18 ideas
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
19043 | Bivalence applies not just to sentences, but that general terms are true or false of each object [Quine] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
19042 | Terms learned by ostension tend to be vague, because that must be quick and unrefined [Quine] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |