460 w. WUNDT'S LOGIK, n. statement of the Cosmological Antinomies has been vitiated by his neglect to realise the distinction in question. The whole discussion is well worth study, but I confess to feeling the same doubts here, as in the mathematical region, as to the propriety of the distinction. If one may raise an objection in a few lines on such a subject, I should suggest that in Mathematics we are dealing mainly with our own constructions and that therefore such infinity as we admit must be of the kind commonly recognised in Mathematics, meaning thereby that we can conceive our adding or diminishing without limit to the magnitudes which we contemplate. But when, as in Physics, we are dealing with what is given to us rather than constructed by us, the infinity which we contemplate. must surely be of the absolute kind. An ' infinite line ' is a finite one which we are to increase without limit, but ' infinite space ' or an ' infinite universe ' is not our making at all, and we cannot thus treat them. 1 We now come to the Logic of the Moral Sciences. This com- mences with Psychology, against the ordinary traditional treatment of which Prof. Wundt has some forcible remarks : " a systematic self-observation as recommended by most psychologists is nothing but a source of self-deception ". We must, he considers, in order to eliminate as much as possible the perturbing influence of the observation itself, direct attention mainly to the accidental and unexpected phenomena ; w r hence the two following rules may be deduced : Depend as much as possible on memory rather than on simultaneous observation ; and let the introspection (or retro- spection) be directed especially to the most definite and voluntary mental acts. Under such conditions as these Psychophysics forms one of our most important helps. It is defined as proposing " to produce by physical modifications or stimuli (Einwirkungen) changes in the states of consciousness, from which conclusions may be drawn as to the origin, combinations, and duration of psychical processes ". More closely scrutinised it divides itself into the three following tasks : (1) the discovery of the relation between the elementary psychical phenomena and their physical 'and physiological accompaniments ; (2) the analysis of composite presentations in respect of their elements and laws of production ; (3) the investigation, in respect of quantity and quality, of the time-element of our presentations. The first of these subdivisions 1 As bearing on Prof. Wundt's use of the term ' transfinite ' in geometry, the following remarks may be quoted : " The point of intersection of two parallel lines has still a geometrical sense when we suppose the parallelism to be complete, and therefore the ^infinity of the distance to be an absolute one " (p. 375). I cannot follow this or comprehend the admission of ' transfiniteness ' into geometry. If we are to talk in any other than a ' limit ' sense of this point of intersection, ought we not to admit two such points, one in each direction, for we have no right then to say that positive and negative infinity are the same thing : and how does this differ from an assertion that two such straight lines enclose a space ?
