idea number gives full details.     |    back to list of philosophers     |     expand these ideas

Ideas of Harold Hodes, by Text

[American, fl. 1990, Professor at Cornell University.]

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