Page:Mind (New Series) Volume 12.djvu/510

 496 G. E. T. BOSS : the disjunctive judgment as used in dilemma is exhaustive- only and not exclusive. Now it is in this form of argument, I submit, that disjunction is most commonly employed. No doubt the dilemma is very frequently dialectical (in the Aristotelian sense) for the reason that an exhaustive minor premiss of the type All not-5 is c is hard to substantiate even when b and not-6 fall within a limited genus x and are not logical contradictories which between them exhaust all reality like S and not-S. " All non-parallel straight lines meet " is an example of a proposition of the kind which is immediate and does not require proof. (It may be called axiomatic but yet it is not a priori in the sense of being drawn from a principle superior to the science of Geometry itself ; it is a peculiar immediate principle of that science.) But it is very difficult to deduce a judgment of this kind. Generally speaking it is impossible to be sure that we have exhaustively divided a genus unless the fundamentum divisionis itself contain distinctions which can be exhaustively enu- merated, e.g., we can divide hawks into long- and short- winged, or organ pipes into closed and open, when those two distinc- tions, while contradictory to each other, are both positive and exhaust the possibilities as to the relation between the end of the pipe and the outside air. Again, when the minor premiss of a dilemma is exhaustive either immediately or as a result of proof, then in those circumstances it is common for one or other of the limbs of the major premiss to be false or at least not to be a necessary truth. For example our man in the burning house says that if he does not jump he is sure to perish by burning, but this being a predication concerning a finite individual is con- tingent ; it can only be a statement of probability. Though the dilemma is thus chiefly employed in ' dialectic ' and many logicians almost omit to mention it on this account, still it is one of the chief arguments in which the disjunctive judgment is employed. Apart from this, the proper place of disjunction in science is in division, which is not proof, but practically a special /tefloSo? by itself. Any attempt to discover the properties of an object by Siaipeais involves a begging of the question at each step in the division. For example, if one begins by dividing all reality by dichotomy and at length arrives at a genus A opposed to not-A which again falls into divisions B and C, then if we independently know that the object of which we are treating