There may appear to be a contradiction here; and this view 415 tends to be confirmed when it is found that the two characteristics of inference referred to are by different schools of logicians used in such a way as between them to deprive the category of inference of any content whatsoever.
On the one hand, by laying stress on the characteristic of novelty, we may be led to doubt whether formal inference of any description can properly be so called. For in all such inference the conclusion is implicitly contained in the premisses, and in uttering the premisses we have virtually committed ourselves to the conclusion. How then can we be said to make any advance to what is really new?
On the other hand, by laying stress on the characteristic of necessity, we may be led to doubt whether any inductive inference can properly be so called. For in such inference the falsity of the conclusion is not demonstrably inconsistent with the truth of the premisses. We may hold that if the premisses are true the conclusion will be true. But can we hold that it must be true, unless we also hold that in affirming the premisses we have virtually affirmed the conclusion too? And then we are back on the other horn of the dilemma.
This is not the place at which to discuss the difficulty from the point of view of inductive logic. We must, however, attempt a solution from the point of view of formal logic.
378. The nature of the difference that there must be between premisses and conclusion in an inference.—In order to find a solution of the difficulty, so far as formal inference is concerned, we must pursue our analysis further. We have said that the conclusion must be different from the premiss or premisses. But we have not yet asked what must be the nature of the difference or wherein it must consist; and it is on the answer to this question that everything turns.
If we consider two sentences we shall find that they may differ from one another from three distinct standpoints, representing three degrees of difference.
(1) In the first place, two sentences may differ from one another from the verbal standpoint only; that is to say, though different in the words of which they are made up, they may have the same meaning, and what the one is intended to convey 416 to the mind may be precisely what the other is intended to convey. In this case, regarded as propositions and not as mere sentences, they cannot be said to be really different at all; for they do not represent different judgments.
This (to take an example from Jevons) applies to two such sentences as Victoria is the Queen of England, Victoria is England’s Queen. It applies also to a statement expressed in a given language and the same statement translated into a second language, assuming that an absolutely literal translation is possible.
It has indeed been maintained by some writers that a difference of expression necessarily involves some difference of thought. But this at any rate appears not to be the case where one single word is substituted for another completely coincident with it both in denotation and in connotation (as thought by the speaker). Where one complex term is substituted for another (for example, England’s Queen for Queen of England) there may no doubt be involved some change in the order of thought; but this does not necessitate any change of meaning in the thought considered as a whole. Again we ought perhaps not to say that the same proposition expressed in two different languages has absolutely the same mental equivalent, since a consciousness of the actual words of which a proposition consists may constitute part of its mental equivalent. But, as before, this makes no difference in the meaning that the proposition is intended to convey.
It should be added that when we have a judgment expressed in two different languages or in two different forms in the same language, there is (or may be) involved the further judgment that the two modes of expression are equivalent. A distinct issue is, however, here raised.[440]