31 ideas
8013 | In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre] |
8021 | The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
8006 | When Aristotle speaks of soul he means something like personality [MacIntyre] |
8002 | Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre] |
8012 | The value/fact logical gulf is misleading, because social facts involve values [MacIntyre] |
8005 | 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre] |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
8001 | 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre] |
8023 | My duties depend on my identity, which depends on my social relations [MacIntyre] |
8022 | I am naturally free if I am not tied to anyone by a contract [MacIntyre] |
8031 | Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre] |
8008 | The Bible is a story about God in which humans are incidental characters [MacIntyre] |