“That we have in our mind the idea of the infinite is certain.... Evidently it has been placed in our mind by God himself, since the finite could not give the idea of the infinite” (p. 91, 92). We undoubtedly have a notion of the infinite; but the author gratuitously assumes that this notion is an _idea_ placed in our minds from without, while the fact is that such a notion is not an _idea_, but a _concept_ of our mind, or a result of intellectual operation. Of course, the finite cannot give us the _idea_ of the infinite; but from the finite we can, and we do, form a _concept_ of the infinite. This is the true and common doctrine. We cannot undertake to give in this place a refutation of ontologism; we only remark that the ontologistic theory is so generally repudiated that it should not find a place in a text‐book for the use of schools. “A material being is one which is essentially extensive and inert” (p. 92). If so, how can the author consider as “more acceptable” the view of Leibnitz, that “a monad is essentially unextensive”? (p. 93). “Spiritual substance is quadruple—namely, God, the angels, the human soul, and the soul of the beasts” (p. 93). The soul of the beasts _spiritual_!—a nice doctrine indeed for the use of schools. Nor is this an oversight of the author; for we find that he endows beasts with _intellect_ also (p. 170). What shall we say, but that we live in an age of progress? “The properties of a being are those parts which constitute the being” (p. 93). We have already observed that the being is constituted by its principles, and not by its properties. “A being is true when it agrees with its own attributes” (p. 94). It would be more philosophical to say that a being is true when its constituent principles agree with one another. “A bad action or a sin is something merely negative” (p. 95). False. The physical action is positive, and its sinfulness is not a negation, but a _privation_, as theologians know. “We may define relation, in general, to be a property pertaining to a being when compared with another being” (p. 95). This is a wrong definition. Relation can hardly be called a property. Distance and time are relations; yet no one would dream of calling them _properties_. “Identity is the perseverance of a being in the same state” (p. 96). The author should have said “in the same entity”; for a mere change of state does not destroy identity. “Space is virtually (_potentia_) infinite, using the word infinite, as we have before explained, in the sense of indefinite. It is also immense and infinitely divisible” (p. 97). The author might have considered that immensity is infinity; and therefore, if space is immense, it is infinite, and not indefinite. “Time is the duration of a being, or the permanence of its existence” (p. 97). Without successivity there is no time; and therefore the definition of time given by the author is essentially defective.