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

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

green numbers give full details    |     back to texts     |     expand these ideas

---

3. Truth / F. Semantic Truth / 2. Semantic Truth

10017

Truth in a model is more tractable than the general notion of truth

10018

Truth is quite different in interpreted set theory and in the skeleton of its language

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

10015

Higher-order logic may be unintelligible, but it isn't set theory

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

10011

Identity is a level one relation with a second-order definition

5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic

10016

When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense'

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers

10027

Mathematics is higher-order modal logic

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic

10026

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

10021

It is claimed that numbers are objects which essentially represent cardinality quantifiers

10022

Numerical terms can't really stand for quantifiers, because that would make them first-level

7. Existence / D. Theories of Reality / 7. Fictionalism

10023

Talk of mirror images is 'encoded fictions' about real facts