48 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] |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 15611 | I develop philosophical science from the simplest appearance of immediate consciousness [Hegel, by Hegel] |
| 8934 | Being is Thought [Hegel] |
| 21774 | Genuine idealism is seeing the ideal structure of the world [Hegel, by Houlgate] |
| 8928 | The Absolute is not supposed to be comprehended, but felt and intuited [Hegel] |
| 8929 | In the Absolute everything is the same [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] |
| 8930 | The in-itself must become for-itself, which requires self-consciousness [Hegel] |
| 22034 | Modern life needs individuality, but must recognise that human agency is social [Hegel, by Pinkard] |
| 8936 | Human nature only really exists in an achieved community of minds [Hegel] |
| 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] |
| 5994 | Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG] |
| 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] |