Ideas from 'Logicism and Ontological Commits. of Arithmetic' by Harold Hodes [1984], by Theme Structure

[found in 'Journal of Philosophy' (ed/tr -) [- ,]].

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3. Truth / F. Semantic Truth / 2. Semantic Truth
Truth is quite different in interpreted set theory and in the skeleton of its language
Truth in a model is more tractable than the general notion of truth
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Higher-order logic may be unintelligible, but it isn't set theory
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
Identity is a level one relation with a second-order definition
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense'
6. Mathematics / A. Nature of Mathematics / 3. Numbers / a. Numbers
Mathematics is higher-order modal logic
6. Mathematics / A. Nature of Mathematics / 3. Numbers / q. Arithmetic
Arithmetic must allow for the possibility of only a finite total of objects
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
It is claimed that numbers are objects which essentially represent cardinality quantifiers
Numerical terms can't really stand for quantifiers, because that would make them first-level
7. Existence / D. Theories of Reality / 6. Fictionalism
Talk of mirror images is 'encoded fictions' about real facts