The philosophy of biology . struct a series of soundseach of which differs from that preceding it by anelemental increment of loudness. Now things that THE CONCEPTUAL WORLD 17 cannot be further decomposed are necessarily equalto each other ; if, for instance, the atoms representthe ultimate units into which we break up the mattercalled oxygen, then these atoms are all equal to eachother. Therefore the increments of loudness areequal to each other. If we plot these equal increments of loudness asthe dependent variable S in a graph, and the amplitudeof the vibrations of the atmosphere as the ind
The philosophy of biology . struct a series of soundseach of which differs from that preceding it by anelemental increment of loudness. Now things that THE CONCEPTUAL WORLD 17 cannot be further decomposed are necessarily equalto each other ; if, for instance, the atoms representthe ultimate units into which we break up the mattercalled oxygen, then these atoms are all equal to eachother. Therefore the increments of loudness areequal to each other. If we plot these equal increments of loudness asthe dependent variable S in a graph, and the amplitudeof the vibrations of the atmosphere as the independentvariable E, we can obtain the following curve If weinvestigate this weshall find that a cer-tain relation exists be-tween the values of the sensation andthe values of the stim-uli that correspond tothem ; a regular in-crease in the loudnessof the sensation cor-responds to a regularincrease in the log-arithms of the strength of the stimuli. Let S = thesensation, E the stimulus, and C and Q constants ;then 5 = C log ;. FIG. 3. so that we seem to establish a mathematical relationbetween the intensity of our sensations and theintensity of the stimuli that give rise to those sensations,but this relation depends on the assumption that whatwe call minimal perceptible differences of sensationare numerical differences that are equal to each other,and this is, of course, an assumption that cannotpossibly be proved. 18 THE PHILOSOPHY OF BIOLOGY Thus we decompose our stream of consciousnessinto a series of quantitatively different and qualitativelydifferent things, upon each of which we confer in-dependent existence. We attribute to these differentaspects of our consciousness extension, but the ex-tension is due only to our analysis ; for the qualitiesof pitch, loudness, colour, odour, etc., which we dis-entangle from each other, did not exist apart from eachother, any more than do the sine and cosine curvesinto which we decompose an arbitrarily drawn curvedline. The multiplicity o
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