QUANTITATIVE ESTIMATES OF SENSORY EVENTS 321 



It is needless to discuss other senses ; in general the varying conditions 

 of perception, coupled also with the variations which take place in our 

 sensory sensitivities, make it impossible to form an associative bond between 

 any perceptible extensive property and the ' thing ' which possesses it. 

 In all cases our perceptual criterion of sameness must involve only the 

 relation-shape of the perceived relation structure and not its relation-size. 



This much is obvious ; but the psycho-physicist is concerned with 

 establishing relations between our sensory criteria and the measurable 

 physical properties of the world, and we must enquire what sameness of 

 perceived relation structure implies with regard to the corresponding 

 physical relations established by processes of measurement. The arbitrary 

 criteria for associating phenomenal relations with numerial relations which, 

 as we have seen, are the basis of any metrical scale, establish a correlation 

 between phenomena and number of such a kind that whenever a given 

 numerical relation between measured magnitudes is repeated, the corre- 

 sponding phenomenal relation will also be repeated. It follows that if the 

 relation shape of the relation structure comprising the metrical relations is 

 repeated so also will the relation shape of the phenomenal relation structure, 

 and vice versa. Therefore, since the recognitive relation of sameness 

 involves only the relation shape of the phenomenal structure, the measur- 

 able property which is recognised must involve only the relation-shape of 

 the metrical structure, in other words the relative quantities of any measur- 

 able magnitudes associated with objects. When we observe a miscellaneous 

 collection of objects of the same type, those which appear to be characterised 

 by the same ratios of the measurable magnitudes will be instinctively classed 

 together in virtue of our perceptually unique relation of recognisability. 



Returning now to our experiment on ' mean-gradation ' we see that the 

 criterion is nothing more than the recognition of the sameness of the 

 relation structures consisting respectively of the bright objects A and B 

 and the bright objects B and G, and that owing to the way in which the 

 relation of sameness has come to acquire its unique importance (by asso- 

 ciation with appearances of ' same ' objects of constant physical properties 

 under varying conditions of perception) this perceptual criterion should 

 only be satisfied if the measured brightnesses of A and B and of B and C 

 are in the same ratio. Our example, and most of the discussion, has been 

 in terms of visible phenomena, but the conclusions are applicable to all 

 experiments of this kind. The grading of a series of stimuli in such 

 experiments should result in steps such that the ratio of each stimulus to 

 the next in order is constant. The measurement does not depend on 

 equality of any sensory magnitude describable either as difference in 

 sensation intensity, or as intensity difference regarded as a magnitude by 

 itself. The concept of sense distances, assumed to be equal for the steps 

 of such a series, is entirely illusory. Nothing is involved but the recog- 

 nition of a relation between the relations which relate the physical intensities 

 of adjacent pairs of stimuli, a relation which does not imply equality of any 

 magnitude, either objective or subjective, but owes its special significance 

 to association with the perceptible aspects of the various kinds of permanent 

 objects or things in terms of which we are accustomed to interpret our 

 experience. Our perceptions will always result in our assigning properties 

 to objective things, and, as we have seen, should result in our grading these 

 things, as far as extensions are concerned, in terms of relative magnitudes. 



Magnitudes observed on separate occasions will be graded by perception 

 in the same way as when observed simultaneously, because the only basis 

 of comparison in such cases is memory, and the same relation determines 

 the comparison as in simultaneous observation. The position we assign to 



M 



