Logic, Inductive and Deductive

by William Minto

It is misleading to suggest, as Mill does, by defining cause as "the sum total of conditions"—a definition given to back up his conception of cause as phenomenal—that science uses the word cause in a different meaning from that of ordinary speech. It is quite true that "the cause, philosophically speaking, is the sum total of the conditions, positive and negative, taken together: the whole of the contingencies of every description, which being realised, the consequent invariably follows". But this does not imply any discrepancy between the scientific or philosophical meaning and the ordinary meaning. It is only another way of saying that the business of science or philosophy is to furnish a complete explanation of an event, an account of all its indispensable antecedents. The plain man would not refuse the name of cause to anything that science or philosophy could prove to be an indispensable antecedent, but his interest in explanation is more limited. It is confined to what he wants to know for the purpose he has in hand. Nor could the man of science consistently refuse the name of cause to what the plain man applies it to, if it really was something in consequence of which the event took place. Only his interest in explanation is different. The indispensable antecedents that he wants to know may not be the same. Science or philosophy applies itself to the satisfaction of a wider curiosity: it wants to know all the causes, the whole why, the sum total of conditions. To that end the various departments of science interest themselves in various species of conditions. But all understand the word cause in the ordinary sense.

We must not conclude from accidental differences in explanation or statement of cause, dependent on the purpose in view, that the word Cause is used in different senses. In answering a question as to the cause of anything, we limit ourselves to what we suppose our interrogator to be ignorant of and desirous of knowing. If asked why the bells are ringing, we mention a royal marriage, or a victory, or a church meeting, or a factory dinner hour, or whatever the occasion may be. We do not consider it necessary to mention that the bells are struck by a clapper. Our hearer understands this without our mentioning it. Nor do we consider it necessary to mention the acoustic condition, that the vibration of the bells is communicated to our ears through the air, or the physiological condition, that the vibrations in the drums of our ears are conveyed by a certain mechanism of bone and tissue to the nerves. Our hearer may not care to know this, though quite prepared to admit that these conditions are indispensable antecedents. Similarly, a physiographer, in stating the cause of the periodical inundation of the Nile, would consider it enough to mention the melting of snow on the mountains in the interior of Africa, without saying anything of such conditions as the laws of gravity or the laws of liquefaction by heat, though he knows that these conditions are also indispensable. Death is explained by the doctor when referred to a gunshot wound, or a poison, or a virulent disease. The Pathologist may inquire further, and the Moral Philosopher further still. But all inquiries into indispensable conditions are inquiries into cause. And all alike have to be on their guard against mistaking simple sequence for consequence.

To speak of the sum total of conditions, as the Cause in a distinctively scientific sense, is misleading in another direction. It rather encourages the idea that science investigates conditions in the lump, merely observing the visible relations between sets of antecedents and their consequents. Now this is the very thing that science must avoid in order to make progress. It analyses the antecedent situation, tries to separate the various coefficients, and finds out what they are capable of singly. It must recognise that some of the antecedents of which it is in search are not open to observation. It is these, indeed, for the most part that constitute the special subject-matter of the sciences in Molar as well as in Molecular Physics. For practical every-day purposes, it is chiefly the visible succession of phenomena that concerns us, and we are interested in the latent conditions only in as far as they provide safer ground for inference regarding such visible succession. But to reach the latent conditions is the main work of science.

It is, however, only through observation of what is open to the senses that science can reach the underlying conditions, and, therefore, to understand its methods we must consider generally what is open to observation in causal succession. What can be observed when phenomena follow one another as cause and effect, that is, when the one happens in consequence of the happening of the other? In Hume's theory, which Mill formally adopted with a modification,[³] there is nothing observable but the constancy or invariability of the connexion. When we say that Fire burns, there is nothing to be observed except that a certain sensation invariably follows upon close proximity to fire. But this holds good only if our observation is arbitrarily limited to the facts enounced in the expression. If this theory were sound, science would be confined to the observation of empirical laws. But that there is something wrong with it becomes apparent when we reflect that it has been ascertained beyond doubt that in many observed changes, and presumably in all, there is a transference of energy from one form to another. The paralogism really lies in the assumption from which Hume deduced his theory, namely, that every idea is a copy of some impression. As a matter of fact, we have ideas that are not copies of any one impression, but a binding together, colligation, or intellection of several impressions. Psychological analysis shows us that even when we say that things exist with certain qualities, we are expressing not single impressions or mental phenomena, but supposed causes and conditions of such, noumena in short, which connect our recollections of many separate impressions and expectations of more.

The Experimental Methods proceed on the assumption that there is other outward and visible evidence of causal connexion than invariability of sequence. In the leading Method it is assumed that when events may be observed to follow one another in a certain way, they are in causal sequence. If we can make sure that an antecedent change is the only change that has occurred in an antecedent situation, we have proof positive that any immediately subsequent change in the situation is a consequent, that the successive changes are in causal sequence. Thus when Pascal's barometer was carried to the top of Puy le Dome, and the mercury in it fell, the experimenters argued that the fall of the mercury was causally connected with the change of elevation, all the other circumstances remaining the same. This is the foundation of the so-called Method of Difference. To determine that the latent condition was a difference in the weight of the atmosphere, needed other observations, calculations and inferences; but if it could be shown that the elevation was the only antecedent changed in a single instance, causal connexion was established between this and the phenomenon of the fall of the barometer.

It is obvious that in coming to this conclusion we assume what cannot be demonstrated but must simply be taken as a working principle to be confirmed by its accordance with experience, that nothing comes into being without some change in the antecedent circumstances. This is the assumption known as the Law of Causation—ex nihilo nihil fit.

Again, certain observable facts are taken as evidence that there is no causal connexion. On the assumption that any antecedent in whose absence a phenomenon takes place is not causally connected with it, we set aside or eliminate various antecedents as fortuitous or non-causal. This negative principle, as we shall see, is the foundation of what Mill called the Method of Agreement.

Be it remarked, once for all, that before coming to a conclusion on the Positive Method or Method of Difference, we may often have to make many observations on the Negative Method. Thus Pascal's experimenters, before concluding that the change of altitude was the only influential change, tried the barometer in exposed positions and in sheltered, when the wind blew and when it was calm, in rain and in fog, in order to prove that these circumstances were indifferent. We must expound and illustrate the methods separately, but every method known to science may have in practice to be employed in arriving at a single conclusion.

[Footnote 1:] This is implied, as I have already remarked, in the word Experimental. An experiment is a proof or trial: of what? Of a theory, a conjecture.

[Footnote 2:] If we remember, as becomes apparent on exact psychological analysis, that things and their qualities are as much noumena and not, strictly speaking, phenomena as the attraction of gravity or the quaquaversus principle in liquid pressure, the prejudice against occultism is mitigated.