Page:Mind (Old Series) Volume 9.djvu/309

 A. SIDGWICK'S FALLACIES. 297 of Fallacies here, we may conveniently stop short with the as- sumption of the fact of such indication. One characteristic consequence of such a scheme meets us at an early stage, in the arrangement of the familiar propositions. According to the common system the distinction into affirmative and negative is considered as at least as fundamental as that be- tween universal and particular, or even more fundamental. Those, however, who have worked at any of the recent systems of gene- ralised or symbolic Logic have mostly found that this relative importance assumes a very different aspect there. Not only does the distinction between universal and particular become more important, but (if we wish to give an adequate interpretation to propositions with highly complex subjects or predicates) we have to credit the particular proposition with the special and peculiar function of guaranteeing the existence of its subject and predi- cate. Mr. Sidgwick's treatment does not lead him quite so far from ordinary convention as this, but it leads him in the same direction. 1 For instance, when we take Indication as our leading principle, the difference between indicating presence and absence becomes of minor importance in itself and is more obviously de- pendent upon the grammatical significance of terms or the con- venience, in any given case, of proving a presence or an absence. That S is a mark of P and therefore the absence of P a mark of the absence of S ; or that the absence of P is a mark of the pre- sence of S and therefore the absence of S a mark of the presence of P, are statements which lead us in and out amongst ordinary affirmatives and negatives without much consciousness of any important change of character. Now contrast with the above a case of wow-indication. Sup- pose we say that S is not a mark of P ; what does this mean and how are we to contraposit it ? The reader unfamiliar with the matter will see his way best by looking at it in the guise of an ordinary proposition. That S is a mark of P implies that all S is P : that S is not a mark of P simply contradicts this, and therefore implies that some S is not P. The desired contraposi- tion therefore is not what a beginner might hastily suggest, viz., that P is not a mark of S, still less that P and S have nothing to do with one another. It is, that absence of P is not a mark of absence of S. This and the original propositions are strictly equivalent and convertible propositions. Indications, therefore, whether of presence or of absence, correspond to universal pro- positions. They are very different in character from non-indica- tions, which again, whether of presence or of absence, correspond to particular propositions. A chapter is devoted to this subject of Contraposition, or rather, 1 "With the exception, however, that, with him (p. 223) particular pro- positions come out as negative, "every 'particular' proposition, so far as it makes a tangible assertion at all, is negative in our sense ". 20