But corresponding to every concept or notion is its negative or opposite concept or notion. As this negative depends necessarily upon certain _particular determinations_ of the same terms that bear the _particular determinations_ and which being singly indeterminate admit of the positive concept or notion, there necessarily must obtain two systems of singly indeterminate _particular determinations_ relative to but incompatible with one another, and so relative that the negation of one set entails the obtaining of the other set, or in other words either set being negated entails the obtaining of the other set. These facts constitute what M. Mouret calls the _principle_ of _incompatibility_ and involve his _Fourth_ condition of _Relativity_ stated by him as follows: “All the particular determinations of the extreme terms must not be compatible with the system and the negation of certain relations of the system must entail the negation of the relation which they make between the extreme terms.” V. REFLECTIONS ON M. MOURET’S THEORY. Now we cannot regard this as a successful attempt to explain the nature and characteristics of relations, or to unfold the involutions of relation-lore. We fully realise that if every concept or relation resolves into a group of relations we must in some form or other take what are relations in reality as data to begin with, but this does not prevent us from taking our datum terms for our turn of explanation as not requiring at present any recognition other than as relational elements. What is needful as a prime requisite on the very start of any research in relation-lore is to obtain a clear idea of what is meant by a relation. Meanings are primarily matters of mental status. We have to determine the relation that subsists between the mind and the object through the mediating interpretation of a word, and the mental affection lies nearest and logically comes first. It may very well be that the mental affection requires correction, but this cannot take place until its faults are observed, and these cannot become evident until the mental affection is itself duly understood. The disciples of that school of logic in which DeMorgan and Boole, both eminent mathematicians, hold so exalted a rank as discoverers, regard cognition as arising in consequence of brain functioning or _mental operation_ and study the results of this operation as yielding their import in dependence upon and only in dependence upon the proper operation in virtue of which they arise.