In his paper ‘On Denoting’ Bertrand Russell claims to provide a theory of ‘denoting’ which is capable of solving the problem of the ambiguity of objects involved when thinking about phrases which denote or which make truth claims about particular objects. These problems are summarised as being connected to an inherent ambiguity within the potential object of denotation. Russell writes that this ambiguity can be determined according to three possible interpretations. These possible interpretations are that; ‘(1) A phrase may be denoting, yet not denote anything…(2) A phrase may denote one definite object…(3) ‘A phrase may denote ambiguously.’ (Russell, 1905. 479)

He then claims to have developed a theory which is capable of removing any complications over this system of denoting and therefore of coping with the problem of substituvity as it applies in when thinking about the nature of denoting sentences. This paper understands that principle to be the thought that where two objects are absolutely indistinguishable from each other then they must share all of the same properties. The rest of this paper will summarise and then asses how this problem concerns Russell, how he attempts to solve and whether or not this solution can be seen as being satisfactory.

The central focus of Russell’s engagement with denoting and therefore with the problem of substitutivity in general is focused around the idea of objects which are potentially non-existent, but which can nonetheless feature in denoting phrases. The example which is most often used in his piece is ‘The King of France.’ This is phrase which may refer to an actual object, but as there is no current King of France and there hasn’t been one for over two hundred years, it clearly does not. In order to attempt to remove the possible ambiguity from such denoting phrases, Russell elaborates what he sees to be exactly at work within such phrases.

At the start of his paper he claims that; ‘The difficulties concerning denoting are…all the result of a wrong analysis of propositions whose verbal expressions contain denoting phrases.’ (Russell, 1905. 480) He then goes on to state, after giving a brief exposition on his way of rendering logical propositions a definition of so called theories of ‘meaning.’ These theories, he writes, are those which regard ‘any grammatically correct denoting phrase as standing for an object.’ (Russell, 1905. 182. Emphasis in the original.) This standing for an object means that even phrases which refer to a wholly fictional or, as in the case of the King of France, a presently non-existent object must be taken to have a referent nonetheless. This leads to potentially contradictory sentences in which one can describe ‘a round-sqaure’ and even if one wishes to assert that it is false, it must nonetheless have some existence attached to it in order to be able to make the statement at all. Russell claims that in order to solve this contradiction one must either ‘provide a denotation in cases in which it is absent, or abandon the view that denotation is what is concerned in propositions which contain denoting phrases.’ (Russell, 1905. 484) Russell claims that the latter position is the correct one and then moves to discuss such propositions from that perspective.

Russell proceeds to make claims about the nature of denoting sentences which may or may not refer to the same object. He states that such sentences can be understood as having possible ‘primary’ and ‘secondary’ instantiations. He writes that this distinction enables one to deal with the problems of non-existent objects and also with aspects of the principle of substitutivity. The principle substitutivity is dealt with in the example sentence: ‘George IV wished to know if Scott was the author of Waverly.’ According to Russell, this sentence can be split into two possible determinations. The primary determination would read; ‘One and only one man wrote Waverly, and George IV wished to know whether Scott was that man.’ (Russell, 1905. 489.) The secondary determination of the sentence would read; ‘George IV wished to know whether one and only man wrote Waverly and Scott was that man.’ (Russell, 1905. 489)

Russell then claims that a division between primary and secondary structures enables one to deal equally well with potentially fictional or imaginary objects. He uses the example of the sentence ‘the King of France is not bald’ and states that the determination ‘There is an entity which is now King of France and he is not bald’ is false, however that the sentence ‘It is false that there is an entity which is now King of France and is bald’ is true. The former sentence refers to primary construction, the latter to a secondary. As such, primary and secondary propositions are used to attempt to deal with both potentially non-existing objects and with the problem substitutivity. He goes onto to claim that it is therefore possible to assign truth content to phrases such to imaginary objects, as when they are understood in their secondary form they may be true, however when they are understood in the primary form i.e. as affirming definite existence to an imaginary object, they will always be false. This applies to both fictional characters such as Hamlet, mythological figures and also those who no longer exist.

In conclusion, the paper has described the way in which Russell attempts to deal with the principle of substitutivity in denoting sentences. It seems that this solution is a good one and deals with the problem effectively as Russell is able to show that problem itself is founded on a conception of denotation and meaning which need not necessarily be included in the ways in which such sentences are understood.