teacher who is weary of the conflict between Science and Religion, between Knowledge and Faith, between the valuable Lessons of Materialism and the consoling belief in the spiritual world; any teacher who sincerely desires, not to make a cheap and noisy fame for himself, but to find Truth and Peace for the young souls committed to his care, might do well to devote a quiet vacation to the study of Gratry's Logique.
Our author begins by clearly recognizing that mathematics is not so much a department of human thought as the ground-plan of all sane thought; he treats mathematical Science, not as a special set of truths, but as a map of the country in which Truth is to be found. He of course entirely repudiates the profane notion that mathematical Logic can afford any proof or disproof of religious truths; but he shows that mathematical reasoning throws light on the nature of valid proof of every kind. The faculties by which the existence of God is revealed to us are hyper-intellectual; the processes by which we learn spiritual truth are extra-syllogistic; and it pleases a certain school of reasoners to deny their validity. Gratry shows that, but for the exercise of similar faculties and the use of similar processes, we could have discovered nothing of the Higher Mathematics. It pleases certain Agnostics to assert that "it is impossible to reason from the finite to the Infinite." The same objection was formerly made against the Integral Calculus, but the Integral Calculus is now an accepted fact; and any one who cares to learn can know exactly how to "integrate a finite expression to Infinity," and can make sure that his results are absolutely correct. No true mathematician depends on testimony for his
