Structural Relativity and Informal Rigour


Authors
Neil Barton
University of Konstanz
Abstract
Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that it is best captured by a logic intermediate between first- and second-order. We argue that the usual division of structures into particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures.
Keywords structuralism  set theory  second-order logic
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

Our Archive
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Managing Informal Mathematical Knowledge: Techniques From Informal Logic.Andrew Aberdein - 2006 - Lecture Notes in Artificial Intelligence 4108:208--221.
An Analysis of the Notion of Rigour in Proofs.Michele Friend & Andrea Pedeferri - 2011 - Logic and Philosophy of Science 9 (1):165-171.
Church's Thesis and the Ideal of Informal Rigour.Georg Kreisel - 1987 - Notre Dame Journal of Formal Logic 28 (4):499-519.
Making Sense of “Informal Logic”.Ralph H. Johnson - 2006 - Informal Logic 26 (3):231-258.
Informal Logic and Epistemology.R. H. Johnson - 2007 - Anthropology and Philosophy 8 (1/2):69-88.
Categoricity and Consistency in Second-Order Logic.Jouko Väänänen - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):20-27.
The Structural Metaphysics of Quantum Theory and General Relativity.Vincent Lam & Michael Esfeld - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (2):243-258.
How Philosophical is Informal Logic?John Woods - 2000 - Informal Logic 20 (2).

Analytics

Added to PP index
2020-03-08

Total views
64 ( #142,000 of 2,311,331 )

Recent downloads (6 months)
64 ( #10,195 of 2,311,331 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature