21 ideas
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
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] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
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] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |