1984 | Logicism and Ontological Commits. of Arithmetic |
p.124 | 10011 | Identity is a level one relation with a second-order definition |
p.139 | 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers |
p.149 | 10027 | Mathematics is higher-order modal logic |
p.131 | p.131 | 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' |
p.131 | p.131 | 10017 | Truth in a model is more tractable than the general notion of truth |
p.131 | p.131 | 10015 | Higher-order logic may be unintelligible, but it isn't set theory |
p.132 | p.132 | 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language |
p.142 | p.142 | 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level |
p.146 | p.146 | 10023 | Talk of mirror images is 'encoded fictions' about real facts |
p.148 | p.148 | 10026 | Arithmetic must allow for the possibility of only a finite total of objects |