Despite some obvious gaps and defects in execution I now want to regard the analysis of the mode of employment of elementary singular terms – those with which one can refer to perceptible objects – as concluded. In this lecture I shall merely summarize what follows from this analysis for the understanding of reference to objects, the explanation of the predicative form of sentence, and the elementary use of the word ‘true’. At the outset I predicted that, contrary to the traditional prejudice, the analysis of the mode of employment of expressions which ‘stand for’ objects would be essentially more complicated than the analysis of the mode of employment of predicates. The extent to which this is grounded in the facts of the case has meanwhile become apparent. The analysis of the mode of employment of these expressions is more complicated because the mode of employment is itself more complicated. It is so because the use of individual singular terms, in contrast to the use of elementary perceptual predicates, is not isolable. Therefore the individual expression cannot be explained by itself. Rather the use of any type of singular term refers (verweist) systematically to the use of singular terms of other types; and in part, as we have seen, this reference is even a reciprocal one.

These references (Verweisungen) are expressed in the replaceability of one expression by other expressions in the predicative sentences in which it is used. This replaceability can itself be asserted in an identity-statement. The replaceability of ‘a’ by ‘b’ expressed in the identity-statement ‘a = b’ however, does not fully bring out the phenomenon which I here call ‘reference’, because in an identity-statement neither of the two terms has a priority over the other, whereas in what I call reference it is always the one term that refers to the other; and this is not convertible except where the reference is a reciprocal one. We first encountered this phenomenon in connection with the question: ‘and which object is a?’ (Lecture 23).