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.
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.
In ordinary algebra we have the disjunctive law that if ab = o, then either a = o or b= o.
It is not syllogism because it is based on the disjunctive, not on the hypothetical relation, and so extends horizontally where syllogism strikes vertically downward.
In indicating specifically, too, the case of conclusion from a copulative major premise with a disjunctive minor, Herbart seems to have suggested the cue for Sigwart's exposition of Bacon's method of exclusions.
It is, as it were, a schedule to be filled in, and is connected with the disjunctive judgment as a schematic setting forth of alternatives, not with the hypothetical, and ultimately the apodictic judgment with their suggestion that it is the real movement of thought that is subjected to analysis.
The Aristotelian formula is " merely the expression, formally expanded and complete, of the truth already embodied in disjunctive judgment, namely, that every S which is a specific form of M possesses as its predicate a particular:modification of each of the universal predicates of M to the exclusion of the rest."
Thus they amplified - the Aristotelian logic by the theory of the hypothetical and disjunctive syllogism, and added to the first figure of the categorical syllogism the five moods out of which the fourth figure was afterwards constructed.
The validity of such arguments depends upon the sense in which we understand the disjunctive proposition: we must assume that the alternatives are mutually exclusive.'
You and I are men, or hypothetical, or disjunctive, &c.
He was, however, the first whose analysis was sufficiently convincing to exorcise the tyranny of grammatical forms. The categorical and disjunctive judgment reduce to the hypothetical.
Whately defined it as "a conditional syllogism with two or more antecedents in the major and a disjunctive minor."