Logic, Inductive and Deductive

by William Minto

(2) We have next to see whether there are any other rational expectations based on observed facts. We may lay down as a principle the following:—

If a conjunction or coincidence has constantly been repeated within our experience, we expect it to recur and believe that it has recurred outside our experience.

How far such expectations are rational, and with what degrees of confidence they should be entertained, are the questions for the Logic of Inference, but we may first note that we do as a matter of habit found expectations on repeated coincidence, and indeed guide our daily life in this way. If we meet a man repeatedly in the street at a certain hour, we go out expecting to meet him: it is a shock to our expectations, a surprise, when we do not. If we are walking along a road and find poles set up at regular intervals, we continue our walk expecting to find a pole coincident with the end of each interval.

What Mill calls the uniformities of Nature, the uniformities expressed in general propositions, are from the point of view of the observer, examples of repeated coincidence. Birth, growth, decay, death, are not isolated or variable coincidences with organised being: all are born, all grow, all decay, and all die. These uniformities constitute the order of Nature: the coincidences observed are not occasional, occurring once in a way or only now and then; they turn up again and again. Trees are among the uniformities on the varied face of Nature: certain relations between the soil and the plant, between trunk, branches, and leaves are common to them. For us who observe, each particular tree that comes under our observation is a repetition of the coincidence. And so with animals: in each we find certain tissues, certain organs, conjoined on an invariable plan.

Technically these uniformities have been divided into uniformities of Sequence and uniformities of Coexistence. Thus the repeated alternation of day and night is a uniformity of Sequence: the invariable conjunction of inertia with weight is a uniformity of Coexistence. But the distinction is really immaterial to Logic. What Logic is concerned with is the observation of the facts and the validity of any inference based on them: and in these respects it makes no difference whether the uniformity that we observe and found upon is one of Sequence or of Coexistence.

It was exclusively to such inferences, inferences from observed facts of repeated coincidence, that Mill confined himself in his theory of Induction, though not in his exposition of the methods. These are the inferences for which we must postulate what he calls the Uniformity of Nature. Every induction, he says, following Whately, may be thrown into the form of a Syllogism, in which the principle of the Uniformity of Nature is the Major Premiss, standing to the inference in the relation in which the Major Premiss of a Syllogism stands to the conclusion. If we express this abstractly denominated principle in propositional form, and take it in connexion with Mill's other saying that the course of Nature is not a uniformity but uniformities, we shall find, I think, that this postulated Major Premiss amounts to an assumption that the observed Uniformities of Nature continue. Mill's Inductive Syllogism thus made explicit would be something like this:—

All the observed uniformities of Nature continue.

That all men have died is an observed uniformity.

Therefore, it continues; i.e., all men will die and did die before the beginning of record.

There is no doubt that this is a perfectly sound postulate. Like all ultimate postulates it is indemonstrable; Mill's derivation of it from Experience did not amount to a demonstration. It is simply an assumption on which we act. If any man cares to deny it, there is no argument that we can turn against him. We can only convict him of practical inconsistency, by showing that he acts upon this assumption himself every minute of his waking day. If we do not believe in the continuance of observed uniformities, why do we turn our eyes to the window expecting to find it in its accustomed order of place? Why do we not look for it in another wall? Why do we dip our pens in ink, and expect the application of them to white paper to be followed by a black mark?