[1] Jevons, loc. cit., esp. quot. from Herschel (p. 234).
The moment you begin accurate observation you get a negative with positive value, which is really the converse by negation of your positive observation, a1 is b1; b2 (which is just not-b1) is a2 (which is just not-a1). Thus the two may be represented as the same judgment in positive and negative forms, which confirm one another. “Yellow is a compound of red and green”—in Experiment, “if, and as far as you take away the red or the green you destroy the yellow.” That describes an experiment with the colour-box. I have inverted the order in the conversions in compliance with the rule of common Logic, that Predicate is wider than Subject; but in accurate matter it is a false rule, and very inconvenient. The common rule means that a man who is drowned is dead, but a man who is dead need not have been drowned; but of course if he has the signs of death by drowning then he has been drowned.
Classification and Generalisation
(g) Classification is a consequence of all systematic theory; it is not a separate method of science. It is merely the arrangement of positive contents negatively related. No doubt where we have a kind of family relations between individuals classification is more prominent, and in the theory of continuous matter or operation, where individualities are not remarkable—e.g. in geometry—it is less prominent. But both are always there—classification and theory. Classification which expresses no theory is worthless, except that intended for convenient reference, such as alphabetical classification.
Under classification I may say a word on generalisation. {160} The common idea of inference from many cases, because they are many, to all cases of the same kind, is quite without justification. The only genuine and fundamental law of generalisation is “Once true always true.” But this might fail to suffice for our practical purposes, because it might save its truth by abstraction. Let us take the example, “Water is made of oxygen and hydrogen.” If that is true once, it is always true in the same sense. If you find some fluid of a different composition which you are inclined to call water, then you must identify or distinguish the two, and this is a mere question of classification. Practically, however, we could not get on unless our knowledge had some degree of exhaustiveness, i.e. unless we knew roughly that most of what we take for water will have the alleged properties. But no Induction or analysis, however accurate, can assure us against confusion and error, viz. assure us that everything we take to be water will be made of oxygen and hydrogen, nor that water will always be found on the earth. I call this accurate analysis, which may be made in a single instance only, and is the only perfectly scientific generalisation, generalisation by mere determination. Its classification is hypothetical, i.e. in it the individuals are merely possible individuals.
But this passes into another kind of generalisation, which may be called generalisation by concrete system, as when we attach scientific analysis to some extensive individual reality, e.g. to the solar system or the race of man. Then our judgments have a place in the real world, and our classification is categorical classification. The generalisation in this case does not follow from the judgment being extended {161} over a great plurality of possible similar subjects, but from the subject to which it applies having as an organised totality a large place in the world; e.g. “The human race alone gives moral interest to the history of bur planet.” These judgments come by making explicit the reality which underlies such hypothetical judgments as “all men are capable of morality.” It means that we actually venture to assign a place in the universe to the system we are speaking of. Then, though it is an individual, and unique, its name has a meaning, and is not a mere proper name. The solar system is good instance. Judgments about it or parts of it are universal but not purely hypothetical, and as our knowledge of this kind increases it becomes even a little exhaustive.
Generalisation by mere likeness or analogy, on the other hand, is precarious. It is what popular theory has in its mind in speaking of Induction, viz. a conclusion from a truth to judgments concerning all similar cases, e.g. from “Water is made of Oxygen and Hydrogen” to “All liquids which we choose to take for water are made of Oxygen and Hydrogen.” No scientific method can possibly give us this result. In as far as it has value it depends upon our guessing rightly by analogy. It may be replied, “that the signs of recognition are set down in the law or truth.” Well, if they are certain, generalisation by mere determination is enough; if they are doubtful, no induction can warrant your judgment of them in particular cases. Practically, of course, we get them right pretty often, although wrong very often.
Hypothesis
(h) Hypothesis is merely supposition; it consists in suggesting a fact as if it were real, when it is the only way of {162} completing given facts into a consistent system. If the hypothesis is proved that is a demonstration. It has been said that “Facts are only familiar theories.” If a bell rings in the house, I say unhesitatingly, “Some one rang that bell.” Once in ten years it may be rung, not by a person, but by some mechanical accident, in which case the “some one” is a hypothesis, but one always treats it as a fact. The only proof of a hypothesis is its being the only one that will fit the facts, i.e. make our system of reality relatively self-consistent. We believe many things we can never verify by perception, e.g. the existence of the centre of the earth, or that you have an idea in your minds; and if we go to ultimate analysis, perception itself involves hypothesis, and a fortiori all experiment involves hypothesis. Every experimental interference with nature involves some supposition as to a possible connection which it is intended to confirm or disprove.
Deduction