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
|