298 A. SIDGWICK'S FALLACIES. to use the term employed by Mr. Sidgwick, to " Counter-indica- tion ". As he remarks, contraposition is generally confined to categorical propositions, whereas a term is wanted which shall apply generally to all cases of indication including of course those which are put for convenience into the hypothetical form. The law is thus stated (p. 86), " All indication of by S (affirmed or denied) is expressible as indication of S by > (affirmed or de- nied), if, and only if, the quality of both S and 3> be changed" : by the ' quality ' being understood the positive or negative character of the indication, that is, the indication of presence or absence. Eelations of this kind are best expressible symbolically. Mr. Sidgwick employs for the purpose the symbols >> and +-). 1 Thus S ) 3> and non-5> ^ non-S, are a pair of such strictly equivalent counter-indications of an affirmative kind ; and S -H) S> and non-5> -f-) non-S, are a similar pair of a negative kind. The full tabular statement contains of course four of each kind. Mr. Sidgwick considers that the law of counter-indication is, however, never applicable directly, that is, never needed, in the case of concrete propositions. I should have thought that it might be equally applicable here. Take, for instance, the concrete and individual observation that my room at an inn has the bed in a certain corner ; on going into a room and not finding the bed there I at once infer that the room is not mine. So in other cases, though, as Mr. Sidgwick says, in many instances we do really insert an intermediate abstract proposition. The foregoing refers mainly to formal considerations. The latter part of the book is occupied with what may be called, by com- parison, somewhat more material topics. The author's scheme, amongst other things, induces him to devote more space to the question of the " Burden of Proof " than is allotted to it in any ordinary handbooks. When we start very definitely with a thesis and the proof of it, the inquiry how we are to regard an unproved thesis, whether this be the one originally assigned or the statement advanced in proof of it, becomes of greater relative importance. Mr. Sidgwick has some good remarks upon this topic, but comes to the conclusion, unavoidable in a formal treatise, that no definite rules can be laid down. In the Law Courts indeed, as he remarks, somewhat stringent rules have to be laid down, for the sake of saving time and excluding needless subtleties, but in a system of formal proof we can say little more 1 These symbols belong to a class which has been employed by a number of different writers to express 'indication' or 'implication'. They belong also to the sub-class of such symbols chosen expressly for the purpose of reminding us that such indications are not reciprocal or simply convertible. This they do by their one-sided aspect. (I see, however, that further on, p. 230, Mr. Sidgwick uses the symbol ( ) for relation generally, which of course is not reciprocal.)
