## 1. Biography




William Stanley Jevons was born in Liverpool on 1 September 1835. His
father Thomas Jevons (1791-1855) was an iron merchant; his
mother Mary Anne Roscoe (1795-1845) grew up in an intellectual
and artistic milieu. The railway boom crisis of 1847 caused the
bankruptcy of the family firm. William Stanley Jevons went to
University College School in London in 1850, and in 1851 to University
College. He studied chemistry under Graham and Williamson, two
pioneers in the development of atomic theory and the theory of
molecular motion. Another major influence at University College was
Augustus De Morgan (1806-1871), with his courses on mathematics
and logic. Jevons left University College without taking his
degree. In 1854 he travelled to Sydney, in order to become an
assayer at the Australian mint. Jevons devoted much time to private
study. His work covered many different areas: railway policy,
meteorology, protection, land policy, cloud formation, gunpowder and
lightning, geology, etc. Jevons left Australia in 1859 and returned to
University College to complete his education. The early 1860s are
important for Jevons' intellectual development, and he reports in his
diary that he received significant insights in both economics and
logic: a "true comprehension of value" (Black 1981: 120,
La Nauze 1953) and the "substitution of similars" (Black
& Konekamp 1972: 179).




Jevons received his MA degree in 1862, and was awarded the gold
medal 'in the third branch' which included logic, moral
philosophy, political philosophy, history of philosophy and political
economy. In 1863 Jevons became a tutor at Owens College,
Manchester, and in 1865 a lecturer in political economy and
logic. In 1867 Jevons married Harriet A. Taylor, and they
subsequently had three children. The family moved to London in
1876, on his taking up a chair at University College. 
Jevons' short life came to an end in 1882, when he drowned near
Hastings.


## 2. The Laws of Thought



 Like many representatives of 19th-century logic and
philosophy of science, Jevons starts his investigation by examining the
nature of the Laws of Thought. Jevons argues that these Laws are
true both "in the nature of thought and things". 
Given that science is in the mind and not in the things, the Laws of
Thought seem to be purely subjective and only verified in the
observation of the external world. However, Jevons argues that it
is impossible to prove the fundamental laws of logic by reasoning,
since they are already presupposed by the notion of a proof. 
Hence, the Laws of Thought must be presupposed by science as "the
prior conditions of all thought and all knowledge". 
Furthermore, our thoughts cannot be used as a criterion of truth, since
we all know that mistakes are possible and omnipresent. Hence, we
need to presuppose objective Laws of Thought in order to discriminate
between correct and incorrect reasoning. It follows that Jevons
regards the Laws of Thought as objective laws.



 The fundamental mental powers for knowledge acquisition are the power
to discriminate, to detect identity and to retain. The
fundamental laws of thought are threefold: the Law of Identity, the Law
of Contradiction and the Law of Duality. The first law is
described as "Whatever is, is" and implies that a thing is
always identical with itself. Jevons does not define the concept
of "identity", and tends to regard it as
self-evident. The second law is the classical law of
contradiction: "A thing cannot both be and not be". 
The third law is the law of the excluded middle: "A thing must
either be or not be." Jevons suggests that these three laws
are merely different aspects of one and the same Law, but considers it
impossible to express this Law in less than three lines. His
symbolic representation of these laws is as follows:



> 
> 
> 
> |  |  |  |
> | --- | --- | --- |
> | (1) | *A* = *A* | Law of Identity |
> | (2) | *Aa* = 0 | Law of Contradiction |
> | (3) | *A* = *AB* *|* *Ab* | Law of Duality |
> 
> 
> 



 The absence of a clear definition of 'identity' is
striking, especially since Jevons recognises that there are different
kinds and degrees of sameness. The main problem is then to point
out a "sufficient degree of likeness or sameness". 
The simplest form of inference is making use of a pattern, proxy,
example or sample. If the sample "exactly represents the
texture, appearance, and general nature" of a certain commodity,
then what is true for the sample will also be true for the commodity as
a whole. This approach evades defining similarity, as it
presupposes that the sample is an 'exact representation' of
the commodity whereas it is unclear under what conditions that would be
the case. All processes of inference are based on the principle
of substitution. All knowledge is derived from sensual
experience, which implies that all knowledge is inductive. 
Deduction is the inverse process of induction, and both rely upon the
nature of identity. 


## 3. Logic



 Like many other logicians of the 19th century, Jevons
wants to establish clear links between mathematics and logic. He would
like to derive mathematics from logic, which is based on the Laws of
Thought, and in doing so he makes (a rather controversial) use of
mathematical symbols when establishing his logical formalism. Jevons
denotes terms by capital letters *A*, *B*, *C*,
etc. and their negative counterparts by small italic letters
*a,b,c*, etc. The relation of identity or sameness is
represented by the sign '='. The expression
'*A* ~ *B*' indicates that *A* and
*B* are not identical with each other; '*A* SS
*B*' indicates that there exists any relation between
*A* and *B*, which includes but is not restricted to the
relations of equality or inequality. The general formula of logical
inference implies that from *A* = *B* SS *C*
we can conclude that *A* SS *C*. Jevons defines the
concept 'term' in his *Pure Logic*:
"*Term* will be used to mean *name*, or any
combination of names and words describing the qualities and
circumstances of a thing". Jevons distinguishes between the
extent and the intent of a term or a name. "The objects denoted
form the *extent* of meaning of the term; the qualities implied
form the *intent* of meaning". It follows that extent and
intent of meaning are negatively correlated: when more qualities are
added to the meaning of a term, less objects will correspond to that
meaning. Abstract qualities, denoted by abstract terms, originate when
objects are compared and resemblances and differences
identified. Abstract terms possess only one kind of
meaning. Substantial terms, such as 'gold', denote
substances. Nothing is denoted by the symbol '0', which in
logic means "the non-existent, the impossible, the
self-inconsistent, the inconceivable". Jevons lists several
"special laws" which govern the combination of terms. The
"Law of Simplicity" implies that a term combined with
itself has no effect, hence *A* = *AA* = *AAA* =
etc. The law of commutativeness indicates that the order of the
combination does not matter, hence *AB* = *BA*,
*ABC* = *ACB* = *BCA* = etc.



 The truths of science are expressed in the form of propositions. 
"Propositions may assert an identity of time, space, manner,
quantity, degree, or any other circumstance in which things may agree
or differ" (Jevons 1874: 36). Simple propositions *A*
= *B* express the most elementary judgment regarding
identity. The use of the mathematical symbol '='
implies that the distinction between subject and predicate vanishes,
which makes quantification of the predicate possible. Several
logicians opted for what Jevons calls the "indeterminate
adjective" 'some', represented symbolically by
'V'. Jevons rejects the usage of indeterminate
symbols and suggests that *A* = V*B* (All *A*s are
some *B*s) should be written as *A* = *AB*. 
Propositions of this kind express an identity between a part of
*B* and the whole of *A*.



 Direct inference consists of applying the 'substitution of
similars' to certain premises in order to arrive at logical
conclusions. Jevons lists several forms of inference:


* immediate inference  
 (*A*=*B* implies
*AC*=*BC*);
* inference with two simple identities  
(*B*=*A* and
*B*=*C* imply *A*=*C*);
* with a simple and a partial identity  
(*A* = *B* and
*B* = *BC* imply *A* = *AC*);
* of a partial from two partial identities  
(*A* = *AB* and
*B* = *BC* imply *A* = *ABC*);
* of a simple from two partial identities  
(*A* = *AB* and
*B* = *AB* imply *A* = *B*);
* of a limited from two partial identities  
(*B* = *AB* and
*B* = *CB* imply *AB* = *CB*);
* and miscellaneous forms of deductive inference.



 Jevons indicates that traditional syllogistic forms such as Barbara,
Celarent, Darii etc. can be represented easily in his logical
system. It is also convenient to represent more complicated
cases, such as inferences derived from more than two premises.




Disjunctive propositions are used whenever an abstract term is
'developed' in its constituent parts or subclasses -
whenever the extent of meaning of a term is explored. In order to
represent disjunctive propositions, Jevons suggests to use the symbol
'*|*'. The words 'and' and
'or', used in everyday language, can denote exclusive or
inexclusive alternatives, but Jevons' symbol
'*|*' refers to alternatives that are not
exclusive. The law of unity, *A* *|* *A* =
*A*, reveals an imperfect analogy between mathematics and
logic. In his earliest work on logic Jevons used the symbol
'+' instead of '*|*', but in
*The Principles of Science* he recognises that the analogy
between logic and mathematics is imperfect. Contemporaries such
as Boole and Robertson were very critical towards Jevons's use
of mathematical symbols in logic.




Indirect inference or indirect deduction consists of pointing out
"what a thing is, by showing that it cannot be anything
else". According to Jevons this is an important method, since
"nearly half our logical conclusions rest upon its
employment". The simplest form of indirect inference starts from
*A* = *AB*. The law of duality implies that *b* =
*Ab* *|* *ab*, or by substitution *b =
ABb* *|* *ab*. Since *ABb* = 0
(a contradiction), it follows that *b* = *ab*. Hence, if
a metal is an element, it follows that a non-element is a
non-metal. Jevons refers to this conclusion as the
"contrapositive proposition" of the original. The
contrapositive of a simple identity *A* = *B* is
*a* = *ab*, and since *A* = *B* implies
*B* = *A* it also follows that *b* =
*ab*. The two contrapositives taken together let us conclude
that *a* = *b*. The method of indirect inference can be
used to describe a class of objects or a term, given certain
conditions. The class is first of all 'developed' using
the law of duality, then alternative expressions taken from the
premises are substituted, and finally all contradictory alternatives
are scrapped. The remaining terms may be equated to the term in
question.



 Jevons introduces the logical alphabet - a series of combinations
that can be formed with a given set of terms. For instance,
*A* and *B* produce the four combinations *AB*,
*Ab*, *aB* and *ab*. Using the logical
alphabet, logic becomes simply an exercise of fully developing all
terms and eliminating the contradictory terms. However, when the
amount of letters increases, the amount of possible combinations
becomes considerable. Jevons considers some techniques and
devices to facilitate these endeavours, such as a 'Logical
slate' (the logical alphabet engraved upon a school writing
slate). Nevertheless, when more than six terms are involved, it
becomes almost impossible to solve the problem. To facilitate
this kind of reasoning Jevons developed a logical abacus, which
operates on simple mechanical principles. It can be seen as one
of the first computers.



 Induction is the inverse process of deduction, but it is a much more
complicated mode of reasoning. Induction proceeds according to
certain rules of thumb, trial and error, and past attempts. 
Induction of simple identities becomes very complex as soon as more
than just a few terms are involved. Induction of partial
identities starts from a certain premise in disjunctive form *A*
= *B* *|* *C* *|* *D*
*|* ... *|* *P*
*|* *Q*, and then we need propositions that
ascribe a certain property to all individuals: *B* =
*BX*, *C* = *CX*, ..., *Q* =
*QX*. Substituting and rearranging yield the desired
result *A* = *AX*. According to Jevons this is the
most important scientific procedure, as "a great mass of
scientific truths consists of propositions of this form *A* =
*AB*". Jevons recognises the problem of induction --
that we can never be sure to predict the future based on past
knowledge. Jevons needs to bring in principles of number and
theory of probability to deal with this matter.


## 4. Philosophy of Mathematics, Theory of Probability and Statistics



 Jevons' principles of number reflect his insistence that
mathematics should be based on logic, not the other way round. He
occupies a somewhat contradictory position in the history of logic,
since his formalism was inspired by the works of Boole, who gave
mathematics priority over logic. Jevons attempts to define
'number' by counting 'units' in space or
time. When counting coins, every coin should receive a proper name: we
should count *C*' + *C*'' +
*C*''' +
*C*'''' + ... The coins are
equal to each other (they all belong to the class *C*); they
are different only because they reside on different points in
space. Before counting, we should reduce all identical alternatives;
the remaining 'units' reside on different points in space
and time. "A unit is any object of thought which can be
discriminated from every other object treated as a unit in the same
problem" (Jevons 1874: 157). The concept of
'unit' encounters some severe difficulties, as noted by
Frege. We can only add up *C*s that are identical, but they
cannot denote different things if the same symbol *C* is
used. Jevons was unable to resolve this contradiction.



 Given these problems, the role and importance of Jevons' system
of logic and philosophy of mathematics seems to be small. It
appears to be limited to a pedagogical aspect: Jevons' writings
on logic, such as his *Elementary Lessons in Logic*, were widely
used as textbooks and saw numerous reprints, up to decades after his
death. This appraisal would not, however, do justice to
Jevons' most important achievement: the introduction of
statistics and econometrics in the social sciences and the use of
empirical data.



 Statisticians in the first part of the 19th century were concerned
with the collection of data, but not with analysis. The data suggested
too many different causes. Statistical journals published tables and
numbers, but graphical representations and analysis remained
absent. In 1863 Jevons published *A Serious Fall in the Value of
Gold*, which investigated the influence of Australian and
Californian gold discoveries of 1851 on the value of gold. For this
purpose he constructed index numbers making use of the geometric
mean. He argued that multiplicative disturbances will be balanced off
against each other when using the geometric mean. There is however no
empirical verification of this 'multiplicative
disturbances' hypothesis. Aldrich (1987) argues that Jevons used
probability in two main patterns of argument: in the determination
whether events result from certain causes or are rather coincidences,
and in the method of the least squares. The first approach entails the
application of the 'inverse method' in induction: if many
observations suggest regularity, then it becomes highly improbable
that these result from mere coincidence. The second
approach, the method of the least squares, appears when Jevons tries
to adjudge weights to commodities (giving more weight to commodities
that are less vulnerable to price fluctuations), and when he tries to
fit empirical laws starting from an a priori reasoning about the form
of the equation. These methods show at least some concern for
probability and the theory of errors. But Jevons worked on
the limits of his mathematical understanding, and many ideas that he
foreshadowed were not developed until decades after his death.



 Jevons' use of statistics in the social sciences was inspired by
Adolphe Quetelet. Jevons distinguishes between a
'mean' (the approximation of a definite existing quantity)
and an 'average' or 'fictitious mean' (an
arithmetical average). The fictitious mean is important, since it
allows us to 'conceive in a single result a multitude of
details'. For instance, Jevons equates aggregate and
average consumption: provided that the community under consideration is
large enough, the average consumption of the aggregate community will
vary continuously due to price changes, whereas individual behaviour is
strongly affected by accidents. If all individuals had exactly
the same features (those relevant for consumption), then the average
laws of supply and demand would be equal to the conduct of every
individual. If however the "powers, wants, habits, and
possessions" of different people were widely different, then the
average would not represent "the character of any existing
thing". The accidents would cancel each other out and a
certain 'typical' consumer would emerge. Although
this is clearly a case of a fictitious mean, it would not be less
useful: "the movements of trade and industry depend upon averages
and aggregates, not upon the whim of individuals".



 Jevons thus recognizes that people are not homogeneous and that it
would be wrong to create 'representative agents' depicting
individual behaviour. In the case of large aggregates however,
disturbing causes would cancel each other out. Here Jevons brings
in the large number argument. If however specific policy
questions are at stake, the heterogeneity of different societal
subgroups has to be accounted for. Jevons uses the concept of
'character' in order to bridge the gap between universal
theory and characteristics of specific subgroups in society, as we will
see in the next section.


## 5. Philosophy of Economics



 Jevons seems to be a mathematical, deductive economist. Market
prices are derived directly from a series of fundamental motive forces,
such as "the mechanics of utility and self-interest". Markets are
depicted in the most abstract fashion and economic agents are perfectly
rational, perfectly foresighted and in possession of perfect
information. A perfectly rational human being would anticipate
future feelings and include discounted future utility in his
calculations. However, this ability varies according to certain
circumstances, as there are "the intellectual standing of the race, or
the character of the individual" (Jevons 1879: 34). The ability
of foresight depends on the state of civilisation: the class or race
with the most foresight will work most for the future, because a
powerful feeling for the future is the main incentive to industry and
saving. Moreover, even the 'quality' of tastes increases with
every improvement of civilisation. Jevons' conception of an
economic agent should therefore be altered according to the
institutional setting in which the agent appears (the class or race to
which the individual belongs).



 Michael White elaborates on Jevons' use of the concepts of
'character' (White 1994a), 'gender' (White
1994b) and 'race' (White 1993). Jevons' work was not
directed to the explanation of the behaviour of specific individuals
per se, unless these individuals were representative for all market
participants of a certain uniform character. The science of economics
deals with the lowest motives, and the *Theory* contains
'representative individuals', which behave in the way
required by the *Theory*. All economic actors do not have to
behave in exactly the same way, but disturbing causes would balance
and therefore the 'representative individual' may be an
appropriate model for the *Theory*. The theory is however
indeterminate in cases when more information is required. For example,
it is unclear whether an increase in the real wage rate, proportionate
to an increase in labour productivity, results in increased or reduced
hours of work. More information about the 'character' of
the person under consideration is required: whereas learned
professionals might be expected to work more severely, common
labourers might prefer idleness over labour and prefer greater
'ease' in the case of rising real incomes. Irish labourers
are said to be responsible for the higher mortality rates in several
districts, because Jevons considered the Irish to be a race that would
become more easily subject to drunkenness. The proper place of women
is the home: women with children younger than three years should not
be allowed to work, as this would only give rise no a neglect of the
children, and would encourage the males to choose for idleness. In all
these cases, the characters of labourers, Irish people or women are
taken for granted, and are not in need of further explanation. The
Victorian middle-class is used as a yardstick for evaluation.


## 6. Unitarianism and Evolutionism




Although the bias regarding class, gender and race is obvious in
Jevons' work, we should add that he was concerned with the
amelioration of society in general and the condition of the working
classes in particular. This attitude was inspired by the
progressive and Unitarian middle-class background from which Jevons
emerged. Some remarks and reflections on religion can be found in
his diary and personal correspondence. 




Although Jevons does not discuss explicitly the Trinity, it is clear
that he believes in the existence of one God. He does not
describe him as a personal being or father, but as a general principle
of abstract goodness (Black 1973: 258). This abstract principle
is in perfect accordance with scientific findings: he reports that his
conception of God is derived from an examination of matter and
mind. The world is a "vast organism" with order and
form expressing intention and mind, which implies that God is
inseparable from his works. He is visible "in the wonderful
order and simplicity of Nature, in the adaptation of means to ends, and
in the creation of man to which everything refers, with power capable
of indefinite improvement" (Black & Konekamp 1972:
155). Jevons founds his faith "on Man and his
feelings", because humanity's mental feelings of love and
sympathy are the only places where intentions of good can be
discovered. Every religion refers to the same eternal principles
or "moral truths", but the state of civilization determines
their degree of misrepresentation. Different religions are merely
costumes thrown over these principles, and Unitarianism contains the
"most simple and truth-like" set of religious
beliefs. God is depicted as a principle of abstract goodness, and
Jesus is seen as the messenger who brought the eternal moral truths to
humankind. Whereas Newton was a genius of natural science and
Mozart of music, Jesus was a moral genius. The history of
Unitarianism is also the history of a rational approach to religion,
and a critical approach to the Holy Scripture. In general,
Unitarians did not oppose scientific development, but on the contrary
they argued that science and religion should be seen as two sides of
the same coin.




The growing critical attitude of Unitarianism coincides historically
with the rise of evolutionary theory: especially Darwinism, but also
wider theory such as the work of Auguste Comte and Herbert
Spencer. Jevons was particularly favourable towards
Spencer's evolutionary ethics. The evolutionary perspective
allows Jevons to integrate his religious beliefs in a view on the world
as growing towards higher moral consciousness and rationality. 
Like Spencer, Jevons argues that there is no conflict at all between
science and religion. On the contrary: they are both directed
towards truth, and therefore they cannot contradict each other. 
Jevons congratulated John Herschel for his condemnation of the
Theological Declaration of Scientific Man, which equated freedom of
inquiry with a tendency to irreligion (Black 1977a: 60). Jevons
even intended to write the Tenth Bridgewater Treatise (following
Charles Babbage's Ninth Bridgewater Treatise) to show the perfect
compatibility between science and religion, but he never completed this
work.




In *The Principles of Science* Jevons devotes a (short)
section on the theory of evolution, followed by a section on the
possibility of divine interference (Jevons 1874, pp. 
761-9). Jevons embraces Spencer's idea that the homogenous
is unstable and differentiates itself in the process of evolutionary
development. This explains why a variety of human institutions
and characters emerged. He recognizes that evolutionary theory
has not been proved, but nevertheless he adheres to its
truthfulness. It is certainly not in conflict with theology,
since it does not lead to the conclusion that creation was and is
impossible. Evolutionary theory discloses several natural laws
that explain how primitive life evolved to humankind by processes of
adaptation to changing circumstances -- but the initial
distribution of atoms in the primeval world is very important as
well. Jevons argues that this initial distribution is the result
of the "arbitrary choice of the Creator", which could have
been very different and therefore present life would have been very
different as well. Evolutionary theory tells us only that similar
circumstances will lead to similar results since the same laws apply,
but this is not in conflict with an initial act of creation. In
close accordance with Spencer's *First Principles*, Jevons
states that it would be absurd to deny that anything exists, and that
it therefore might be equally conceivable that the world was created
out of nothing or that it existed from eternity. He also states
clearly that science cannot disprove the possibility of divine
intervention, which implies that a positivist attitude does not
necessarily lead to materialism or atheism. Jevons also takes
distance from Comte's positivistic philosophy, by arguing --
like Spencer -- that scientific reflection on higher notions of
creation must necessarily end up in contradictions.


## 7. Implications for Economic and Social Policy




Black (1995) recognizes that, after 1867, Jevons'
"increasing faith in the validity of Spencer's theory of
evolution was combined with decreasing faith in the validity of
laissez-faire as a guide for economic policy". Unitarians
struggled with the 'contradiction' between the need for
individual self-improvement on the one hand, and active interventionism
on the other hand. This 'contradiction' can also be
depicted as a tension existing between a belief in scientific
principles on the one hand -- the laws of economics -- and
the recognition that moral and intellectual self-improvement is
impossible as long as the first necessaries of life are still out of
reach. Unitarians concluded that a rational mode of living had to
be imposed on the poor before they could benefit from education. 
Jevons tried to resolve this paradox by restricting the scientific
analysis to what can be accounted for in terms of the accumulation of
wealth, and by suggesting that a 'higher' calculus of
pleasures and pains is needed when 'higher' motives
interfere. Interventionism could then be justified by pointing
out those 'higher' motives. The scientific basis of
Jevons' economics is utilitarianism and the mechanics of utility
and self-interest; like many Unitarians this scientific belief is
combined with an emphasis on active interventionism directed towards
more possibilities for self-improvement; and evolutionary theory does
not only show that there *should* be development towards the
'good' and the 'happy', but also that there
*will* be such a development (at least in Jevons'
interpretation). 




Material nature does not contain goodness; it can only be found in
the human mind. Nature is depicted as a mechanical machine and
should be studied by the natural sciences. Abstract economic
theory is the mechanical analogy of these natural sciences: it is
restricted to an investigation of the social world as a mechanical
machine, and no ethical or religious considerations are taken into
account. Jevons refutes the claims of some "sentimental
writers" who regard economics as a "dismal science",
because its scope is restricted to wealth. These authors depict
economics as a mechanical and miserable body of theories, whereas they
hold true that a moral science should be concerned with sympathies,
feelings and duties. Jevons uses an analogy from the natural
sciences to refute this opinion: division of labour implies that some
people investigate the mechanical aspects of iron, while other
researchers devote their time to the study of its electrical or
magnetic aspects. A physician may conclude that the health of a
particular person will be fostered if he goes to the sea, but this
person may decide otherwise by taking other considerations into
account. This is the position of economics: charity for
humanitarian reasons remains possible, but abstract economic theory
shows that this may endanger future accumulation of wealth (Black
1977d, pp. 7-8).




Earlier we discussed Jevons' use of 'representative
individuals' and the notion of 'character'. It
is also the case that Unitarians believe that the formation of an
improved character is essential, since otherwise no religious warmth
can emerge. It is unclear to what extent improvement of people
with presumed inferior character (due to class, race or gender) can be
done. In Jevons we encounter a mixture of enlightened belief in
education and prejudiced opinions against certain parts of the
population, which is certainly not unusual for the 19th
century. Nevertheless, Jevons does believe that policies to
ameliorate working class conditions and attitudes are possible,
desirable and required.