Page:Mind (New Series) Volume 8.djvu/267

 A. MEINONG, Ueber die Bedeutung des Weberschen Gesetzes. 253 Comparison of parts and measurement form the subject of the third section. The author recognises, what is so often overlooked, that numerical measurement proper depends upon divisibility, and is therefore inapplicable to quantities which are relations. He points out, nevertheless, that, where indivisible quantities have divisible correlates, all the practical advantages of measurement may often be obtained by means of these correlates. Measure- ment proper is either mediate or immediate : the latter is only applicable to space and time. But there is, for intensive quantities, a third kind of measurement, which the author calls substitutive (turrogativ), because what is really measured is an extensive sub- stitute. For example, distance, being a relation, is indivisible ; but it is always associated with a length, which is divisible. Distances, therefore, are regarded as measured by means of the correlated lengths. Similarly velocities are regarded as measured by means of the lengths traversed in a given time. In such cases, though another quantity is really measured in place of the quantity in question, we regard the latter as measured, because the operation ensures one or more of the three advantages derived from measure- ment proper. These advantages are : (1) That an element of a continuum is replaced by a discrete term, namely a number, and the intractability of the continuum is relegated to the unit ; (2) that the number thus obtained has the same relation of magnitude to other numbers as the correlated quantities have ; (3) that the absolute limits, zero and infinity, which have validity for indivisible as well as for divisible quantities, are the same for the numbers and for the corresponding quantities. All these advantages are secured in measuring distances and velocities ; the first only is secured in measuring temperature by the thermometer. This last case illustrates that measurement is not sharply separated from mere determination without measurement. This excellent discussion of the sense in which indivisible quanti- ties can be measured is applied, in the fourth section, to the measurement of the dissimilarity between quantities of the same kind. Dissimilarity is a relation, and therefore indivisible. In the case of two quantities of the same kind, their dissimilarity appears to be also a quantity. 1 With space and time, the distance is associated with an intervening length ; but in some cases where dissimilarity is a quantity there is, according to Herr Meinong, no intervening length. By an intervening length he means, apparently, no more than the power of continuous variation from the one term to the other. As an instance where this is not possible, he gives the dissimilarity of a colour and a tone. This, however, is not properly a quantity, but a difference of content. In all cases where dissimilarity is a quantity, there must be, I think, an inter- 1 ' Dissimilarity " is not quite an adequate translation of Verschieden- heit, but the word " difference " is required in the mathematical sense, and 'it is necessary to preserve the distinction by using different words for the two ideas.