The Manchester School Vol 70 No. 2
1463^6786 262^278
March 2002
JEVONS'S DEBT TO BENTHAM: MATHEMATICAL
ECONOMY, MORALS AND PSYCHOLOGY*
by
NATHALIE SIGOT {
PHARE (Universitës Paris I/Paris X) and Universitë du Littoral Coªte d'Opale
The aim of this paper is to show that Jevons's utilitarianism is to be
related to his attempt to build a mathematical theory of economics:
the `felici¢c calculus' provides the instrument for transforming
sensations into quantities. The ¢rst section shows that Jevons referred
to Bentham's calculus but made it much simpler to enable the
mathematical instrument to be introduced. The second section is
devoted to his rejection of Mill's attempt to make utilitarianism a
morally reasonable philosophy by introducing qualities of feelings. But
I endeavour to show that avoiding Mill's interpretation did not mean
that Jevons gave up on moral matters.
"
Introduction
Utilitarianism was the prevailing philosophy in England at the time of
Jevons: John Stuart Mill's Utilitarianism in four-article form was published
for the ¢rst time in 1861 in Fraser's Magazine.1 This gave rise to
considerable debate involving Grote, Whewell and Sidgwick, in particular.
The exchanges between the supporters of utilitarianism and those opposed
to it were signi¢cant: one of its opponents clearly stated in 1876 that
`modern utilitarianism [is] our most fashionable philosophy' (F. H. Bradley,
quoted by Schneewind, 1976, p. 35). Sidgwick (1872, p. 662), despite his
support for utilitarianism, was more cautious: `If anyone interested in
observing contemporary opinion were asked what was the prevailing moral
system in England at the present day, he would probably answer
utilitarianism.' Therefore, it is quite natural for Jevons to have been
in£uenced by this philosophy.
* Manuscript received 17.8.00; ¢nal version received 25.7.01.
{ I am grateful to Richard Arëna, Carlo Benetti, Ghislain Deleplace, Franc°ois Etner, Andrë
Lapidus and Philippe Steiner for helpful comments and suggestions on earlier drafts of
this paper. I would also like to thank the members of the seminar Phare, particularly
Sandrine Leloup, Antoine Rebeyrol and Nicolas Rieucau, and two anonymous referees
of this journal. Pierre Crepel gave me some very useful indications about mathematical
concepts in Jevons's time. A previous version of this paper was presented also in the
University of Nice (Latapses) where I bene¢ted from comments by Samuel Hollander
and J. Ravix. The English language has been reviewed and revised by David Eckersley.
1
Mill's Utilitarianism was edited later in a single volume in 1863; it was re-edited 15 times
between 1863 and 1907. About its in£uence, see Schneewind (1976).
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262
Jevons's Debt to Bentham
263
But the dominant utilitarianism was not that of Bentham. Both J. S.
Mill and then Sidgwick contributed towards creating a morally acceptable
version of the doctrine. Before that time, according to Mill, `the school
of Bentham has always been regarded (I say it with regret) as an
insigni¢cant minority' (1856^64, p. 747; quoted by Schneewind, 1976,
p. 35). Bentham's philosophy was criticized even though it was neither well
known nor understood.2 Indeed, many people associated his utilitarianism
with political economy, the latter being accused by some of inhumanity
as it was not seen to address the problem of increasing pauperism (see De
Marchi, 1974, pp. 123^135). Economists in general were aware of this
and many were alarmed at what Cairnes called `the repugnance, and even
violent opposition' of the working classes to political economy (1870,
p. 260; see White, 1996, p. 115). It was at this time that Jevons nevertheless
decided to base his economic theory on Bentham's work, rather than on
Mill's.
In this paper I aim at clarifying the reasons why Jevons paid tribute
to Bentham's felici¢c calculus, whilst rejecting Mill's philosophy. I shall
concentrate mainly on Jevons's Theory of Political Economy (hereafter
TPE): I hope to shed some light on the relationship between his conception
of a `true theory of Political Economy' (1871, p. 4) and the hedonistic
premises he admitted. Indeed, when dealing with Jevons's utilitarianism, a
further legacy may be considered: as is widely known, utilitarianism is
not only a psychological law stating that pleasure and pain actually guide
human actions, it is also a normative principle according to which the
greatest happiness of the greatest number is the ultimate goal of society.
In Wicksteed's opinion (1906, p. 476), the only `Benthamite' aspect of
Jevons's theory consisted of this reference to `the greatest happiness'. I
agree that this legacy appears, for instance, in The State in Relation to
Labour (1910 [1882]). Here, Jevons intended to evaluate the e¡ects of any
reform by the yardstick of its consequences on collective happiness. But
the purpose of the present paper is not to discuss this legacy for two main
reasons. On the one hand, in the nineteenth century, it was not considered
very original. Prior to Jevons, numerous writers had expressed their desire
to estimate the e¡ects of such and such a measure in terms of collective
welfare, to such an extent that Edgeworth de¢ned utilitarianism only in
the light of the principle of the greatest happiness. He distinguished the
`Economic Calculus', based on the assumption that `every agent is
actuated only by self-interest', from the `Utilitarian Calculus' `in which
2
Bowring's edition of Bentham's works [1838^43] is `defective in content as well as
discouraging in form' (Bentham Committee, 1968, p. v; see also the 1843 review article
published in Edinburgh Review which summed up its de¢ciencies); between 1823 and
1876, moreover, there was no separate re-edition of one of Bentham's major writings,
Introduction to the Principles of Morals and Legislation (Schneewind, 1976, p. 36).
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each and all tend to maximum universal utility' (1881, pp. 15^16).3 On
the other hand, Jevons hardly ever quoted Bentham when referring to the
goal of maximum collective happiness. According to Peart, this part of
Jevons's theory shows that the latter owed Mill a debt.4 Here, a distinction
needs to be drawn between what Jevons called the `abstract and general'
theory on the one hand and the `applied' theory on the other. The ¢rst
owes its generality to the regularities which come from the calculus of pain
and pleasure; whilst the second, which deals with the rules of economic
policy, is characterized by a certain amount of pragmatism: `Nothing but
experience and argument from experience can in most cases determine
whether the community will be best served [...]' (Jevons, 1867, p. 278).
Hence, a great deal of attention was devoted to the question of
Jevons's utilitarianism. With regard to its relationship with hedonism,
however, it generally addressed Bentham's in£uence on Jevons's subjective
theory of utility: Jevons's utilitarianism is frequently understood as a ¢rst
step toward his psychological theory of value. For instance, according to
Black (1972, p. 122), two things had an in£uence upon Jevons: the ¢rst
was the result of Bentham's thinking and led to `the introduction into
economics of psychological hedonism'. The second was De Morgan, who
spoke of `mathematical and quantitative techniques'. I, on the contrary,
wish to suggest that Jevons's mathematical method is the key to
understanding his interest in Bentham's calculus of pain and pleasure. This
involves returning to Jevons's mathematical conception of economics.
First of all, turning economics into a mathematical science provided
economics with a scienti¢c nature: `I contend that all economic writers
must be mathematical so far as they are scienti¢c at all' (1879b, p. xxi); or
`It is clear that economics, if it is to be a science at all, must be a
mathematical science' (1871, p. 3; see also 1874a, Vol. II, pp. 457^458).
Moreover, the mathematical nature of economic science is justi¢ed by the
subjects with which it deals: economics is concerned with pain and
pleasure which are `notions admitting quantity' (1957, p. 10); or `we may
treat pleasure and pain as positive and negative quantities in algebra'
(1871, p. 32). Jevons writes about this very close relationship between
hedonism and mathematical method in the preface of his second edition of
TPE. He speaks of `those authors who [...] have nevertheless carefully
attempted to reach precision in their treatment of quantitative ideal, and
have thus been led to a more or less complete comprehension of the true
theory of utility and wealth' (1879b, p. xxv; italics added). The `arithmetic'
3
Edgeworth's way of understanding utilitarianism is very di¡erent from that of Jevons. The
reason for such a di¡erence might be found in their respective legacies: while Jevons
claimed that of Bentham, Edgeworth referred mainly to Sidgwick (1881; see for instance
p. 102).
4
I discuss this assumption infra.
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Jevons's Debt to Bentham
265
conception of pleasure and pain then leads to the `true' theory of utility;
hedonism appears to be a necessary heuristic condition for the
development of this `true' theory. Without calculus, hedonism was not
su¤cient. But only Bentham's hedonism was appropriate for Jevons, and
he rejected that of Mill. I will endeavour to show that, as a consequence
of his interest in mathematics, Jevons simpli¢ed Bentham's theory
(Section 2) and rejected Mill's peculiar conception of utilitarianism
(Section 3).
á
Jevons's Simplification of Bentham's felicific calculus
Jevons resorted to the Benthamian calculus in order to deal with `Pleasure
and pain as Quantities' (1957, p. 28) on which his theory was to be based.
He recalled that Bentham de¢ned seven circumstances (or dimensions)
valuing feelings: intensity, duration, certainty, propinquity, fecundity,
purity and extent. In fact, Jevons selected only two of them and this
simpli¢cation enabled him to represent utility on a two-dimensional graph.
In other words, the mathematization of economics leads him to make
utilitarianism simpler. In order to be considered as a science, economics
had to adopt a speci¢c method: bringing to light empirically debatable but
theoretically reasonable laws. This implied that reality ought to be
simpli¢ed as `The motives and conditions are so numerous and
complicated, that the relating actions have the appearance of caprice, and
are beyond the analytic powers of science' (Jevons, 1957, p. 15; see also
p. 89). Added to this was the emphasis that Jevons placed on the
continuity of the utility function to introduce di¡erential calculus: his
argument was also based on theory (1957, pp. 15^16; see Schabas, 1990,
pp. 35^37). His simpli¢cation took place in two stages.
In the ¢rst stage, only the ¢rst four dimensions were considered as
relevant. The others were `of high importance as regards the theory of
morals; but they will not enter into the more simple and restricted problem
which we attempt to solve in Economics' (1957, p. 29). Jevons thus
excluded the dimensions of fecundity, purity and extent from his study.
However, in Bentham's analysis, these dimensions contributed to the
valuation process of feeling just as much as the others. If one admits the
possibility of such a valuation process, it is clear that these three
dimensions would not preclude the development of scienti¢c economics.
And Jevons was well aware of that: he rejected these dimensions in morals
but he did believe that the latter were open to improvement through the
use of mathematics. He then stated that:
Any complete theory of morals must deal with quantities of pleasure
and pain, as Bentham pointed out, and must sum up the general
tendency of each kind of action upon the good of the community. If
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The Manchester School
we are to apply scienti¢c method to morals, we must have a calculus
of moral e¡ects, a kind of physical astronomy investigating the
mutual perturbations of individuals. (1874a, Vol. II, p. 458)
He argued only by referring to the frontiers of economics in order to
justify the exclusion of the three dimensions concerned. But we must take
this reference seriously because it is a fundamental one.5 With regard to
`political economy', he stated:
It is called a dismal science. It has been called mechanical, hard
hearted, miserable and even wicked. There is a certain class of
sentimental writers who think [...] that a moral science ought to be
moral in all kinds of sympathies and feelings, duties etc. But this is a
most super¢cial and absurd objection, for this reason, that you cannot
take the whole of the moral sciences into any one science, any more
than you can take all the physical sciences into chemistry or
astronomy. You might as well object to the astronomer for regarding
the planets as mere matter. [...] In short, any particular person must
be regarded as governed by various considerations of which wealth is
only one. But then there are principles governing the accumulation
of wealth. These principles are totally di¡erent from the principles of
morals. (1875^6a, p. 7)
From this defence of economics, it is clear that Jevons tried to establish
that his pure theory was not inconsistent with the moral debates of the
time: he achieved this by separating pure economics from morals and
stating that the ¢rst had to be based on morally reasonable foundations
(see infra).
In the second stage, Jevons spoke of the four remaining dimensions:
intensity, duration, certainty and propinquity. He did not place all of them
on the same plane: the utility curve which he traced related only to
intensity and duration (1957, pp. 30^31). Certainty and propinquity were
then introduced, explaining such phenomena as savings, investment or
insurance. The two dimensions have a di¡erent in£uence on the value of
feeling. The degree of propinquity alters the intensity of pleasure or pain:
`The intensity of present anticipated feeling must [...] increase as we
approach the moment of realisation' (1957, p. 34). Hence, intensity re£ects
propinquity; while these two dimensions were independent in Bentham's
analysis, they merge in that of Jevons. In fact, Jevons was not quite so
5
One might have expected other justi¢cations related to the fact that fecundity, purity and
extent raise two problems: externalities and exogeneity of preferences (see Lapidus and
Sigot, 2000). Both problems make the theory more complicated; this would thus be a
reason for Jevons to rule these three dimensions out of economics. But such arguments
are not to be found in his theory.
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Jevons's Debt to Bentham
267
explicit, but the following statement does allow one to draw such a
conclusion:
So far we have taken no account of the varying in£uence of an event
according to its propinquity or remoteness. To secure a maximum of
bene¢t in life, all future events, all future pleasures or pains, should
act upon us with the same force as if they were present, allowance
being made for their uncertainty. The factor expressing the e¡ect of
remoteness should, in short, always be unity, so that time should have
no in£uence. (1957, p. 72)
Jevons recognized that `no human mind is constituted in this perfect way:
a future feeling is always less in£uential than a present one' (1957, p. 72).
Despite this, he illustrated this observation while showing that the
dimension of propinquity is to be taken into account only when prediction
matters (1957, pp. 73^74). The problem of propinquity then disappears,
making way for that of `probability'. The latter modi¢es the value of
feeling, in an ex ante manner: `If the probability is only one in ten that I
shall have a certain day of pleasure, I ought to anticipate the pleasure with
one-tenth of the force which would belong to it if certain' (1957, p. 36).
However, Jevons did not take the probability into account. The reason is
to be found in A Brief Account of a General Mathematical Theory of
Political Economy: `the e¡ect of foresight merely complicates without
altering the other parts of the theory' (1862, p. 305). Here we ¢nd a
common argument according to which some aspects of the agent's real
behaviour may be neglected, in so far as they do not modify the conclusion
of the theory. Jevons's simpli¢cation of Bentham's calculus should be
related to his conception of an `abstract [economical] science', which is
both abstract and general. Abstraction leads Jevons to neglect propinquity, whereas generality leads him to overlook uncertainty.
Hence, only the dimensions of duration and intensity remain from
the Benthamian process (1957, p. 29). They give rise to a measuring scale
enabling individuals to compare all sorts of pains and pleasures: `if the
intensity [...] varies as some function of the time, the quantity of feeling is
got by in¢nitesimal summation or integration' (1862, p. 305). Jevons's
method has something similar to Bentham's: he generalized the latter's
attempt to multiply intensity by duration, in order to have what he called
`amplitude' or `magnitude' of the feeling (Bentham, ca. 1782, p. 563).
By considering only the dimensions of duration and intensity, Jevons
was henceforth able to treat utility as a subjective and measurable item. In
his view, its subjective character did not pose too many problems: on
several occasions he made the claim that utility is `an attraction between a
wanting being and what is wanted' (1874b, p. 80). He linked subjectivity
with neutrality: economists must not judge the utility of a good. The only
`criterion' one should take into account is `the will or inclination of the
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The Manchester School
person immediately concerned' (1957, p. 39): `Whatever can produce
pleasure or prevent pain may possess utility. [...]; but we must beware of
restricting the meaning of the word [utility] by any moral considerations'
(1957, p. 38; italics added in the second part).
In fact, looking at the other two protagonists of the so-called
Marginalist Revolution,6 the problem appears much more complicated.
On the one hand, Ja¡ë stressed in 1976 that, in the case of Walras, `It is as
if he thought that the economist, qua economist interested in market
behavior, had no more competence to derive utility functions from
consumers' sensations than he had to derive these sensations from their
presumed physiological, psychological and sociological determinants'
(1976, p. 315). He contrasted Jevons's `bestowed concentrated e¡ort on an
attempt to reduce utilitarian speculations to an exact science which would
be useful as a foundation for the theory of value in exchange' with
Walras's approach which `peremptorily and nonchalantly [...] postulated a
measurable marginal utility theory' (1976, p. 318). On the other hand,
the most recent developments concerning Austrian economists have made
it clear that, in contrast to Walras's analysis, Menger's subjectivism is both
very speci¢c and in£uential throughout his theory. Menger's main aim
was to `discover those laws governing market phenomena which can be
traced back to their ultimate genetic determinants in man's physiological,
psychological and social nature' (Ja¡ë, 1976, p. 322). Hence, in Menger,
the equilibrium price is the result of bargaining between two agents: `The
level of relative or monetary prices should be included in an interval whose
limits correspond to the respective values de¢ned by the subjectivity of
both agents and the ¢nal actual price level will result from a bargaining
process between agents' (Gloria-Palermo, 1999). Walras's taªtonnement
process, on the other hand, involved a ¢ctitious auctioneer who announces
prices and changes them according to excess demands. In this respect, the
di¡erence between Menger and Walras leads Gloria-Palermo to oppose
two conceptions of subjectivism with each other: `static subjectivism',
defended by Walras, versus `dynamic subjectivism', by Austrians.
What about Jevons? Surprisingly few elements in Jevons's analysis
make it possible to determine his position. There is neither a mechanism
such as a ¢ctitious auctioneer announcing prices nor a bargaining process
a© la Menger. In fact, there is scarcely anything in Jevons about the price
determination process. In his TPE, the price generally appears as an item
but certain passages appear to involve a bargaining process. Jevons agreed
with Thornton's On Labour (1869) which he quoted as `exactly express[ing]
the problem: ªThere are two opposite extremesöone above which the
6
I shall neither discuss this Revolution, its existence or non-existence, nor its characteristics.
On this question, see for instance Black et al. (1972), Ja¡ë (1976) and, relating to Jevons,
Steedman (1997).
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Jevons's Debt to Bentham
269
price of a commodity cannot rise, the other below which it cannot fall.
The upper of these limits is marked by the utility, real or supposed, of the
commodity to the customer; the lower, of its utility to the dealer. [...] The
price eventually given and taken may be either at one of the opposite
extremes, or may be anywhere intermediate between them'' ' (1957,
p. 123). He illustrated this with an example in which there are two agents,
a seller and a buyer. The ¢rst asks for »1200 whereas the second o¡ers only
»800. Jevons then explains that the equilibrium price will be `the result of
a bargain [which] will greatly depend upon the comparative amount of
knowledge of each other's position and needs which either bargainer may
possess or manage to obtain in the course of transaction' (1957, p. 124).
And he added: `It may be that indeterminate bargains of this kind are best
arranged by an arbitrator or third party' (1957, p. 125). But there is
nothing more. There are two explanations for this. The ¢rst is that the
result of such bargaining is supposed to depend on `motives more or less
extraneous to a theory of Economics' (1957, p. 125), for instance
`disposition and force of character of the parties' or `feelings of justice'
(1957, p. 124). The second is that the price is merely for Jevons something
empirical, the interest of which lies in the possibility of measuring a
theoretical element, i.e. marginal utility (see below).
The question of measurement deserves special attention. From the
beginning to the end of TPE, Jevons stressed the possibility of quantifying
utility: he stated for instance that utility is `a quantity of two dimensions'
(1957, p. 47). But he was very careful when it came to the measurement of
such a quantity:
I hesitate to say that men will ever have the means of measuring
directly the feelings of the human heart. A unit of pleasure or of pain
is di¤cult even to conceive; but it is the amount of these feelings
which is continually prompting us to buying and selling, borrowing
and lending, labouring and resting, producing and consuming; and it
is from the quantitative e¡ects of the feelings that we must estimate their
comparative amounts. (1957, p. 11)
A comparison of the ¢rst edition of TPE with the subsequent ones makes
it clear that Jevons was much more cautious in 1871 than later. In 1871, he
wrote: `Far be it from me to say that we ever shall have means of
measuring directly the feelings of the human heart' (1871, p. 13). But even
if his statement was not as strong in subsequent editions, it has nothing
in common with the position of one of his followers: in 1881, Edgeworth
envisaged a `hedonimetry', i.e. `a psychophysical machine, continually
registering the height of pleasure experienced by an individual', varying
`from moment to moment' (1881, p. 101).
In fact, Jevons expected price to be an indirect measurement of the
utility of a good: `The price of a commodity is the only test we have of the
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The Manchester School
utility of the commodity to the purchaser' (1871, p. 140; see also Jevons
[1872] in 1863^72, p. 246). This suited him in so far as it enabled feelings
to be treated as mathematical data and it became possible to compare
feelings for the same individual:
I have granted that we can hardly form the conception of a unit of
pleasure or pain, so that the numerical expression of quantities of
feeling seems to be out of the question. But we only employ units of
measurement in other things to facilitate the comparison of
quantities; and if we can compare the quantities directly, we do not
need the units. (1957, p. 12)7
Hence, `we may estimate the equality or inequality of feelings by the
decisions of the human mind' (1957, p. 11). This approach displays two
characteristics, the ¢rst of which treats feelings as quantities making it
possible to express them mathematically. The notion of individual
equilibrium has been derived from this: `The most important parts of the
theory will turn upon the exact equality, without regard to sign, of the
pleasure derived from the possession of an object, and the pain encountered in its acquisition' (1957, pp. 32^33; italics added). Second,
Jevons clearly refused any possibility of interpersonal comparisons of
feelings: `The reader will ¢nd, again, that there is never, in any instance,
an attempt made to compare the amount of feeling in one mind with that
in another' (1957, p. 14).8
â
Jevons's Rejection of the Complexity of Mill's Utilitarianism
As we have already stated, Jevons believed that the subjective nature of
utility implied that any `moral considerations' must be ruled out of
economics. Therefore it is not surprising that he challenged Mill's
inclusion of quality as a characteristic of pleasurable experience. Not only
was Mill's conception unable to reach a subjective theory of utility, it
was also open to methodological criticism. Mill sought to make utilitarianism a morally reasonable philosophy: the method used was that of
distinguishing high and low quality pleasure and pain.9 The implications
of Mill's idea of the quality of feelings were far-reaching in that they did
not enable Jevons to treat economics as a mathematical science.
`The verdict which Mill takes in favour of his high-quality pleasures
7
Such a comparison in all sciences prevents the mind from misinterpreting conclusions; it is
not the case when reasoning upon absolute values (see Jevons, 1874a, Vol. I, pp. 327 et
seq.).
8
On this matter, if Jevons's position is clear in the TPE, this is not the case in other writings:
see Peart (1996).
9
`some kind of pleasure are more desirable and more valuable than others', Mill wrote
(1861, p. 211).
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Jevons's Debt to Bentham
271
is entirely that of a packed jury', said Jevons (1879a, p. 532; italics added).
In his opinion, Mill's revised version of utilitarianism implies an external
authority in charge of judging the morality of behaviour and choices of
man. It is clear that the problem comes from the exogenous character of
judgement, for it means that people are viewed as incapable of proper
judgement:
It is on a par with the verdict which would be given by vegetarians
in favour of a vegetable diet. No doubt, those who call themselves
vegetarians would almost unanimously say that it is the best and
highest diet; but then, all those who have tried such diet and found it
impracticable have disappeared from the jury together with all those
whose common sense, or scienti¢c knowledge, or weak state of health,
or other circumstances, have prevented them from attempting the
experiment. (1879a, p. 532)
Consequently, the value of a feeling produced by a commodity, for
instance, could not yet be measured by its price. It is clear that Mill's
philosophy is inconsistent with subjective utility theory. The example of
the vegetable diet will provide a useful point of departure: according to
Mill's position, whatever the taste of an individual the value of the
pleasure produced by a vegetable diet will be superior to other (low)
pleasures if an external judge considers this sort of food to be healthy; its
value thus depends on the speci¢cation of the good. In the light of this, it
is not surprising that Jevons reacted negatively: whenever he expounded
his value theory, he asserted that utility refers to an `abstract quality'
(1957, p. 38). He clearly regretted that `most persons confuse the utility
with the physical qualities' (1905, p. 2) and he explicitly referred to Mill
(1874b, p. 78). In accordance with Jevons's subjective theory of utility, the
value of a vegetable diet is superior to any other type of food for a
vegetarian, but inferior for people eating meat.10
Understanding the `qualities' of feelings in this way would hamper
Jevons's treatment of economics as a mathematical science. Clearly, it was
not the idea of quality which he called into question but the principle of
exogenous judgement on quality. Such judgements do not enable pleasure
and pain to be reduced to a numerical value expressing what the individual
feels. This was the reason why, in `John Stuart Mill's Philosophy Tested',
Jevons blamed Mill for changing the sense of utilitarianism by trying to
introduce a moral aspect into it: `In removing the obstacles to the
reception of his [Mill's] favourite doctrine he removed its landmarks too,
10
Jevons opposed exogenous judgement in matters of individual behaviour as it does not
allow a subjective theory of utility to be developed. But he did not speak of Bentham's
position which accepted the Legislator's exogenous judgements when dealing with
collective utility.
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The Manchester School
and confused everything' (1879a, p. 523); then he concluded: `Mill's
attempt to reconcile his ideas on the subject with the utilitarian theory
hopelessly fails' (1879a, p. 532). This did not necessarily mean that all
types of pleasure and pain are to be ranked on the same level:
utilitarianism had already been su¤ciently criticized for its lack of
morality. That Jevons was also concerned with this bad reputation is clear
from his declaration that he was `not denying the moral superiority of
some pleasures and courses of life over others' (1879a, p. 532). His
position was very subtle: it consisted in converting Bentham's philosophy
into a morally acceptable doctrine so as to use it as a foundation for his
economic theory, but without giving up the measurable nature of utility
present in Bentham's theory.
In Jevons's words, to suppose some pleasures to be superior to others
is a petitio principii. He accused Mill of having displayed such a
shortcoming while Bentham had managed to avoid it: `In all that Bentham
says about pleasure and pain, there is not a word about the intrinsic
superiority of one pleasure to another' (1879a, p. 527). Jevons was right: if
one goes back to Bentham's well-known Introduction, it is clear that no
moral judgement is to be found on the quality of feelings: `there is no such
thing as any sort of motive that is in itself a bad one' (1789, p. 100). On
the other hand, Jevons explained that, in contrast with Mill who
maintained it dogmatically, Bentham `had analysed' the idea of quality:
`Nor is it to be supposed that Bentham, in making his analysis of the
conditions of pleasure, overlooked the di¡erence of high and low ...'
(1879a, p. 533). But no external judge is involved in his approach. Quality,
then, is no longer an exogenous characteristic. On the contrary, it is
endogenous in so far as the individual himself judges the quality of the
pleasure or pain he anticipates. At the risk of giving an inadequate
interpretation of Bentham's text, Jevons explained that when someone
values a feeling he deals with quality via certain dimensions of the
calculus: `A pleasure to be high must have the marks of intensity, length,
certainty, fruitfulness, and purity, or of some of these at least; and when
we take Altruism into account, the feelings must be of wide extentöthat
is, fruitful of pleasure and devoid of evil to great numbers of people'
(1879a, p. 533). This interpretation of Bentham's theory made the quality
of feelings quanti¢able, in a form consistent with utility theory:
It is a higher pleasure to build a Free Library than to establish a
new Race Course; not because there is a Free-Library-building
emotion, which is essentially better than a Race-Course-establishing
emotion, each being a simple unanalyzable feeling; but because we
may, after the model of inquiry given by Bentham, resolve into its
elements the e¡ect of one action and the other upon the happiness of
the community. (1879a, p. 533)
ß Blackwell Publishers Ltd and The Victoria University of Manchester, 2002.
Jevons's Debt to Bentham
273
In short, Jevons was faced with the problem of avoiding Mill's
peculiar interpretation of the quality of sensations without giving up
on moral matters. He did this by pinpointing the subject of political
economy.
As we have seen, Jevons's interpretation assumes purity and
fecundity to be taken in a very wide sense because they represent the
repercussions of an act on the welfare of the community. Consequently
political economy is not concerned with these two dimensions, since it
treats `only welfare so far as it is dependent on wealth' (1869, p. 56). In
other words,
Each science must treat one subject, or there would be such a
confusion of facts and principles that no science could exist. But then
we must not suppose that one science will give absolute indications
of what should be done. [...] It does not follow that because the poor
rate subtracts from the wealth of the country that we are to have no
poor rate. Poor relief and voluntary charity is [sic] given for the most
part on moral considerations with which Political Economy has
nothing to do. But Political Economy will show, to some extent, how
it may best be raised and expended. Political Economy thus gives us
quali¢ed or partial advice, and the statesman or the individual should
take it into account quantum valeat, or for as much as it is worth.
(1869, p. 57)
Despite Jevons's interpretation having little in common with Bentham's
position, it is consistent with utilitarianism as consequentialism. But the
dimensions of `purity' and `fecundity' of feelings did not involve anyone
else in Bentham's individual calculus: `fecundity [means] the chance it
[pleasure or pain] has of being followed by sensations of the same kind:
that is, pleasures, if it be a pleasure: pains, if it be a pain' and `purity', `the
chance it has of not being followed by sensations of the opposite kind [...]'
(1789, p. 39). Externalities do not fall into these two dimensions, but into
the `extent' dimension, i.e. `the number of persons [...] who are a¡ected by
it [the act]' (1789, p. 39). But the latter dimension raises the speci¢c
problem of social evaluation that Jevons ignores in his TPE. He did not
neglect it, however, since he mentioned it in other writings. He was not in
favour of a direct measure of social utility via a collective function of
utility. Neither did he accept Bentham's procedure claiming that `money is
the instrument for measuring the quantity of pain or pleasure' (ca. 1782,
p. 562; see Sigot, 2001). He introduced the concept of `multiplication of
utility' (1881, p. 29; 1905, pp. 36^43) and explicitly used it in the context
of the utility of free public libraries. Concerning the practice of the
Melbourne Public Library which consisted in lending books to other
libraries for three months and more, Jevons stated: `The number of
volumes thus circulated in 1876^7 was 8000, and by the multiplication of
ß Blackwell Publishers Ltd and The Victoria University of Manchester, 2002.
274
The Manchester School
utility they were rendered equivalent to 32000 volumes' (1881, p. 39). The
multiplication process does not concern utility, but goods. Indeed, such a
process does not enable Jevons to value the social utility of libraries and
he simply concluded: `The main raison d'eªtre of Free Public Libraries [...]
is the enormous increase of utility which is thereby acquired for the
community at a tri£ing cost' (1881, p. 29).
Jevons's method means reconsidering the relationship between
economics and morals. For Jevons, the three dimensions of `purity',
`fecundity' and `extent' belong to Morals, and therefore must be excluded
from Economics. But, because they are supposed to express the quality of
individual motivations in Bentham's theory, they make it possible to
ground economic theory in a reasonable philosophy regarding morality.
On the other hand, economic theory requires simpli¢cation in order to
become a science;11 drawing a clear boundary between Morals and
Economics strengthens the process of simpli¢cation: `It is the lowest rank
of feelings which we here treat' (1871, p. 32). Or,
Objects intended for immoral or criminal purposes [...] also have
utility. [...] It belongs to other branches of the moral and social
sciences to investigate the ultimate e¡ects of actions. In economics we
treat only of proximate e¡ects. (1905, p. 12)
The issue is clearly the relationship between, not economics and
psychology, but economics and morals: if the reference to utility leads
Jevons to a hedonistic approach, he breaks with Mill's philosophy when
denying that one should judge the type of needs expressed by individuals.12
Even when Jevons condemned `the bad habits of a population' (1878,
p. 1)ösuch as alcoholismöand strongly recommended that new types of
`amusements' should be created in order to develop a `higher Civilisation'
(1878, p. 7), he was not guided by moral concerns alone. For instance,
musical entertainment is assumed to be superior to any other because it
provides e¡ortless relaxation to the working classes. This is not the case
for other types of recreational activities such as museums, for example:
A comfortable seat, a supply of fresh air, and a quiet audience, are
requisite physical conditions for the enjoyment of music [...]. There is
no straining of the nerves or muscles, no e¡ort of any kind, but mere
11
12
Jevons used the same argument to leave out the dimension of probability: see supra.
In fact, there are not two but three standard critiques of `utility': the moral one, the
psychological one and the linguistic one. Jevons was aware of the latter (for instance,
1875^6b, pp. 10^12) with which many of his contemporaries agreed (like Wicksteed,
Marshall, Pareto, Fisher). It deals with the confusion between `utility' and `usefulness'
(see for instance Fisher, 1918, p. 335). This critique led to several attempts to replace
`utility' by other terms, like `desirability' (Fisher) or `ophelimity' (Pareto).
ß Blackwell Publishers Ltd and The Victoria University of Manchester, 2002.
Jevons's Debt to Bentham
275
passive abandonment of the mind to the train of ideas and emotions
suggested by the strains. (1878, p. 9).13
ã
Conclusion
It has sometimes been said that Jevons's references to Bentham were
inconsequential. When discussing this legacy, Mays (1962, p. 224) says that
it was only a `fac°on de parler'; Robertson (1951, p. 149) had previously
written:
Yet, one has the feeling as he reads Chapter II of the Theory, the
chapter on pleasures and pains, that Jevons is simply going through
the motions of citing an unquestioned authority [Bentham] before
proceeding to an altogether di¡erent kind of analysis. [...] The words
pleasure and pain are used, but they are scarcely the pleasure and pain
of the Bentham Calculus. [...] A pleasure is simply any motive which
attracts to a certain action, and a pain is any motive which deters
action. It is as simple as that; and Bentham is not simple. Yet there
can be little doubt that the Benthamite approach was thoroughly
understood by Jevons and subtly rejected.
I wish to argue that it is misleading to give the impression that the search
for an undisputable authority14 led Jevons to refer to Bentham's
utilitarianism. I point out that there is a major reason why Benthamian
analysis was of great importance in Jevons's conception of political
economy: it is related to his attempt to build mathematical economics.
Given present-day knowledge, it is easy to see that such a legacy was
not necessary from a strictly logical point of view. The best proof may lie
in Walras's theory: at the same time as Jevons, Walras looked for a
mathematical economics, but without hedonistic premises (Ja¡ë, 1976,
p. 318) because he was opposed to utilitarianism (see Rebeyrol, 1999, p. 16,
n. 1). And yet, both Walras and Jevons faced the same di¤culty regarding
the relationship between economics and morals. But the way in which
Jevons chose to deal with it reveals his support for utilitarianism: political
economy and morals share the same origin, i.e. Bentham's felici¢c calculus.
Of course, it must be understood that economics is concerned with only a
13
Peart (1996) interprets such a stance as the proof of Jevons's debt to Mill, and Mosselmans
(2000) as the expression of Jevons's unitarianism. But these viewpoints seem to me to
be distorting: Jevons was not concerned with purely economic matters since he adopted
`a layman's point of view' (1878, p. 15). A moral position may be adopted without
signi¢cance for economics.
14
One may question this search for an `undisputable authority' about an author who
concluded his major economic writing by a violent attack on `The Noxious In£uence of
Authority' (1957, pp. 275^277): `In matters of philosophy and science authority has ever
been the great opponent of truth' (pp. 275^276).
ß Blackwell Publishers Ltd and The Victoria University of Manchester, 2002.
276
The Manchester School
speci¢c part of this calculusöas morals are with a di¡erent part. As a
result, Jevons used a substantially di¡erent concept of individual calculus
from Mill's. He came to regard the latter as inconsistent with `a true
theory of political economy', and his own is closer to Bentham's, which he
transformed without garbling its deep meaning.
The question now is: why did Jevons take the unnecessary perspective
of hedonistic analysis as a prerequisite for mathematical economics?
Nobody can answer this question. But the modern case against Jevons's
hedonism has overlooked what Jevons himself said about his utilitarianism
and his method; this illustrates what Black called `an understandable, but
regrettable, vice of the intellectual historianöthat of trying to explain the
thinking of his subject, not in relation to the thought of the subject's own
time, but in relation to the ideas of the present time' (1972, p. 123). On the
contrary, I have taken Jevons's stance seriously. And I believe that it
reveals how the relationship between ethics and economicsöa relationship
which in the view of certain modern authors such as Sen is really in need
of clari¢cation in the present dayöhas been treated by one of the founders
of marginalism. Here, methodological issues play a great part:
mathematization gave rise to a simpli¢cation of a concept originating in
moral philosophyöthe utilitarian calculusöin order to establish a new
approach to political economy.
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