On the notion of indiscernibility in the light of Galois-Grothendieck Theory

Abstract

We analyze the notion of indiscernibility in the light of the Galois theory of field extensions and the generalization to K-algebras proposed by Grothendieck. Grothendieck's reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a duality between G-spaces and the minimal observable algebras that separate theirs points. In order to address the Galoisian notion of indiscernibility, we propose what we call an epistemic reading of the Galois-Grothendieck theory. According to this viewpoint, the Galoisian notion of indiscernibility results from the limitations of the `resolving power' of the observable algebras used to discern the corresponding `coarse-grained' states. The resulting Galois-Grothendieck duality is rephrased in the form of what we call a Galois indiscernibility principle. According to this principle, there exists an inverse correlation between the coarsegrainedness of the states and the size of the minimal observable algebra that discern these states.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,100

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

Binary Relations and Permutation Groups.Hajnal Andréka & Ivo Düntsch - 1995 - Mathematical Logic Quarterly 41 (2):197-216.
An invitation to model-theoretic galois theory.Alice Medvedev & Ramin Takloo-Bighash - 2010 - Bulletin of Symbolic Logic 16 (2):261 - 269.
Motives for perfect PAC fields with pro-cyclic Galois group.Immanuel Halupczok - 2008 - Journal of Symbolic Logic 73 (3):1036-1050.
Differential Galois theory II.Anand Pillay - 1997 - Annals of Pure and Applied Logic 88 (2-3):181-191.
Fuzzy Galois Connections.Radim Bêlohlávek - 1999 - Mathematical Logic Quarterly 45 (4):497-504.
Relativized Grothendieck topoi.Nathanael Leedom Ackerman - 2010 - Annals of Pure and Applied Logic 161 (10):1299-1312.
Fuzzy Galois connections on fuzzy posets.Wei Yao & Ling-Xia Lu - 2009 - Mathematical Logic Quarterly 55 (1):105-112.

Analytics

Added to PP
2015-09-07

Downloads
33 (#485,976)

6 months
2 (#1,203,099)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton, N.J.: Princeton University Press. Edited by Olaf Helmer-Hirschberg & Frank Wilczek.
Identity in physics: a historical, philosophical, and formal analysis.Steven French & Decio Krause - 2006 - New York: Oxford University Press. Edited by Decio Krause.
Primitive thisness and primitive identity.Robert Merrihew Adams - 1979 - Journal of Philosophy 76 (1):5-26.
Primitive Thisness and Primitive Identity.Robert Merrihew Adams - 2004 - In Tim Crane & Katalin Farkas (eds.), Metaphysics: a guide and anthology. Oxford University Press UK.
Physics and Leibniz's principles.Simon Saunders - 2003 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. Cambridge University Press. pp. 289--307.

View all 11 references / Add more references