The Structuralist Thesis Reconsidered


Authors
John Wigglesworth
University of Vienna
Georg Schiemer
University of Vienna
Abstract
Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this paper, we argue that the structuralist thesis, even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/bjps/axy004
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 47,122
Through your library

References found in this work BETA

On the Plurality of Worlds.William G. Lycan - 1988 - Journal of Philosophy 85 (1):42-47.
On the Plurality of Worlds.Allen Stairs - 1986 - Philosophy and Phenomenological Research 49 (2):333-352.
On The Plurality of Worlds.Graeme Forbes - 1986 - Philosophical Quarterly 38 (151):222-240.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
The Foundations of Arithmetic.Gottlob Frege - 1953 - Evanston: Ill., Northwestern University Press.

View all 34 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Structuralism with and Without Causation.Juha Saatsi - 2017 - Synthese 194 (7):2255-2271.
Three Views of Theoretical Knowledge.W. Demopoulos - 2011 - British Journal for the Philosophy of Science 62 (1):177-205.
Properties of Being in Heidegger’s Being and Time.Joshua Tepley - 2014 - International Journal of Philosophical Studies 22 (3):461-481.
Haecceities and Mathematical Structuralism.Christopher Menzel - 2018 - Philosophia Mathematica:84-111.
The Semantic Plights of the Ante-Rem Structuralist.Bahram Assadian - 2018 - Philosophical Studies 175 (12):1-20.
What Are Structural Properties?†.Johannes Korbmacher & Georg Schiemer - 2018 - Philosophia Mathematica 26 (3):295-323.
Realization and Causal Powers.Umut Baysan - 2014 - Dissertation, University of Glasgow
Invariants and Mathematical Structuralism.Georg Schiemer - 2014 - Philosophia Mathematica 22 (1):70-107.
Ontic Structural Realism.Kerry McKenzie - 2017 - Philosophy Compass 12 (4):e12399.
What a Structuralist Theory of Properties Could Not Be.Nora Berenstain - 2016 - In Anna Marmodoro & David Yates (ed.), The Metaphysics of Relations. OUP. Oxford University Press.
Looking Forward, Not Back: Supporting Structuralism in the Present.Kerry McKenzie - 2016 - Studies in History and Philosophy of Science Part A 59:87-95.
Tractarian Objects in a Structural Setting.Martin Schmidt - 2009 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 16 (3):328-343.

Analytics

Added to PP index
2018-01-31

Total views
21 ( #449,255 of 2,289,307 )

Recent downloads (6 months)
3 ( #408,430 of 2,289,307 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature