20 ideas
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] |
12797 | If plural variables have 'some values', then non-count variables have 'some value' [Laycock] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
12794 | Plurals are semantical but not ontological [Laycock] |
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] |
18253 | I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege] |
17694 | Some non-count nouns can be used for counting, as in 'several wines' or 'fewer cheeses' [Laycock] |
17695 | Some apparent non-count words can take plural forms, such as 'snows' or 'waters' [Laycock] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
18166 | The loss of my Rule V seems to make foundations for arithmetic impossible [Frege] |
12792 | The category of stuff does not suit reference [Laycock] |
12799 | Descriptions of stuff are neither singular aggregates nor plural collections [Laycock] |
12818 | We shouldn't think some water retains its identity when it is mixed with air [Laycock] |
18269 | Logical objects are extensions of concepts, or ranges of values of functions [Frege] |
12795 | Parts must be of the same very general type as the wholes [Laycock] |
17696 | 'Humility is a virtue' has an abstract noun, but 'water is a liquid' has a generic concrete noun [Laycock] |
12791 | It is said that proper reference is our intellectual link with the world [Laycock] |