22 ideas
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [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] |
9809 | Mathematics inscribes being as such [Badiou] |
9811 | It is of the essence of being to appear [Badiou] |
9969 | The empty set is the purest abstract object [Jubien] |
13332 | Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K] |
13333 | The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K] |
13326 | A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K] |
13327 | A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K] |
13329 | An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K] |
13330 | An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K] |
13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |