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 2007,9780195325928]].
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5. Theory of Logic / A. Overview of Logic / 7. SecondOrder Logic
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Various strategies try to deal with the ontological commitments of secondorder logic

6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / d. Hume's Principle
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Neologicism founds arithmetic on Hume's Principle along with secondorder logic

6. Mathematics / B. Foundations for Mathematics / 4. Definitions of Number / e. Caesar problem
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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
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Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neologicism
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Logicism might also be revived with a quantificational approach, or an abstractionfree approach

18. Thought / E. Abstraction / 7. Abstracta by Equivalence
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One firstorder abstraction principle is Frege's definition of 'direction' in terms of parallel lines
