[440] This issue is, I think, involved in an argument used by Miss Jones (in an article in Mind, April, 1898) in support of the doctrine that we have inference whenever we pass from a given proposition to another that is verbally different from it; for example, from Victoria is Queen of England to Victoria is England’s Queen. The passage from one of these propositions to the other is, in Miss Jones’s view, not indeed a formal immediate inference, but a syllogism in which an understood premiss has to be supplied: thus, Victoria is Queen of England, The Queen of England is England’s Queen, therefore, Victoria is England’s Queen. It may, Miss Jones adds, seem futile or even puerile to set out at length what everybody or nearly everybody knows without telling; but there may be cases (e.g., the case of a child or of a foreigner learning the English language) in which a reasoning of this kind has to be gone through.
It appears to me that there is here a failure to distinguish between two different points of view. We may no doubt draw an inference as to the equivalence of meaning of two terms or two expressions, where the whole argument is concerned with the meaning of terms or the force of expressions. Thus, to take (or, rather, adapt) another of Miss Jones’s examples, we may readily admit that there is inference if a German argues that because the word Valour is equivalent in meaning to the word Tapferkeit, and the word Bravery is also equivalent in meaning to the word Tapferkeit, therefore, the words Valour and Bravery are equivalent in meaning. Again, a child or a foreigner may arrive by a process of inference at the equivalence of such forms as Queen of England and England’s Queen. But in the syllogism given above the first premiss and the conclusion are statements of fact, while the second premiss is a statement as to modes of expression, its import being “The expression Queen of England is equivalent to the expression England’s Queen.” Hence there are more than three terms and we have not properly any syllogism at all. So far as there is inference in the case supposed, it will be something like the following,—“The form of words Queen of England is equivalent in meaning to the form of words England’s Queen,” therefore, “The judgment which is expressed in the form Victoria is Queen of England may also be expressed in the form Victoria is England’s Queen.” This is the inference, if any, that a foreigner studying the language would make; and it is very different from professing to pass from the judgment Victoria is Queen of England to the judgment Victoria is England’s Queen.
417 (2) In the second place, we may have a difference which goes beyond mere difference of expression, and constitutes a difference in subjective meaning, though there may still be no difference from the objective standpoint. In this case we have two distinct propositions, not merely two different sentences, and these propositions are the expressions of two different judgments.
This relation holds in my view between a proposition and its contrapositive; for example, between Euclid’s twelfth axiom, “If a straight line meet two straight lines so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines, being continually produced, shall at length meet on that side on which are the angles that are less than two right angles,” and the second part of the twenty-ninth proposition of his first book, “If a straight line fall on two parallel straight lines, it shall make the two 418 interior angles on the same side together equal to two right angles.” It cannot be said that in such a case as this we have any objective difference, any difference in the matter of fact asserted; but at the same time we hold that the two judgments to which expression is given are not to be regarded as identical quâ judgments.
To this distinction we shall return shortly from a more controversial point of view.
(3) In the third place, our sentences may differ not merely from the verbal and subjective standpoints, but also from the objective standpoint; they may affirm distinct matters of fact. As, for example, if one of them states that all potassium with which we have experimented takes fire when thrown on water, and the other that a piece of potassium with which we have not yet experimented will do the same.
Now in all three of these cases we have novelty, and the question to be decided is which of the three kinds of novelty is requisite in order that we may have inference. I hold the right answer to be that, for inference, subjective novelty is necessary and sufficient.
There is practically universal agreement that something more than mere difference of verbal expression is requisite for inference.[441]
[441] Miss Jones holds that verbal difference suffices; but this is only because she also holds, as we have seen, that we cannot have mere verbal difference, that is, difference of expression without difference of thought.
Objective novelty is certainly sufficient, but is it requisite? It is affirmed to be so by writers of the school of Mill. This may of course be a mere question of definition; that is to say, inference may be defined ab initio in such a way as to require that the conclusion reached shall express some objective fact not contained in the data on which it is based. The matter being thus decided by definition, it follows without controversy that contraposition, syllogism, and other formal inferences (so called) are not properly to be spoken of as inferences at all. But there a good deal more than a mere question of definition involved. Those who demand objective novelty appear to hold that without it we cannot have more than mere 419 verbal novelty. They overlook, or at any rate practically deny, the possibility of taking an intermediate course whereby we may have something more than verbal novelty, but something less than objective novelty.