Abstract
When Russell set out to develop a logical atomism based on his multiple-relation theory of judgment and correspondence theory of truth, he began to doubt the primitivist view he once adopted from G. E.
Moore that truth is a simple and indefinable property of propositions. The primitivist theory of truth has not been understood properly and, as a consequence, Russell's transition from it to the correspondence theory has remained blurred.
The primitivist theory, as I shall show, is established by an argument from vicious circularity against any attempt, including the correspondence theory, to define truth. 'The treadmill argument', as it is called in the literature, was widely recognized as being set forth by Frege who also adhered to the primitivist view, but it was not properly discussed in connection to Moore and Russell. First, I shall provide a formal exposition of the argument drawing from the textual evidence from all three authors.
A sequential model of propositional knowledge is the most important premise of the argument. This model which I call 'the doctrine of judgment' will be defined, and I shall also define the associated notion of a robust property.
Second, I shall explain that in 1906 Russell proposed a refutation of the doctrine of judgment as a consequence of his adopting the correspondence theory, explaining in the paper titled 'On the nature of truth and falsehood' that the correspondence theory and the multiple-relation theory have 'the merit of distinguishing between the perception of a fact and the judgment which affirms the same fact.' Embracing the possibility of perception of a fact or, more generally, acquaintance with a fact, Russell eventually departed from the doctrine of judgment. It is the refutation of this doctrine that freed Russell from the commitment to the conclusion of the treadmill and thus allowed him to define truth and falsehood as a definable property of correspondence between a belief and a fact.