1 Jan 2009

Bergson, Time and Free Will, Chapter 1, §44 "Fechner's Method of Minimum Differences"

by Corry Shores
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[The following is summary; my commentary is in brackets.]

Bergson, Time and Free Will

(Essai sur les données immédiates de la conscience)

Chapter I, "The Intensity of Psychic States"

Part XIV: "Psychophysics"

§44 "Fechner's Method of Minimum Differences"

Fechner's method placed our sensations into a continuum of intensity: there is a series of minimum differences in our sensation, even though the corresponding stimulus values needed to make these sensation-changes may not correspond in a one-to-one fashion [For more on Fechner's method, see this entry and the entries for §41; §42; and §43.] For, we can gradually and steadily increase the stimulus, but the rate of minimum sensations might vary disproportionately. This does not matter so much, because we at least have a homogeneous scale of intensity-increases that we may then correlate to the stimulus-increases, as irregular as those correspondences may be. (64b.c)

So because we have a homogeneous continuum of minimum differences in sensation, we can put aside the "shade" or quality of each difference. [For example, when we touch a piece of ice that is warming slowly, and when we touch something burning hot that is cooling slowly, we experience more than just quantitative changes. There is something qualitatively different about touching something frozen and touching something burning hot, which cannot be reduced to their differences in temperature gradient. But, Fechner's method allows us to put aside such qualitative differences, and speak about sensation itself quantitatively. We look merely at quantitative sensation-changes of a certain quality, regardless of the shades of qualitative difference we experience at those different quantities of the quality.] So because each minimal difference has the same value as the others, and because we are putting aside their subtle qualitative differences, each of these minima are thought to be identical to one another.

Now that we can regard sensation purely in terms of quantitative units, we may now consider the addition of these units. To get from one sensation to the next, we would add the initial sensation, "S", to the change in "S" needed to arrive at the final sensation. We call ΔS this change in S. Thus, we denote the value for the second sensation S + ΔS. So here we see that the second S can be determined by summing all the minimum differences that the changing value passed-through to arrive at the second S.

But, how do we determine that value of the first S? If it is a sensation, it will have a greater value than zero. But that means it can be considered as a change from zero to its value. Thus even the first S can be considered a sum of minimum differences.

We now have two steps remaining:

1) We need to establish the relation between differences ΔS and ΔE.

2) We need to substitute-in differentials so to determine the relation between just the variables S and E.

However, there are three possible objections to this procedure:

1) Mathematicians might object that we cannot substitute the differential relation dS / dE for the difference ΔS / ΔE.

2) The psychologist might wonder if the quantity ΔS itself varies at different given levels of sensation. [Say we set our beginning sensation value as x. Then we slowly and continuously decrease the stimulus so that we feel minimal sensation changes one-by-one. Say that to get to zero sensation, we felt ourselves go through 4 minimal changes. So we set x at 4. And we call the change from 3 to 4: "ΔS1." Now consider the possibility that we are less sensitive to changes in sensation at a higher level of sensation. This would mean that ΔS2 at the higher level is disproportional to ΔS1. So imagine that we increase from 4 until we feel twice the sensation as 4. The problem is that we might need to go through more than 4 ΔS1's to feel twice the sensation. We might pass through the 8th ΔS1 before reaching twice the sensation, because the closer we get to twice the sensation, the less sensitive we are to change. That is to say, as we get closer to twice the sensation, we might not be sensing very many ΔS2's. So someone might object that there is no homogeneous regularity across the continuum of sensation-changes; because, at some sensation level, ΔS might be half the value of ΔS at another sensation level. For, at that other level, we might perceive minimum changes at a proportionally lower ratio.]

3) Suppose we take for granted that a sensation is the sum of minimal sensations. The third possible objection is that this tells us nothing about any real given sensation. For, it merely tells us some self-evident arithmetical principle regarding any possible sensation regarded abstractly.

Bergson's responds that merely because ΔS is considered a quantity, and because S is regarded as a sum, we should still be able find the numerical relations between them using mathematical operations. (65c)

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Images from the pages summarized above, in the English Translation [click on the image for an enlargement]:

Images from the pages summarized above, in the original French [click on the image for an enlargement]:

Bergson, Henri. Time and Free Will: An Essay on the Immediate Data of Consciousness, Transl. F. L. Pogson, (New York: Dover Publications, Inc., 2001).

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French text from:

Bergson, Henri. Essai sur les données immédiates de la conscience. Originally published Paris: Les Presses universitaires de France, 1888.

Available online at:


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