The Argument against Relation Instances in The Principles of Mathematics

Christine Richard (1)

1 LHSP - Laboratoire d'Histoire des Sciences et de Philosophie - Archives Henri Poincaré

Bertrand Russell's argument against relation instances in The Principles of Mathematics (chapter IV, § 55) is so well-known that it is a paradigmatic argument in analytical metaphysics. But because his argument is paradigmatic now, we don't pay attention to the reasoning framework in which Russell inserts it initially: “[The] argument for this thesis [that if relations are particularized, the same relation cannot hold between different set of relata] is extremely curt and is mixed with an analysis of unity constituting a relation complex, or what Russell called at this time a ‘proposition'.” And on account of this lack of attention, the aim of Russell's argument is not really understood. For instance J. Winslade claims that Russell wants to reject nominalism about universals . The purpose of the following paper is to argue against these interpretations which are unwarranted. The criticism of the relation instances is not only “mixed” with an analysis of the propositional unity, but is really part of Russell's analysis. This paper emphasizes that Russell doesn't argue against nominalism but against F. H. Bradley's idealism. In order to justify this interpretation, we should examine two issues. Why does Russell use an argument about relation instantiation in his analysis of the propositional unity? And why shouldn't relations be instantiated?

Mots clés: Bertrand Russell; proposition; instanciation; endless regress

Mots clés: régression à l'infini

Domaines: Philosophie; Histoire et perspectives sur les mathématiques [math.HO]; Logique [math.LO]

Christine Richard. The Argument against Relation Instances in The Principles of Mathematics. 2006. ⟨halshs-00089166⟩