2. What the phenomena are which cannot be comprehended therein. In general, it may be said that all those perceptions and assertions of the mind, which are instinctive, and which it involuntarily qualifies as universal and necessary, are not, and cannot be comprehended in Sir William Hamilton's scheme. To give an exhaustive presentation of all the _a priori_ laws of the mind, would be beyond the scope of the present undertaking, and would be unnecessary to its success. This will be secured by presenting a classification of them, and sufficient examples under each class. Moreover, to avoid a labor which would not be in place here, we shall attempt no new classification; but shall accept without question, as ample for our purpose, that set forth by one of our purest and every way best thinkers,--Rev. Mark Hopkins, D. D., President of Williams College, Mass. "The ideas and beliefs which come to us thus, may be divided into, first, mathematical ideas and axioms. These are at the foundation of the abstract sciences, having for their subject, quantity. In the second division are those which pertain to mere being and its relations. Upon these rest all sciences pertaining to actual being and its relations. The third division comprises those which pertain to beauty. These are at the foundation of aesthetical science. In the fourth division are those which pertain to morals and religion. Of these the pervading element is the sense of obligation or duty. Of this the idea necessarily arises in connection with the choice by a rational being of a supreme end, and with the performance of actions supposed to bear upon that."--_Moral Science_, p. 161. First.--Mathematical ideas and axioms. Take, for instance, the multiplication table. Can any one, except a Limitist, be induced to believe that it was originally _constructed_; that a will put it together, and might take it apart? Seven times seven now make forty-nine. Will any one say that it might have been made to make forty-seven; or that at some future time such may be the case? Or again, take the axiom "Things which are equal to the same thing are equal to one another." Will some one say, that the intellectual beings in the universe might, with equal propriety, have been so constructed as to affirm that, in some instances, things which are equal to the same thing are _unequal_ to one another? Or consider the properties of a triangle. Will our limitist teachers instruct us that these properties are a matter of indifference; that for aught we know, the triangle might have been made to have three right angles? Yet again. Examine the syllogism. Was its law constructed? All M is X; All Z is M; All Z is X.