326 REPORTS ON THE STATE OF SCIENCE, ETC. 



The data on sound, despite wide differences in the results obtained by 

 different experimenters using different experimental devices, definitely 

 tend to show that stimulus gradings by the j.n.d. and mean-gradation 

 methods are very similar and that in both cases the grading places stimuli 

 approximately in a geometrical progression over a large range of intensity, 

 the two results which we have predicted. 



The results depend solely on the unique recognitive significance of 

 sameness of relation-shape of apparent relation structures and provide no 

 information whatever about quantitative relations of sensation intensities. 

 All we are able to say about the correspondence which must exist between 

 psychological relation structures and the phenomenal relation structures to 

 which they are linked by association is that the psychological relation between 

 psychological relation structures in virtue of which we are aware that the 

 relation of sameness of relation-shape exists between phenomenal relation 

 structures must, like the phenomenal relation itself, be symmetrical and 

 transitive and so cannot involve absolute extensions of any psychological 

 magnitude : also, that sensation intensities must increase with increase of 

 stimulus intensity. But we cannot deduce the law of variation. The 

 association of sensation intensity and stimulus intensity may be of an elastic 

 kind, as in fact we know it to be from the phenomena of adaptation. 



Why do we assume that there must be a quantitative relation between 

 stimulus and sensation ? Quantitative relations only hold for relation 

 structures composed of measureable magnitudes. Our familiarity with the 

 multitudinous quantitative relations established by the methods of physics, 

 and by the cruder but equivalent methods we employ in estimating measur- 

 able magnitudes in everyday life, induces the feeling that every relation 

 between things for which the relations greater or less are significant must 

 be a quantitative relation expressible by its numerical equivalent. This 

 feeling has apparently led to the universal conviction that sensation intensity, 

 to which the terms greater or less are obviously relevant, has an inherent 

 association with number only awaiting discovery. It is assumed that 

 between two sensation intensities S-^ and S2 there is a ' true ' relation, 

 •S1/S2 = n, where n is some number, and that the problem we are up 

 against is to find some way of determining n in any given case, or of deducing 

 it indirectly from the result of some experiment which depends on it. As 

 I see it this is not the position. There is no relation S1/S2 = n until we 

 have defined 5 as a measurable magnitude by a practical criterion of equality 

 and a practical operation of addition. Unless this is done — and no one 

 argues that it can be done — there is no basis of association between members 

 of the class of sensation intensities and members of the class of numbers, 

 and no meaning in a numerical relation between sensation intensities. 

 Equality of these intensities presents no difficulty, but no operation analogous 

 to addition is possible. Every psychologist agrees that this is so ; but it is 

 not realised that without it we are not merely unable to discover quantitative 

 laws involving sensation intensity, but that there are not in fact any quanti- 

 tative laws to discover. 



The theory here advanced to explain the significance of the unique 

 relation which determines the grading of stimuli by the mean-gradation 

 rnethod as derived from associative experience, is put forward solely on 

 the grounds that when one is endeavouring to destroy the foundations of 

 any firmly rooted belief it is desirable, where possible, to lay the foundations 

 of a new one to take its place, and not to confine oneself to purely destructive 

 criticism. The mistake must not, however, be made of regarding the 

 alternative explanation as an integral part of the case against the old one. 

 Whether the explanation here given proves to be acceptable or not, the 



