
22034 | Modern life needs individuality, but must recognise that human agency is social [Hegel, by Pinkard] |
21987 | History is the progress of the consciousness of freedom [Hegel] |
8931 | The movement of pure essences constitutes the nature of scientific method [Hegel] |
8933 | Science confronts the inner necessities of objects [Hegel] |
21775 | The God of revealed religion can only be understood through pure speculative knowledge [Hegel] |
6917 | God is the essence of thought, abstracted from the thinker [Hegel, by Feuerbach] |
6915 | Hegel made the last attempt to restore Christianity, which philosophy had destroyed [Hegel, by Feuerbach] |