more on this theme | more from this thinker
Full Idea
A model is created when a language is 'interpreted', by assigning non-logical terms to objects in a set, according to a 'true-in' relation, but we must bear in mind that this 'interpretation' does not associate anything like Fregean senses with terms.
Gist of Idea
When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense'
Source
Harold Hodes (Logicism and Ontological Commits. of Arithmetic [1984], p.131)
Book Ref
-: 'Journal of Philosophy' [-], p.131
A Reaction
This seems like a key point (also made by Hofweber) that formal accounts of numbers, as required by logic, will not give an adequate account of the semantics of number-terms in natural languages.
| 10011 | Identity is a level one relation with a second-order definition [Hodes] |
| 10027 | Mathematics is higher-order modal logic [Hodes] |
| 10021 | It is claimed that numbers are objects which essentially represent cardinality quantifiers [Hodes] |
| 10016 | When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes] |
| 10017 | Truth in a model is more tractable than the general notion of truth [Hodes] |
| 10015 | Higher-order logic may be unintelligible, but it isn't set theory [Hodes] |
| 10018 | Truth is quite different in interpreted set theory and in the skeleton of its language [Hodes] |
| 10022 | Numerical terms can't really stand for quantifiers, because that would make them first-level [Hodes] |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |