Any argument which _deceives_ us, by seeming to prove what it does not really prove, may be called a '=Fallacy=' (derived from the Latin verb _fallo_ "I deceive"): but the particular kind, to be now discussed, consists of a Pair of Propositions, which are proposed as the Premisses of a Syllogism, but yield no Conclusion. When each of the proposed Premisses is a Proposition in _I_, or _E_, or _A_, (the only kinds with which we are now concerned,) the Fallacy may be detected by the 'Method of Diagrams,' by simply setting them out on a Triliteral Diagram, and observing that they yield no information which can be transferred to the Biliteral Diagram. 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 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_. pg082 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 (xm_{0} + ym_{0}), with or without x_{1}, y_{1}. These, set out on Triliteral Diagrams, are xm_{0} + ym_{0} x_{1}m_{0} + ym_{0} ·---------------· ·---------------· | | | | (I) | | ·---|---· | | ·---|---· | | |(O)|(O)| | | |(O)|(O)| | |---|---|---|---| |---|---|---|---| | |(O)| | | | |(O)| | | | ·---|---· | | ·---|---· | | | | | | | ·---------------· ·---------------·