42 ideas
9786 | Philosophers working like teams of scientists is absurd, yet isolation is hard [Cartwright,R] |
9784 | A false proposition isn't truer because it is part of a coherent system [Cartwright,R] |
13941 | Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R] |
13942 | Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R] |
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] |
9783 | While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R] |
14961 | Clearly a pipe can survive being taken apart [Cartwright,R] |
14962 | Bodies don't becomes scattered by losing small or minor parts [Cartwright,R] |
13952 | Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R] |
13954 | The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R] |
13955 | Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R] |
13953 | An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R] |
13945 | A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
13950 | People don't assert the meaning of the words they utter [Cartwright,R] |
13948 | For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R] |
13944 | We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R] |
13947 | 'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R] |
13943 | We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R] |
13946 | To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R] |
13951 | Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R] |
536 | We should follow the law in public, and nature in private [Antiphon] |
1557 | To gain the greatest advantage only treat law as important when other people are present [Antiphon] |
540 | The way you spend your time will form your character [Antiphon] |
539 | Nothing is worse for mankind than anarchy [Antiphon] |