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As stated here on Wikipedia: 1

Weber's law states that the-just-noticeable-difference (JND) of an intensity of a stimuli divided by the intensity of that stimuli is always constant.

Mathematically: $\Delta(I)/I=Constant$

... where $I$ here means the physical intensity of sound, light and so on. $\Delta(I)$ is the-just-noticeable-difference.

Then came Fechner and assumed that the-just-noticeable-difference "in sensation" of a stimuli is constant as well, hence: $\Delta(I)/I = Constant = \Delta(S)$

$\Delta(S)$ stands for the-just-noticeable-difference "in sensation."

On what basis was Fechner justified in assuming that the-just-noticeable-difference in sensation is constant?

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It was not an assumption; it was a decision. It allowed for better quantification, it gave an operational definition in increase in sensation, which allowed for more common ground in research between different labs. In a way, it's a definition by pure counting: when the subject feels a change in sensation, add one. Then this absolute scale is plotted against the ratio scale of increase in stimulation.

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  • $\begingroup$ If I got you correctly, Fechner associated Weber's fraction(the constant) with the difference in sensation for the sake of being able to talk about sensation in a rigorous manner? But this implies that sensation is to some degree subjective and arbitrary, so that you can not in an absolute sense say 'I hear this sound twice as intense as the other', can we? $\endgroup$
    – Omar Nagib
    Commented May 18, 2015 at 0:10
  • $\begingroup$ You can (I think), but this is not what Fechner did: he decided that a just noticeable difference in stimulation ('now that I've added another gram to the weight in this hand, I can feel that this is heavier than that') should be equal to a single unit on the scale of sensation. $\endgroup$
    – Ana
    Commented May 18, 2015 at 17:37

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