On Some Characteristics of Symbolic Logic
Christine Ladd Franklin · The American Journal of Psychology · 1889
It is now thirty-five years since the publication of Boole's Laws of Thought. It has frequently happened, of course, that a great advance in the work of extending scientific ways of thinking over regions which are still in the hands of the natural man has failed to meet with the recognition that it deserved, but, none the less, every fresh instance of a misfortune of this kind is a fresh subject for regret. The task which Boole accomplished was the complete solution of the problem:-given any number of statements, involving any number of terms, mixed up indiscriminately in the subjects and the predicates, to eliminate certain of those terms, that is, to see exactly what the statements amount to irrespective of them, and then to manipulate the remaining statements so that they shall read as a description of a certain other chosen term (or terms) standing by itself in a subject or a predicate. Ordinary syllogism consists of elimination in the simplest possible case; when we infer from kings are tyrants, and all tyrants are assassinated, that all kings are assassinated, what we do is to gather up all the information which is conveyed by both premises together, exclusive of that which concerns tyrants. It is plain that ordinary syllogism is of very little avail when there are several premises of such complexity as this, for instance :- Every a is one only of the two, x and y, unless it is z or w; in the former of which cases it is both x and y, and in the latter case neither of them.