32 ideas
12619 | We have no successful definitions, because they all use indefinable words [Fodor] |
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] |
12620 | If 'exist' is ambiguous in 'chairs and numbers exist', that mirrors the difference between chairs and numbers [Fodor] |
12613 | Empiricists use dispositions reductively, as 'possibility of sensation' or 'possibility of experimental result' [Fodor] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
12617 | Associationism can't explain how truth is preserved [Fodor] |
12615 | Mental representations are the old 'Ideas', but without images [Fodor] |
6650 | Fodor is now less keen on the innateness of concepts [Fodor, by Lowe] |
12618 | It is essential to the concept CAT that it be satisfied by cats [Fodor] |
12614 | I prefer psychological atomism - that concepts are independent of epistemic capacities [Fodor] |
12621 | Definable concepts have constituents, which are necessary, individuate them, and demonstrate possession [Fodor] |
12622 | Many concepts lack prototypes, and complex prototypes aren't built from simple ones [Fodor] |
12623 | The theory theory can't actually tell us what concepts are [Fodor] |
12616 | English has no semantic theory, just associations between sentences and thoughts [Fodor] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |