40 ideas
| 23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
| 5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
| 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] |
| 22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
| 22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
| 22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
| 22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
| 5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
| 5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
| 5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
| 5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
| 5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
| 5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
| 5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
| 5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
| 5848 | All good things can be misused, except virtue [Aristotle] |
| 5853 | The best virtues are the most useful to others [Aristotle] |
| 5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
| 5859 | Rich people are mindlessly happy [Aristotle] |
| 5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
| 1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
| 5861 | People assume events cause what follows them [Aristotle] |