Ideas from 'Logicism in the 21st Century' by B Hale / C Wright [2007], by Theme Structure

[found in 'Oxf Handbk of Philosophy of Maths and Logic' (ed/tr Shapiro,Stewart) [OUP 2007,978-0-19-532592-8]].

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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Various strategies try to deal with the ontological commitments of second-order logic
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
Neo-logicism founds arithmetic on Hume's Principle along with second-order logic
6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / e. Caesar problem
The Julius Caesar problem asks for a criterion for the concept of a 'number'
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
18. Thought / D. Concepts / 6. Abstract Concepts / g. Abstracta by equivalence
One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines