Page:Mind (New Series) Volume 12.djvu/505

THE DISJUNCTIVE JUDGMENT. 491 angles. But in this and all similar examples the disjunction proper, the relation asserted between the two predicate terms, is derived a priori, that is to say, it is deduced not from some principle peculiar to the science with which we are dealing, but from one of the KOLVO, a^u^^ara common to all thought, in fact, in this case disjunction the law of excluded middle. When we say that triangles are either right-angled or not we are simply giving an instance of the principium exclusi tertii, which could be equally well illustrated by the predication of any other attribute appropriate to the science in question and its contradictory. Now the hypotheticals into which it is claimed by the exclusi vist theory that a disjunction can be analysed are " If A (which is assumed to be X) is not b it is c " (categori- cally, " All uot-b l is c = b' ac ") together with its equi- valent, "If A is not c it is 6," together with the other geometrically converse non-inferable hypothetical, "If A is b it is not c" (categorically "No b is c = b e c"). The first hypothetical shows that the disjunction is exhaustive, the second that it is exclusive. But in the case we were discussing, that of a priori dis- junction, the alternatives are given as b and b'. So that our statement is analysable into the two jejune truths " All not- b is b' = b' a b' " and "No b is &' = No b is not-6 ". Obvi- ously if the terms of our disjunction are given as b and b', i.e., a positive concept and its corresponding nomen inde- finitum (which, though it be restricted in range, is still indefinite as containing a possible endless internal plurality), then our judgment is both exhaustive and exclusive. But such a judgment is of no importance in itself and finds no place in the science within which the subject of predication lies. It is an empty truth and we do not get real disjunction 1 1 hope my symbols may not be misunderstood. Strictly the cate- gorical judgments which should represent "A is either b or c " are "All A which is not b is c " and (on the exclusivist theory) " No A which is 6 is. c," or perhaps "All A (agreed to be X) which is not b is c" and the corresponding negative. But for brevity the reference to the v A or AX may be left out, as it is, so to speak, a common factor in all the judgments and does not enter specially into our further reasoning. That part of the content of thought through synthesis with which fresh de- terminations are added to the subject is represented by the concepts b and c. N.B. The symbols a and e refer nowhere to terms, but indicate the quantity and quality of the judgment as in Mr. Keynes's scheme. The .symbols S and P which in his scheme represent the terms are inadmis- sible here, as the alternatives b and c are generally viewed equally as subjects (S) when viewed as subjects, and equally as attributes (P) when viewed as attributes.