The proper approach to the views of the author is through his doctrine of definition. Usually definition is regarded as finding its main motive and utility in the convenience of social converse. The meaning of any term is regarded as resting not in the choice of him who utters it, but in the suppositions of those who are addressed. It is true that a license is accorded to any one upon a sufficient occasion to give a special intent to some word, but only upon condition that that intent shall be made sufficiently express, in other words well understood by those addressed. Hence definition is usually taken to mean the recital or the precision of the meaning of a term by means of language naturally apt for that end. There is no good sense in pretending to effect either one of these ends by language that lacks natural ability on that behalf. Now Mr. Dixon holds, if we understand him, that conventional usage is of very subordinate consequence in this matter, that it pertains to the prerogative of an author to throw upon those whom he addresses the task of gathering his meanings as best they can; that even when he professes to explain his meanings he need not seek and employ any plain, direct speech, but may supply his instruction indirectly: may ask his audience to solve a problem, or to rightly guess what certain hints mean; may require them to extract the meaning in question out of a set of assertions that involve the same in a collateral way only. This he calls “implicit definition.” It is analogous, he tells us, to an unsolved equation or set of equations in algebra. So far as we are aware no one can claim priority of the author in respect to this expedient. He seems to regard it as of great importance, and proposes by its aid to overcome the difficulties that environ the fundamentals of geometry. We think that the author is led to put undue confidence in his implicit definition, by his peculiar views upon propositions. He holds that all propositions can, without loss or gain in the meanings as originally stated, be reduced to statements of strict identity. This done, propositions can, as he thinks, be operated upon after the fashion usual with equations. But we submit that between a logical proposition and an algebraic equation there is a difference that is in general irreducible. For example take this proposition, Every parent loves children. To alter this to, Every parent is identical with some [or every] person that loves children, as is, we think, the prescription of Mr. Dixon, will not serve; for by reading our identity in the reverse order we have: Some [or every] person that loves children is identical with every parent.