21 ideas
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
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] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
9969 | The empty set is the purest abstract object [Jubien] |
7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |