The two are complementary, and the reinstatement of the disjunctive judgment to the more honourable role in inference has been made by so notable a modern logician as Lotze.
Hence it does not follow, by disjunctive syllogism, that H1 is true.
It is perhaps not wholly fanciful to connect with this attitude the fact that Aristotle's pupils dealt with a surer hand than the master with the conclusions from premises of unlike modality, and that a formal advance of some significance attributable to Theophrastus and Eudemus is the doctrine of the hypothetical and disjunctive syllogisms.
Disjunctive " Syllogisms" are those in which one premise is a disjunctive proposition, the other a categorical proposition which states or denies one of the two alternatives set forth.
But even Sigwart's errors are outdone by Lotze, who not only reduces " Every NI is P " so " If S is M, S is P," but proceeds to reduce this hypothetical to the disjunctive, " If S is NI, S is P L or P 2 or 1 33, " and finds fault with the Aristotelian syllogism because it contents itself with inferring " S is P " without showing what P. Now there are occasions when we want to reason in this disjunctive manner, to consider whether S is I n or P 2 or P 3, and to conclude that " S is a particular P "; but ordinarily all we want to know is that " S is P "; e.g.
