3IO REPORTS ON THE STATE OF SCIENCE, ETC. 



but in the general case it is implicitly defined by the form postulated for 

 9(5) taken in conjunction with the criterion of addition. 



We see at once, without examining either of these criteria in detail, that 

 something must be wrong somewhere. The scale purports to measure an 

 A magnitude, yet its defining relations involve measurable quantities of 

 another magnitude — stimulus intensity. We have already seen that the 

 relations defining the scale of an A magnitude must be independent of any 

 quantitative relation (other than equality) for other magnitudes. Fechner's 

 principles do not lead to a scale of this kind for sensation, and so do not 

 measure sensation as an A magnitude. Nor do they measure it as a jB 

 magnitude. The only way to treat sensation as a jB magnitude is to define 

 5 by a postulated relation to /. We shall return to this later ; at present 

 we are only concerned to note that Fechner's principles do not do this. 

 They introduce criteria of equality and of addition of sensation magnitudes, 

 forming the basis of some association of sensation with "number independent 

 of the association established for stimulus magnitudes. 



The S obtained by Fechner's principles is therefore neither an A magni- 

 tude nor a B magnitude, but has some of the properties of both, which 

 means it has not the necessary and sufficient properties of either. Fechner's 

 principles do not therefore enable us to measure any magnitude. It may 

 be useful to examine in more detail why this is so. First consider the 

 criterion of equality as applied to some pair of A5s, say A5i and ASg. 

 A^i is the sensation increment associated with a j.n.d. at intensity 7i, 

 while AS 2 is the sensation increment associated with a j.n.d. at some other 

 intensity /g. These two statements taken together form the only specified 

 relation between AS'j and A52. The relation is not symmetrical : it 

 ceases to be true if A5i and AS2 are interchanged. It is therefore not a 

 relation of the kind necessary for providing the practical criterion of equality 

 in a system of measurement. This one consideration alone renders super- 

 fluous all the semi-metaphysical arguments which have centred round the 

 question whether or not equal, in the sense of equally noticeable, necessarily 

 means ' really ' equal. A symmetrical transitive relation is essential as a 

 practical criterion of equality in measurement. 



Further, the proposed criterion of equality, being defined in terms of 

 j.n.ds., has no meaning when applied to quantities of sensation other than 

 those associated with j.n.ds. Thus it is quite meaningless to say that 

 S = A^i + ASg + . . . A5n by Fechner's criterion of equality. We 

 cannot apply the same practical criterion to the comparison of 5 with 

 AS I + AiSa + • • • ASn as we use to establish the equality of the A^Ss. 

 Fechner's definition of equality, in addition to its failure to fulfil the require- 

 ments of symmetry also fails to fulfil the requirement of applicability 

 throughout the scale of magnitude. It is a gross logical error to use ' equal ' 

 in one sense for liminal magnitudes and in some quite different sense for 

 supraliminal magnitudes. In regard to sensation intensities we have the 

 ordinary intuitive criterion of equality which we employ whenever we judge 

 that of two stimuli neither is greater than the other. This is the only kind 

 of equality which has any meaning at all sensation intensities, and as we 

 must accept this criterion of equality for sensation intensities in the general 

 field of sensory experience we cannot admit a different one in some special 

 part of the field. We see therefore that Fechner's second principle, that we 

 may arbitrarily postulate equality (or any other relation which implies an 

 arbitrary definition of equality) for the ASs of a j.n.d. series is wrong. We 

 may not do this because there is already, in our psychological constitution, 

 a criterion of equality which we cannot ignore or modify. Fechner's 

 postulate is not therefore a postulate but an assumption that the A5s are 



