On De Morgan's argument (Q1844200)

\textit{R. G. Wengert} has suggested [ibid. 15, 165--166 (1974; Zbl 0236.02008)] that the common formulation of the conclusion of the following traditional argument is defective: ``Every man is an animal; therefore, the head of a man is the head of an animal.'' While the normal formulation is \[ ``(x) ((\exists x)(Fx.Hyx)\supset (\exists x) (Gx.Hyx))", \] Wengert suggests it should be \[ ``(x) (y)(Fx.Hyx. \supset .Gx.Hyx)''. \] He also seems to contend that the latter interpretation better expresses De Morgan's intentions in emphasizing the argument. This paper questions whether De Morgan's symbolism could have expressed the proposed interpretation. The first part points out that De Morgan's view of generalizations with vacuous antecedents, which resembles Strawson's, would preclude either interpretation. The second and more important part claims that De Morgan's conservative analysis of relational inferences would not allow the cross-referencing between subject and predicate which is essential to Wengert's formulation; i.e., to state that the animal of which \(x\) is the head is the same as the man of which \(x\) is the head. However, De Morgan's later logic of relations might, with some ingenuity, contain such a means of expression.