39 ideas
11257 | The Pythagoreans were the first to offer definitions [Politis, by Politis] |
11235 | 'True of' is applicable to things, while 'true' is applicable to words [Politis] |
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] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [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] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [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] |
11277 | Maybe 'What is being? is confusing because we can't ask what non-being is like [Politis] |
11248 | Necessary truths can be two-way relational, where essential truths are one-way or intrinsic [Politis] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
20289 | Ethics is universalisable - it must involve an impartial and universal view of things [Singer] |
20286 | Following an inner voice for morality is irresponsible in a rational agent [Singer] |
20282 | The sanctity of a human life depends either on being of our species, or on being a person [Singer] |
20278 | 'Marginal utility' says something is more useful if it is in short supply [Singer] |
20281 | Why should I do anything for posterity? What has posterity ever done for me? [Singer] |
20276 | Conflict of rules might be avoided by greater complexity, or by a hierarchy of rules [Singer] |
20290 | Psychopaths may just be bored, because they cannot participate in normal emotional life [Singer] |
20288 | You can't condemn violent revolution without assessing the evils it prevents [Singer] |
21997 | In Marxism the state will be superseded [Singer] |
20287 | If 49% of the population can be wrong, so can 51% [Singer] |
21993 | Materialist history says we are subject to incomprehensible forces [Singer] |
20277 | Equality of interests is a minimal principle, not implying equal treatment [Singer] |
20279 | Equality of opportunity unfairly rewards those lucky enough to have great ability [Singer] |
20285 | If a right entails having the relevant desire, many creatures might have no right to life [Singer] |
20284 | Why should a potential person have the rights of an actual person? [Singer] |
20283 | Killing a chimp is worse than killing a human too defective to be a person [Singer] |