PERFORMANCE OF LOGICAL INFERENCE. 
517 
and j indicates inclusion in the predicate and exclusion from the subject of an equational 
proposition or identity, from which also results inconsistency. Inclusion in both terms 
is indicated by y, and exclusion from both {f, in which case the combination is consistent 
with the proposition. 
54. To the reader of the preceding paper it will be evident that mechanism is capable 
of replacing for the most part the action of thought required in the performance of 
logical deduction. Having once written down the conditions or premises of an argument 
in a clear and logical form, we have but to press a succession of keys in the order cor- 
responding to the terms, conjunctions, and other parts of the propositions, in order to 
effect a complete analysis of the argument. Mental agency is required only in inter- 
preting correctly the grammatical structure of the premises, and in gathering from the 
letters of the abecedarium the purport of the reply. The intermediate process of deduc- 
tion is effected in a material form. The parts of the machine embody the conditions of 
correct thinking ; the rods are just as numerous as the Law of Duality requires in order 
that every conceivable union of qualities may have its representative ; no rod breaks the 
Law of Contradiction by representing at the same time terms that are necessarily incon- 
sistent ; and it has been pointed out that the peculiar characters of logical symbols 
expressed in the Laws of Simplicity and Commutativeness are also observed in the action 
of the keys and levers. The machine is thus the embodiment of a true symbolic method 
or Calculus. The representative rods must be classified, selected, or rejected by the 
reading of a proposition in a manner exactly answering to that in which a reasoning 
mind should treat its ideas. At every step in the progress of a problem, therefore, the 
abecedarium necessarily indicates the proper condition of a mind exempt from mistake. 
55. I may add a few words to deprecate the notion that I attribute much practical 
utility to this mechanical device. I believe, indeed, that it may be used with much 
advantage in the logical class-room, for which purpose it is more convenient than the 
logical abacus which I have already employed in this manner. The logical machine 
may become a powerful means of instruction at some future time by presenting to a 
body of students a clear and visible analysis of logical problems of any degree of com- 
plexity, and rendering each step of its solution plain. Its employment, however, in this 
way must for the present be restricted, or almost entirely prevented, by the predominance 
of the ancient Aristotelian logic, and the almost puerile character of the current logical 
examples. 
56. The chief importance of the machine is of a purely theoretical kind. It demon- 
strates in a convincing manner the existence of an all-embracing system of Indirect 
Inference, the very existence of which was hardly suspected before the appearance of 
Boole’s logical works. I have often deplored the fact that though these works were 
published in the years 1847 and 1854, the current handbooks, and even the most exten- 
sive treatises on logic, have remained wholly unaffected thereby*. It would be possible 
* Professor Bain’s treatise on ‘ Logic,’ which has been published since this paper was written, is an exception. 
In the first Part, which treats of Deductive Logic, pp. 190-207, he gives a description and review of Boole’s 
