25 ideas
1597 | Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales] |
10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
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)] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
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)] |
3013 | Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius] |
1494 | Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle] |
1713 | Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle] |
1742 | Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius] |