22 ideas
10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
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] |
10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
18946 | Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer] |
10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
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] |
10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
10063 | Formalism is a bulwark of logical positivism [Musgrave] |
10787 | Is being just referent of the verb 'to be'? [Marcus (Barcan)] |
10789 | Nominalists say predication is relations between individuals, or deny that it refers [Marcus (Barcan)] |
10796 | If objects are thoughts, aren't we back to psychologism? [Marcus (Barcan)] |
10797 | Substitutivity won't fix identity, because expressions may be substitutable, but not refer at all [Marcus (Barcan)] |
10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |