35 ideas
| 9921 | 'True' is only occasionally useful, as in 'everything Fermat believed was true' [Burgess/Rosen] |
| 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] |
| 9924 | Modal logic gives an account of metalogical possibility, not metaphysical possibility [Burgess/Rosen] |
| 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] |
| 9933 | The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set [Burgess/Rosen] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 9928 | Mereology implies that acceptance of entities entails acceptance of conglomerates [Burgess/Rosen] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 9926 | A relation is either a set of sets of sets, or a set of sets [Burgess/Rosen] |
| 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] |
| 9932 | The paradoxes no longer seem crucial in critiques of set theory [Burgess/Rosen] |
| 9923 | We should talk about possible existence, rather than actual existence, of numbers [Burgess/Rosen] |
| 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] |
| 9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
| 9934 | Number words became nouns around the time of Plato [Burgess/Rosen] |
| 9918 | Abstract/concrete is a distinction of kind, not degree [Burgess/Rosen] |
| 9929 | Much of what science says about concrete entities is 'abstraction-laden' [Burgess/Rosen] |
| 9927 | Mathematics has ascended to higher and higher levels of abstraction [Burgess/Rosen] |
| 9930 | Abstraction is on a scale, of sets, to attributes, to type-formulas, to token-formulas [Burgess/Rosen] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 9922 | If space is really just a force-field, then it is a physical entity [Burgess/Rosen] |