Innovation and Certainty

An overview of how mathematics' traditional domains of 'number and figure' have been vigorously displaced since the nineteenth century.

Mark Wilson (Author)

9781108742290, Cambridge University Press

Paperback / softback, published 7 January 2021

75 pages
22.9 x 15.2 x 0.7 cm, 0.138 kg

'Each new addition fills an unwanted gap and Wilson's aim is to get philosophers to pay attention to the seemingly un-mathematical ways mathematicians plug up theoretical holes and the philosophical consequences these measures have.' Mark Zelcer, Metascience

Beginning in the nineteenth century, mathematics' traditional domains of 'number and figure' became vigorously displaced by altered settings in which former verities became discarded as no longer sacrosanct. And these innovative recastings appeared everywhere, not merely within the familiar realm of the non-Euclidean geometries. How can mathematics retain its traditional status as a repository of necessary truth in the light of these revisions? The purpose of this Element is to provide a sketch of this developmental history.

Preface
1. Suggestions from the Symbols
2. Innovation and Error
3. Logicist Reconstruction
4. Set Theoretic Ladders
5. If -Thenism
6. Exploratory Mathematics
7. Unsuspected Kinships and Disassociations
8. The Enlarging Architecture of Mathematical Reasoning.

Subject Areas: Applied mathematics [PBW], Mathematics [PB], Philosophy [HP]