Note 8 — Chapter II

§ 15. Returning then to Locke's comparison between the certainty of this argument and that which proves the sum of the angles of a triangle to be equal to two right-angles, I should say that there is a virtual, though not a formal, fallacy in his presentation. For mathematical science being confessedly but of relative significance, any comparison between the degree of certainty attained by reasoning upon so transcendental a subject as the present, and that of mathematical demonstrations regarding relative truth, must be misleading. In the present instance, the whole strain of the argument comes upon the adequacy of the proposed test of truth, viz., our being able to conceive it if true. Now, will any one undertake to say that this test of truth is of equivalent value when it is applied to a triangle and when it is applied to the Deity. In the one case we are dealing with a geometrical figure of an exceedingly simple type, with which our experience is well acquainted, and presenting a very limited number of relations for us to contemplate. In the other case we are endeavouring to deal with the summum genus of all mystery, with reference to which experience is quite impossible, and which in its mention contains all the relations that are to us unknown and unknowable. Here, then, is the oversight. Because men find conceivability a valid test of truth in the affairs of everyday life—as it is easy to show à priori that it must be, if our experience has been formed under a given code of constant and general laws—therefore they conclude that it must be equally valid wherever it is applied; forgetting that its validity must perforce decrease in proportion to the distance at which the test is applied from the sphere of experience.[8]