  The theory of intentional objects, however, may derive support from the following, arguably counterintuitive, consequences of Frege’s and Russell’s views, respectively. Frege’s theory faces two problems. First (13a)-(15a) would appear to express truths. But on Frege’s view, they lack a truth-value, since they involve singular terms devoid of reference and, according to Frege, if part of a sentence lacks a reference, then the sentence itself fails to have a truth-value (see section 4).  Secondly, the inferences in (13)-(15) appear to be valid. But on Frege’s view, one cannot validly infer (13b) from (13a) if (13a) has no truth-value. Similarly for the other pair of sentences (14) and (15).  Russell’s view faces two analogous problems. First, as noted above, (13a)-(15a) appear to be true. But on Russell’s analysis, proper names such as “Zeus” in (13a) and “Sherlock Holmes” in (15a) are abbreviated definite descriptions and, given his analysis of definite descriptions, both (13a) and (15a) turn out to express false existentially quantified propositions (see section 5). Secondly, if (13a)-(15a) are indeed false, as Russell’s view would have it, then one cannot validly infer (13b)-(15b), respectively, from their corresponding premisses. For a recent novel account of the distinction between true and false thoughts about non-existent objects, cf. Crane (2013) and for further discussion of the general topic of existence, see the SEP entry on existence.