42 ideas
| 21584 | A sense of timelessness is essential to wisdom [Russell] |
| 21572 | Philosophical disputes are mostly hopeless, because philosophers don't understand each other [Russell] |
| 21571 | Philosophical systems are interesting, but we now need a more objective scientific philosophy [Russell] |
| 21574 | Hegel's confusions over 'is' show how vast systems can be built on simple errors [Russell] |
| 21587 | Philosophers sometimes neglect truth and distort facts to attain a nice system [Russell] |
| 21582 | Physicists accept particles, points and instants, while pretending they don't do metaphysics [Russell] |
| 21573 | When problems are analysed properly, they are either logical, or not philosophical at all [Russell] |
| 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] |
| 21588 | Logic gives the method of research in philosophy [Russell] |
| 21586 | The logical connectives are not objects, but are formal, and need a context [Russell] |
| 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] |
| 21585 | The tortoise won't win, because infinite instants don't compose an infinitely long time [Russell] |
| 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] |
| 21684 | Atomic facts may be inferrable from others, but never from non-atomic facts [Russell] |
| 22316 | A positive and negative fact have the same constituents; their difference is primitive [Russell] |
| 21576 | With asymmetrical relations (before/after) the reduction to properties is impossible [Russell] |
| 21575 | When we attribute a common quality to a group, we can forget the quality and just talk of the group [Russell] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 21580 | Science condemns sense-data and accepts matter, but a logical construction must link them [Russell] |
| 21583 | When sense-data change, there must be indistinguishable sense-data in the process [Russell] |
| 21577 | Empirical truths are particular, so general truths need an a priori input of generality [Russell] |
| 21579 | Objects are treated as real when they connect with other experiences in a normal way [Russell] |
| 21578 | Global scepticism is irrefutable, but can't replace our other beliefs, and just makes us hesitate [Russell] |
| 6416 | Other minds seem to exist, because their testimony supports realism about the world [Russell, by Grayling] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 21581 | We never experience times, but only succession of events [Russell] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |