332 REPORTS ON THE STATE OF SCIENCE, ETC. 



While Mr. Guild professes to eschew metaphysics his whole description 

 of the phenomenal world as composed of ' relation structures,' and a large 

 part of his discussion of measurement is essentially metaphysical. It is 

 perhaps true that ' there is nothing inherently numerical in the structure 

 of the phenomenal world,' but it is true only because numeration is a con- 

 ceptual process involved in our cognition of the phenomenal world. It is 

 our knowledge of the phenomenal world that is really in question, not the 

 phenomenal world as such. At this point let me correct a piece of bad 

 psychology which crops up again and again in Mr. Guild's statement, 

 especially in its later parts. He says ' we are so familiar with the description 

 of phenomena in numerical terms that the association has become instinctive.' 

 It is not a matter of association at all, except in so far as particular number 

 names are associated with the number concepts — ' four ' for the Englishman, 

 ' quatre ' for the Frenchman, ' char ' for the Hindu. This associationism rims 

 riot all through the later parts of the statement, and in so far as it affects the 

 argument the psychologist rejects it in toto. The thinking of relations is 

 never explicable in terms of association. 



The exposition of the principles of measurement is based on the distinc- 

 tion drawn by Dr. Norman Campbell between A magnitudes and B magni- 

 tudes, and only A magnitudes — that is magnitudes which can be measured 

 by processes which do not imply the measurability of other magnitudes — 

 are, strictly speaking, measurable. This would appear to mean that, strictly 

 speaking, measurement reduces itself to enumeration, and that spatial 

 magnitudes, or even lines only, are measurable. This is virtually a reduc- 

 tion of measurement to pre-history conditions. The important considera- 

 tion from our present point of view is that it leads to the view that in order 

 to establish a quantitative relation between two entities both entities must 

 be measured each in terms of some unit appropriate to itself. Hence in 

 order that we may be able to establish a quantitative relation between the 

 intensity of the physical stimulus and the intensity of the sensation, we must 

 be able to measure not only the physical stimulus in physical units but the 

 sensation in sensation units. This is, I believe, an error, but it is an error 

 which has been made by many psychologists as well as Mr. Guild, and the 

 physicists for whom he speaks. 



The theoretical possibility of measuring sensation intensity as such 

 measurement was interpreted by Delboeuf , that is as distance on an imagi- 

 nary scale of sensation intensity, as, for example, a loudness scale, must be 

 admitted, even if we accept Mr. Guild's contention. Greys differ in degree 

 of brightness, sounds differ in degree of loudness. Theoretically at least 

 an individual can construct for himself a scale of brightness of greys, in 

 which each grey appears a definite and equal distance away from the next 

 grey on either side, and any new grey can be assigned its place on the scale. 

 As regards an analogous loudness scale the position is somewhat compli- 

 cated by the fact that loudnesses are not co-presentable in time, as the greys 

 are, for reasons depending on the nature of the phenomena themselves, 

 and here neither the scale itself nor measurement by means of the scale 

 will be so accurate. The scale is an imaged • scale as it were. But the 

 theoretical position is not thereby affected. In the case of the loudness 

 scale the specification of the various points on the scale including the zero 

 will necessarily be in physical terms : to this point and to what it involves 

 return will be made presently. What must be emphasised here is the 

 theoretical possibility of the construction of such scales. The practical 

 consideration upon which the most serious criticism of such scales can be 

 based is that in strictness they are scales for the one individual only who 

 constructs them, and for the time at which and the conditions, subjective 



