Objection inapplicable to the inductive Syllogism.—Nor does the objection apply again to the inductive syllogism, in which the conclusion is more comprehensive than the premiss. The objection applies, in fact, only to the deductive syllogism, and to that only in its synthetic form, and to that only as figured, and as presenting, in its major premiss, other than a singular proposition.
Major Premiss, whence derived.—But whence, it may still be asked, comes the general proposition which every deductive syllogism contains, whether analytic or synthetic, the proposition e. g., that all men are mortal? Whether this be stated before or after the conclusion is a mere matter of form; but what is our authority for stating such a proposition at all? How do we know that which is here affirmed?
I reply, it is a truth reached by previous induction. Every deduction implies previous induction. I observe the mortality of individuals, x, y, z. I find no exceptions. My observation extends to a great number of cases, insomuch that I am authorized to take those cases as fairly representing the whole class to which they belong. I conclude, therefore, that what I have observed of the many is true of the whole. So comes the general proposition, All men are mortal.
Authority for this Belief.—But what reason have I to believe that what is true of the many is true of the whole, and how do I know this? I reply, I do not know it by observation, nor by demonstration; my belief of it rests upon, and resolves itself into, that general law or constitution of the mind according to which I am led to expect, under like circumstances, like results, in other words, that nature acts uniformly. This is my warrant, and my only warrant, for the inference, that what I have observed in many cases is true in others that I have not observed.
A Difficulty suggested.—But in what manner, now, shall this mere belief of mine, for it is nothing more, come to take its place as a general proposition, as positive categorical affirmation in the syllogism whose major premiss reads, All men are mortal?
A law of the mind may be a sufficient explanation of my belief; but the science of syllogisms cannot take cognizance of laws of the mind, as such, and has nothing to do with beliefs, but is concerned only with the forms in which an argument shall be presented. Those forms must be conclusive. How shall I convert, then, my conjecture, my plausible belief, in the present case, into that general positive affirmation which alone will answer the demands of the syllogism?
The Process explained.—The process is this: The precise result of my observation stands thus—x, y, z, are mortal. But I know that x, y, z, are so numerous as fairly to represent the class to which they belong. On the strength of this position, the inductive syllogism takes its stand, and overlooking the fact that there are some cases which have not fallen under my observation, positively affirms what I only believe and presume to be true, and the argument then reads, x, y, z, are mortal. But x, y, z, are all men, therefore, all men are mortal.
The general proposition thus reached by induction becomes, in turn, the major premiss of the deductive syllogism, which concludes, from the mortality of all men, that of Socrates in particular.
Position of Mill.—An able and ingenious writer, Mr. Mill, in his treatise on logic, takes the ground that we have no need to embody the result of our observations in the form of a general proposition, from which again to descend to the particular conclusion, but that, dispensing with the general proposition altogether, and with the syllogism of every kind and form, we may, and virtually do, reason directly from one particular instance to another, as, e. g., x, y, z, are mortal; therefore, f, g, h, are so. "If from our experience of John, Thomas, etc., who were once living, but are now dead, we are entitled to conclude that all human beings are mortal, we might surely, without any logical inconsequence, have concluded at once, from those instances, that the Duke of Wellington is mortal. The mortality of John, Thomas, and company, is, after all, the whole evidence we have of the mortality of the Duke of Wellington. Not one iota is added to the proof by interpolating a general proposition." Our earliest inferences, he contends, are precisely of this sort. The child burning his fingers, reasons thus: "That fire burnt me, therefore this will." He does not generalize, "All fire burns; this is fire; therefore, this will burn." The only use of a general proposition, Mill contends, is simply to furnish collateral security for the correctness of our inference.