But suppose we were working by the ‘Method of Subscripts,’ and had to deal with a Pair of proposed Premisses, which happened to be a ‘Fallacy,’ how could we be certain that they would not yield any Conclusion?
Our best plan is, I think, to deal with Fallacies in the same was as we have already dealt with Syllogisms: that is, to take certain forms of Pairs of Propositions, and to work [pg082] them out, once for all, on the Triliteral Diagram, and ascertain that they yield no Conclusion; and then to record them, for future use, as Formulæ for Fallacies, just as we have already recorded our three Formulæ for Syllogisms.
Now, if we were to record the two Sets of Formulæ in the same shape, viz. by the Method of Subscripts, there would be considerable risk of confusing the two kinds. Hence, in order to keep them distinct, I propose to record the Formulæ for Fallacies in words, and to call them “Forms” instead of “Formulæ.”
Let us now proceed to find, by the Method of Diagrams, three “Forms of Fallacies,” which we will then put on record for future use. They are as follows:—
(1) Fallacy of Like Eliminands not asserted to exist.
(2) Fallacy of Unlike Eliminands with an Entity-Premiss.
(3) Fallacy of two Entity-Premisses.
These shall be discussed separately, and it will be seen that each fails to yield a Conclusion.
(1) Fallacy of Like Eliminands not asserted to exist.
It is evident that neither of the given Propositions can be an Entity, since that kind asserts the existence of both of its Terms (see [p. 20]). Hence they must both be Nullities.
Hence the given Pair may be represented by (xm0 † ym0), with or without x1, y1.
These, set out on Triliteral Diagrams, are