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]].

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

---

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

8784	Neo-logicism founds arithmetic on Hume's Principle along with second-order logic

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem

8787	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

8788	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

8783	Logicism might also be revived with a quantificational approach, or an abstraction-free approach

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

8786	One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines