19 ideas
10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
10011 | Identity is a level one relation with a second-order definition [Hodes] |
10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
10027 | Mathematics is higher-order modal logic [Hodes] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
9969 | The empty set is the purest abstract object [Jubien] |
4577 | There is no necessity higher than natural necessity, and that is just regularity [Quine] |