Russell, Bertrand Arthur William (1872–1970)

DOI: 10.4324/9780415249126-DD059-1
Version: v1,  Published online: 1998
Retrieved September 23, 2020, from

10. Theories of truth and judgment

The theory of incomplete symbols made possible Russell’s substitutional theory, in which class names and relations were treated as incomplete symbols. The appearance of a propositional paradox in the substitutional theory convinced Russell that propositions should also be treated as incomplete symbols. This was accomplished by his multiple relation theory of judgment which became part of the philosophical underpinnings of ramified type theory. In Russell’s early realism, true and false propositions alike were treated as subsistent complexes and belief as a relation between a mind and a proposition. This leaves it obscure why we prefer to believe true propositions. In the multiple relation theory, belief and other ‘propositional’ attitudes were treated as many-place (‘multiple’) relations between a mind and the individual constituents of the erstwhile proposition. Thus ‘m believes that aRb’ has the form ‘B(m, a, R, b)’, not ‘B(m, p)’. Apparent references to propositions are eliminated by subsuming their constituents within an actual psychological complex including a mind and related by some ‘propositional’ attitude. Propositions thus become fabrications of the mind. The belief represented by ‘B(m, a, R, b)’ will be a true belief just in case there is a complex a-R-b .

Russell had considered such a theory as early as 1906, but put it aside while he worked on the substitutional theory in which propositions were needed as entities. The theory was taken up again and developed in writings from 1910 to 1913. The final development of the theory, inTheory of Knowledge (1913), was left unpublished by Russell because of criticisms from Wittgenstein, then his student at Cambridge. Wittgenstein’s criticisms are perhaps most simply expressed as a dilemma. Either the constituents of a belief (a, R and b in the example above) are assigned to types or they are not. If they are not, then the ‘propositions’ fabricated by thought will not be subject to the ramified type hierarchy (it will be possible to judge nonsense, as Wittgenstein puts it) and the paradoxes will reappear. If they are, then they must be assigned to types by some prior judgment, to which the same considerations apply, and an infinite regress results (Sommerville 1981; Griffin 1985).

Citing this article:
Griffin, Nicholas. Theories of truth and judgment. Russell, Bertrand Arthur William (1872–1970), 1998, doi:10.4324/9780415249126-DD059-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2020 Routledge.

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