Page:Mind (New Series) Volume 8.djvu/114

100 CRITICAL NOTICES : be deduced from Logical ones ; the same is true of the rules of relation in every ' system ' or body of related facts or things of family and political relationships, of the parts of any organism or machine, even of the causal relation of succession in time. It is perhaps partly to this drastic separation from Logic of Mathematics, with its imposing system of inexhaustible co-exist- ences, that is due Mr. Eead's slighting treatment of Co-existence in comparison of Sequence (in which he follows Mill). Dr. Venn goes far towards recognising that Co-existence is of no less im- portance for Induction than Succession is ; and it is difficult to see how it could ever have been seriously doubted that uniformities of Succession ;nust presuppose uniformities of Co-existence. The principle of Identity, says Mr. Eead, " assumes that some- thing is, and that it may be represented by a term . . . further, it is assumed that of the same thing another term may be predi- cated again and again in the same sense". How a "principle" that is fairly expressed as A is A (or even If B is A, B is A which Mr. Eead prefers) can have any logical connexion with the as- sumption that " of the same thing another term may be predi- cated "it is not easy to see ; and indeed it is perhaps too much to expect that as long as a Law of Identity expressible as A is A is put forward as a fundamental Law of Thought of Thought which proceeds by judgments of the form S is P anything satisfactory should or could be said on the subject. After Lotze's determined effort and signal failure, the case may well seem hopeless. The following account of the two other " Laws of Thought," the Principles of Contradiction and Excluded Middle, is interest- ing but perhaps a little fanciful. They are, it is said, inseparable ; " implicit in all distinct experience, and may be regarded as indicat- ing the two aspects of Negation. The principle of Contradiction says : B is either A or not-A, as if not-A might be nothing at all ; this is abstract negation. But the principle of Excluded Middle says : Granting that B is not A, it is still something namely, not- A ; thus bringing us back to the concrete experience of a con- tinuum in which the absence of one thing implies the presence of something else. Symbolically : to deny that B is A is to affirm that B is not A, and this only differs by a hyphen from B is not-A. But if any one holds that the hyphen makes all the difference, I give it up." To sum up, it may be said that Mr. Eead does not perhaps undertake to carry us, in Formal Logic, much beyond current handbooks, nor in Induction much beyond Mill ; and granting this, he is somewhat better than his undertaking, and though careful not to innovate, he does his readers the service of putting them at a point of view from which the ultimate unity of Logic, and final elimination of contradictions between opposing views, seem natural as well as desirable. It is difficult without going into elaborate detail, to convey the impression of compactness, vigour, keenness, and unsparing pains which a perusal of the