QUANTITATIVE ESTIMATES OF SENSORY EVENTS 333 



and objective, under which they are constructed. It must, I think, be 

 admitted that the subjectivity of a scale of this sort damns it from a practical 

 point of view. But the subjectivity is a necessary consequence of the ille- 

 gitimate demand that there must be a sensation scale in sensation units as 

 well as a physical scale in physical units before sensation can be related to 

 physical stimuli by way of measurement. The fact is that the demand, 

 and indeed the greater part of Mr. Guild's argument relevant to the demand, 

 implies a metaphysical theory even when it is not explicitly metaphysical. 



We can only free ourselves from the incubus of this metaphysic by an 

 entirely new start. First with regard to the evolution of measurement. 

 The concepts of number and of magnitude are the two fundamental, and in 

 part independent, notions from which measurement springs. Measurement 

 necessarily involves comparison. Nothing is measured in terms of itself, 

 except in the case of mere enumeration, and even that is not measurement, 

 where there is not some comparison explicit or implicit. It is true that we 

 can make the statement that there are twenty individuals in a group, when 

 the number 20 may be taken as a measurement of the group in terms of the 

 individual, but the notion of measurement in any such case only arises 

 when the comparison of one group with another is in question, which means 

 that ' greater,' ' less,' and ' equal ' are the basal ideas in all measurement. 

 The questions ' how much greater ? ' or ' how much less ? ' are raised later. 

 The first answers to these questions are given in terms of the other, ' twice 

 as large,' ' half as large,' and so on — and the principle at once emerges that 

 everything is measured not in terms of itself, but in terms of something else. 

 The next step in the evolution of measurement is the measurement by 

 means of standards which may be applied to the various magnitudes to be 

 compared, and at this stage there is nothing incongruous in measuring 

 space in terms of time and time in terms of space. Actually, for practical 

 purposes all measurement is ultimately in terms of space. Our only means 

 of measuring time, in fact, would seem to be in terms of space. When 

 time units have been determined in this way, it becomes possible to measure 

 motion — both constant and variable — in terms of time and space. 



It would appear, therefore, that there is no difficulty whatever in finding 

 analogies to the measurement of sensation intensity in terms of stimulus 

 intensity without the necessity of measuring each in the first instance in 

 terms of its own units. There would rather seem to be difficulty in finding 

 analogies to the kind of measurement Mr. Guild contends for in the initial 

 measurement of any aspect of the phenomenal world. Moreover it would 

 also appear that if B is measurable in terms of A we only seek to devise a 

 scale in terms of B units provided we wish to use B to measure something 

 else. Measurement is not an end in itself. It is merely a means to the 

 more exact representation, and therefore clearer understanding of the 

 various connections and relations in the phenomenal world, which is of 

 course the world of our sense experience. The ' relation-structure ' which 

 Mr. Guild mistakes for the phenomenal world is a conceptual construct, 

 arrived at as a result of, and by way of, measurement of the objects and 

 events in the experienced world of sense. 



We may take it then that in order to relate quantitatively stimulus intensity 

 and sensation intensity, it is not necessary that we should be able to measure 

 each in units of the same kind, but merely to measure the one — the stimulus 

 intensity — and determine the manner in which the other — sensation 

 intensity — varies in dependence upon the former. That loudness is a 

 function of sound intensity does not admit of any doubt whatever, and a 

 similar statement can be made of brightness, sweetness, and so on, in 

 relation to their respective physical stimuli. The essential problem is the 



