The study of M. Mouret since it starts with relations combining them under the conditions of Solidarity Co-Existence, Abstraction and Relativity, (which are nothing else than other relations or compounds of relations,) does not seem to us to advance us at all in the most fundamental requisite. He says no more than to say that in order for the groups of relations to generate further definite relations the relations thus grouped together must be related to one another and then that most of these relations must be disregarded. M. Mouret distinguishes, with respect to a relation three factors, the _Matter_, or the relational elements grouped together, the _Form_, or the order in which the relational elements are arrayed, and the _Foundation_. As his study of the topic of relations is professedly for the purpose of enabling him the better to solve the nature of the relation of mathematical equality, his success may be estimated by reference to his conclusions in regard to that relation. These are as follows: “The relation of equality is formed of undetermined matter, it possesses a binary form, and has for a condition a relation of indiscernibility between the two elements.” Such conclusions appear to us to be impotent not to say erroneous. If two things obtain at all, they obtain as two and not one, in very virtue of being distinguished the one from the other. Except with regard to some more or less arbitrary distinctions, like the distinction between coincident points, all distinctions obtain only in virtue of some relation that can be nothing else than a point of _discernibility_. Numbers and other mathematical things are taken as not-different not because they are in truth indiscernible but because for the turn in hand their points of difference are irrelevant. Concerning the much mooted question of the proper field of logic as a science M. Mouret holds it to be the “science of relations and general concepts.” Although we hold that logic is particularly concerned with the lore that is more directly related to the phenomena of erroneous thinking and its correction, the view of M. Mouret is not unacceptable. “Reasoning consists in the observation that where certain relations subsist certain others are found,” as Mr. Peirce has remarked. VI. CONCERNING MEANINGS AND EXPLANATIONS.