nature of his mode of deducing them. Conclusions which he could obtain only by pages of intricate calculation, are exhibited by the machine after one or two minutes of manipulation. And not only are those conclusions easily reached, but they are demonstratively true, because every step of the process involves nothing more obscure than the three fundamental Laws of Thought.
The Order of Premises.
Before quitting the subject of deductive reasoning, I may remark that the order in which the premises of an argument are placed is a matter of logical indifference. Much discussion has taken place at various times concerning the arrangement of the premises of a syllogism; and it has been generally held, in accordance with the opinion of Aristotle, that the so-called major premise, containing the major term, or the predicate of the conclusion, should stand first. This distinction however falls to the ground in our system, since the proposition is reduced to an identical form, in which there is no distinction of subject and predicate. In a strictly logical point of view the order of statement is wholly devoid of significance. The premises are simultaneously coexistent, and are not related to each other according to the properties of space and time. Just as the qualities of the same object are neither before nor after each other in nature (p. 33), and are only thought of in some one order owing to the limited capacity of mind, so the premises of an argument are neither before nor after each other, and are only thought of in succession because the mind cannot grasp many ideas at once. The combinations of the logical alphabet are exactly the same in whatever order the premises be treated on the logical slate or machine. Some difference may doubtless exist as regards convenience to human memory. The mind may take in the results of an argument more easily in one mode of statement than another, although there is no real difference in the logical results. But in this point of view I think that Aristotle and the old logicians were clearly wrong. It is more easy to gather the conclusion that “all A’s are C’s” from “all A’s are B’s and all B’s are C’s,” than from the same propositions in inverted order, “all B’s are C’s and all A’s are B’s.”
The Equivalence of Propositions .
One great advantage which arises from the study of this Indirect Method of Inference consists in the clear notion which we gain of the Equivalence of Propositions. The older logicians showed how from certain simple premises we might draw an