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examples of Cournot, Renan, and Sainte-Beuve on this point have not caught on. It is surprising that
even among logicians, demi-assertions do not count. I do not know why, particularly with syllogisms,
we always reason as if we were affirming or denying the premises with equal energy and without any
doubt whatsoever. Let us try to take into account, in major and minor premises, the various degrees of
intensity of affirmation and negation.
As a hypothesis I affirm, with an intensity equal to 5, that all bodies have weight, and, with an
intensity equal to 10, that air is a body. Is it not clear that the conclusion—air has weight—should be
affirmed with an intensity equal to 5 and not 10? I forcefully assert that no animal is insensitive. I
timidly add that I am inclined to believe the sponge insensitive. The conclusion must be that I am
inclined to believe that the sponge is not an animal. Experiments can be made on all sorts of
syllogisms, and it will always be found that the lesser of the two degrees of affirmation or negation
contained in the premises is the only one which subsists in the resulting proposition.
This simple observation enables us to explain the necessity of the often observed deep and
incurable skepticism into which logicians are led by the abuse of deduction. All the force of our
belief and our desire, which flows—albeit with leakage—into our behavior and thoughts, is produced
or rather provoked by the continual experiences of our senses. It is the nature of this double power to
transmit itself in order to be preserved, but to be preserved only through dispersal. As we have just
seen, logical transformation requires an expenditure of faith tantamount to sheer loss, like the
expenditure of useless force required by a machine to function. If, then, without checking these
conclusions in order to augment or cancel out the proportion of belief accruing to them, we use them
just as they are for new deductions, the newly engendered conclusions will be less affirmative than
their predecessors, and, from one extension to the next (the first ideas ordinarily being forgotten
rather than simply becoming enlarged by the new ones), we shall end up ineluctably with no belief at
all. Up against this inability to believe anything, the logician has left to him only one resource: to
conjecture that nothing is believable. Analogously, the moralist, too proud of having eradicated all his
passions, becomes inert and calls himself a quietist. *2
Attention given in logic to the quantitative character of belief would introduce many changes that I
cannot go into here, but I cite the above remark as an example.
Having demonstrated the measurability of individual belief and desire, we must now ask if the
beliefs and desires of different individuals taken together can be legitimately considered as a totality.
They can if one considers that the act of desiring or rejecting, of affirming or denying, abstracted from
the objects or the sensations and memories to which it applies, is constantly the same not only from
one moment to another in a given individual but also from one individual to another. It is not the
immediate perception that proves this, as above, but an unavoidable induction. That attests to it. We
have reason to believe that the ways of experiencing odors and tastes, of seeing blue, of hearing the
sound of a violin, of experiencing the sixth sense impressions differ from Peter to Paul, from John to
James. The outstanding example of colorblindness, of people who have a bad ear or a head cold,
proves this point. We can comprehend that Peter lacks a sensation and that Paul has one of a special
kind; in fact the daily enthusiastic practice of an art or doctrine by a fervent religious sect that has
long prevailed without opposition has led to the formation here and there if not of sensations, at least
of accessory quasi-sensations on the way to becoming true sensations. There was a Hegelian spirit in
Germany, a Christian spirit in the Middle Ages; and there is still a poetic spirit, a legal spirit of
things. It may be said in passing that with regard to these slow acquisitions of our senses we take the
transformation of reiterated judgments into ideas and of ideas into sensations at face value, an