Sec. 37. To begin then. In the last resort, the value of every probability is fixed by "ratiocination." In endeavouring, therefore, to fix the degree of strictly formal probability that is present in any given case, our method of procedure should be, first to ascertain the ultimate ratios on which the probability depends, and then to estimate the comparative value of these ratios. Now I think there can be no doubt that the value of any probability in this its last analysis is determined by the number, the importance, and the definiteness of the relations known, as compared with those of the relations unknown; and, consequently, that in all cases where the sum of the unknown relations is larger, or more important, or more indefinite than is the sum of the known relations, it is an essential principle that the value of the probability decreases in exact proportion to the decrease in the similarity between the two sets of relations, whether this decrease consists in the number, in the importance, or in the definiteness of the relations involved. This rule or canon is self-evident as soon as pointed out, and has been formulated by Professor Bain in his "Logic" when treating of Analogy, but not with sufficient precision; for, while recognising the elements of number and importance, he has overlooked that of definiteness. This element, however, is a very essential one--indeed the most essential of the three; for there are many analogical inferences in which either the character or the extent of the unknown relations is quite indefinite; and it is obvious that, whenever this is the case, the value of the analogy is proportionably diminished, and diminished in a much more material particular than it is when the diminution of value arises from a mere excess of the unknown relations over the known ones in respect of their number or of their importance. For it is evident that, in the latter case, however little value the analogy may possess, the exact degree of such value admits of being _determined_; while it is no less evident that, in the former case, we are precluded from estimating the value of the analogy at all, and this just in proportion to the indefiniteness of the unknown relations. Sec. 38. Now the particular instance with which we are concerned is somewhat peculiar. Notwithstanding we have the entire sphere of human experience from which to argue, we are still unable to gauge the strictly logical probability of any argument whatsoever; for the unknown relations in this case are so wholly indefinite, both as to their character and extent, that any attempt to institute a definite comparison between them and the known relations is felt at once to be absurd. The question discussed, being the most ultimate of all possible questions, must eventually contain in itself all that is to man unknown and unknowable; the whole orbit of human knowledge is here insufficient to obtain a parallax whereby to institute the required measurements.