13 ideas
21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
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] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
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] |
17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |