On the notions of indiscernibility and indeterminacy in the light of the Galois–Grothendieck theory

Synthese 191 (18):4377-4408 (2014)
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We analyze the notions of indiscernibility and indeterminacy 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 Galois–Grothendieck duality between \(G\) -spaces and the minimal observable algebras that discern (or separate) their points. According to the natural epistemic interpretation of the original Galois theory, the possible \(K\) -indiscernibilities between the roots of a polynomial \(p(x)\in K[x]\) result from the limitations of the field \(K\) . We discuss the relation between this epistemic interpretation of the Galois–Grothendieck duality and Leibniz’s principle of the identity of indiscernibles. We then use the conceptual framework provided by Klein’s Erlangen program to propose an alternative ontologic interpretation of this duality. The Galoisian symmetries are now interpreted in terms of the automorphisms of the symmetric geometric figures that can be placed in a background Klein geometry. According to this interpretation, the Galois–Grothendieck duality encodes the compatibility condition between geometric figures endowed with groups of automorphisms and the ‘observables’ that can be consistently evaluated at such figures. In this conceptual framework, the Galoisian symmetries do not encode the epistemic indiscernibility between individuals, but rather the intrinsic indeterminacy in the pointwise localization of the figures with respect to the background Klein geometry



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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. New York: Oxford University Press.
Physics and Leibniz's principles.Simon Saunders - 2002 - In Katherine Brading & Elena Castellani (eds.), Symmetries in Physics: Philosophical Reflections. New York: Cambridge University Press. pp. 289--307.

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