49 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] |
| 7077 | The true is the whole [Hegel] |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| 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] |
| 19699 | A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington] |
| 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] |
| 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] |