22 ideas
13655 | The Löwenheim-Skolem theorems show that whether all sets are constructible is indeterminate [Putnam, by Shapiro] |
9915 | V = L just says all sets are constructible [Putnam] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
9913 | The Löwenheim-Skolem Theorem is close to an antinomy in philosophy of language [Putnam] |
9914 | It is unfashionable, but most mathematical intuitions come from nature [Putnam] |
1630 | We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine] |
5747 | "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
7925 | There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine] |
13387 | Our conceptual scheme becomes more powerful when we posit abstract objects [Quine] |
8277 | I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine] |
1631 | You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine] |
1632 | Translation of our remote past or language could be as problematic as alien languages [Quine] |