The Significance of Russell's Theory of Descriptions for His Theory of Propositions as Incomplete Symbols
Abstract
Russell's Theory of Descriptions maintains that denoting (or descriptive) phrases are incomplete symbols. This has been widely discussed in the literature.
The thesis which Russell introduced in 1910 that propositions (as declarative sentences) are incomplete symbols attracted, on the contrary, much less attention and remains shrouded in obscurity. There are at least two reasons for that, both of them coming from the fact that Russell's thesis about propositions was intimately tied to his controversial multiple-relation theory of judgment.
First, Russell did not offer a sufficiently detailed exposition of this incompleteness aspect of the multiple-relation theory. We have only his rather fragmentary remarks in the first vol. of Principia Mathematica and some other texts written between the years 1910-14, including the manuscript Theory of Knowledge.
Second, many scholars focused on trying to understand Wittgenstein's criticisms of the multiple-relation theory and endeavored to show that the theory failed to do justice to those criticisms. This focus is a distraction from Russell's thesis that propositions qua linguistic symbols are semantically incomplete.
Wittgenstein's criticisms (at least prima facie) have nothing to do with that thesis. I shall reconstruct Russell's thesis of the incompleteness of propositions and develop the idea suggested in Principia that whenever we engage in asserting truth or falsehood, the proposition be taken as a description of a fact and analyzed by the Theory of Descriptions.
I shall also criticize David Hyder's account of this theory in his The Mechanics of Meaning (2005), arguing that resulting existential formulas cannot be identified with which was originally asserted or judged, on pain of a vicious circle when Principia's theory of orders is adopted.