In the desire after immortality also, the influence of the principle of summation is manifest. Thus Helmholtz, (über die Entstehung des Planetensystems, lecture delivered at Heidelberg and Cologne, 1871), in seeking to offer a hopeful prospect to those who cherish this desire, says: “The individual (if that which we achieve can ennoble the lives of those who succeed us) may face fearlessly the thought that the thread of his own consciousness will one day be broken. But to the thought of a final annihilation of the race of living mortals, and with them, the fruits of the striving of all past generations, even men of minds so unfettered and great as Lessing and David Strauss could scarcely reconcile themselves.” When it is scientifically shown that the earth will one day be incapable of supporting living beings, then, he thinks, the need of immortality will irresistibly return, and we shall feel bound to cast about for something which will afford us the possibility of assuming it.
[67] (p. 34). Metaph. Δ 10.
[68] (p. 37). This is the standing doctrine of the great theologians, as e.g. Thomas Aquinas in his Summa Theologica. Only certain nominalists, like Robert Holcot, teach the complete arbitrariness of the divine commands. Cf. my essay on the Geschichte der kirchlichen Wissenschaften im Mittelalter, in Möhler’s Church History (published by Gams, 1867) vol. ii. 526 seq., respecting which, however, the reader is asked not to overlook the revision of the printer’s errors in the “errata,” p. 103 seq., at the end of that work.
[69] (p. 39). At a time when psychology was far less advanced and inquiries into the province of the calculation of probability had not brought sufficient clearness into the process of rational induction, it was possible even for a Hume to fall a victim to this gross confusion. Cf. his Enq. concern. Hum. Underst., chaps. v. and vi. More striking is it that James Mill and Herbert Spencer have still not advanced in the slightest degree beyond Hume; (Cf. Anal. of the Phen. of the Hum. Mind, vol. ii. chap. ix. and note 108), and that even the acute thinker, J. S. Mill, although Laplace’s Essai Philosophique sur les Probabilités lay at his disposal, never arrived at a clear distinction of the essential difference between these two forms of procedure. This hangs together with his failure to appreciate the purely analytic character of mathematics and the import of the deductive procedure in general. Indeed he has absolutely denied that the syllogism leads to new knowledge. Whoever bases the whole of mathematics upon induction cannot possibly justify mathematically the inductive procedure. It would be for him a circulus vitiosus. It is here beyond question that Jevon’s Logic takes a truer view.
Even in the case of Mill, it sometimes appears as if an inkling of the immense difference had begun to dawn upon him, as when, in a note to his Analysis of the Phenomena of the Human Mind (vol. i., chap. xi. p. 407), in criticizing his father’s theory, he says: “If belief is only an inseparable association, belief is a matter of habit and accident and not of reason. Assuredly an association, however close, between two ideas is not a sufficient ground (the italics are his own) of belief; it is not evidence that the corresponding facts are united in external nature. The theory seems to annihilate all distinction between the belief of the wise, which is regulated by evidence and conforms to the real successions and co-existences of the facts of the universe, and the belief of fools which is mechanically produced by any accidental association that suggests the idea of a succession or co-existence to the mind; a belief aptly characterized by the popular expression, believing a thing because they have taken it into their heads.” This is all excellent. But it is robbed of its most essential worth, when, in a later note (vol. i. p. 438. note 110) we hear J. S. Mill say: “It must be conceded to him (the author of the Analysis) that an association sufficiently strong to exclude all ideas that would exclude itself, produces a kind of mechanical belief, and that the processes by which the belief is corrected, or reduced to rational bounds, all consist in the growth of a counter-association tending to raise the idea of a disappointment of the first expectation, and as the one or the other prevails in the particular case, the belief or expectation exists or does not exist exactly as if the belief were the same thing with the association,” and so on.
There is much here that calls for criticism. When ideas are mentioned which mutually exclude one another it may well be asked what kind of ideas these are? According to another utterance of Mill’s (vol. i. p. 98 seq. note 30 and elsewhere), he knows “no case of absolute incompatibility of thought except between the thought of the presence of something and that of its absence.” But are even these incompatible? Mill himself teaches elsewhere the very opposite when he thinks that along with the idea of existence there is always given at the same time the idea of non-existence (p. 126, note 39; “we are only conscious,” he says, “of the presence of an object by comparison with its absence”). Apart, however, from all this, how strange is it that Mill here overlooks the fact that he abandons entirely the distinctive character of self-evidence, and retains only that blind and mechanical formation of judgment, which he rightly treats with contempt. The sceptic Hume stands in this respect far higher, since he at least sees that such an empirical (empiristisch) view of the process of induction does not satisfy the requirements of our reason. Sigwart’s criticism of Mill’s theory of Induction (Logic, vol. ii. p. 371) contains here much that is true, though in appealing to his postulates he has certainly not substituted anything truly satisfactory in the place of what is defective in Mill.
[70] (p. 40). Cf. Hume, Enquiry concerning Human Understanding, vol. ii. towards the end.