The truths of science are expressed in the form of propositions. Propositions of this kind express an identity between a part of B and the whole of A. Jevons lists several forms of inference:. Jevons indicates that traditional syllogistic forms such as Barbara, Celarent, Darii etc. It is also convenient to represent more complicated cases, such as inferences derived from more than two premises. Contemporaries such as Boole and Robertson were very critical towards Jevons's use of mathematical symbols in logic.
Hence, if a metal is an element, it follows that a non-element is a non-metal. The method of indirect inference can be used to describe a class of objects or a term, given certain conditions. 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. 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. 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. 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. 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. 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.
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In Jevons published A Serious Fall in the Value of Gold , which investigated the influence of Australian and Californian gold discoveries of 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. Aldrich 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 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.
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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. 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 seems to be a mathematical, deductive economist. 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.
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. 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. 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 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.
Papers and Correspondence of William Stanley Jevons: Volume V Correspondence, 1879-1882
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. 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 This paper does not appear to have attracted much attention either in or on its publication four years later in the Journal of the Statistical Society ; and it was not till , when the Theory of Political Economy appeared, that Jevons set forth his doctrines in a fully developed form.
It was not till after the publication of this work that Jevons became acquainted with the applications of mathematics to political economy made by earlier writers, notably Antoine Augustin Cournot and HH Gossen.
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As regards the discovery of the connection between value in exchange and final or marginal utility, the priority belongs to Gossen, but this in no way detracts from the great importance of the service which Jevons rendered to British economics by his fresh discovery of the principle, and by the way in which he ultimately forced it into notice. In his reaction from the prevailing view he sometimes expressed himself without due qualification: the declaration, for instance, made at the commencement of the Theory of Political Economy , that value depends entirely upon utility, lent itself to misinterpretation.
But a certain exaggeration of emphasis may be pardoned in a writer seeking to attract the attention of an indifferent public. The Neoclassical Revolution , which would reshape economics, had been started.
Black, R(obert) D(enis) Collison
Jevons did not explicitly distinguish between the concepts of ordinal and cardinal utility. Cardinal utility allows the relative magnitude of utilities to be discussed, while ordinal utility only implies that goods can be compared and ranked according to which good provided the most utility. Although Jevons predated the debate about ordinality or cardinality of utility, his mathematics required the use of cardinal utility functions.
For example, in The Theory of Political Economy, Chapter II, the subsection on "Theory of Dimensions of Economic Quantities", Jevons makes the statement that "In the first place, pleasure and pain must be regarded as measured upon the same scale, and as having, therefore, the same dimensions, being quantities of the same kind, which can be added and subtracted Note that cardinality does not imply direct measurability, in which Jevons did not believe.
It was not, however, as a theorist dealing with the fundamental data of economic science, but as a brilliant writer on practical economic questions, that Jevons first received general recognition. A Serious Fall in the Value of Gold and The Coal Question placed him in the front rank as a writer on applied economics and statistics; and he would be remembered as one of the leading economists of the 19th century even had his Theory of Political Economy never been written. Amongst his economic works may be mentioned Money and the Mechanism of Exchange , written in a popular style, and descriptive rather than theoretical, but wonderfully fresh and original in treatment and full of suggestiveness, a Primer on Political Economy , The State in Relation to Labour , and two works published after his death, namely, Methods of Social Reform and Investigations in Currency and Finance , containing papers that had appeared separately during his lifetime.
The last-named volume contains Jevons' speculations on the connection between commercial crises and sunspots. He was engaged at the time of his death upon the preparation of a large treatise on economics and had drawn up a table of contents and completed some chapters and parts of chapters. This fragment was published in under the title of The Principles of Economics: a fragment of a treatise on the industrial mechanism of society, and other papers. In The Coal Question , Jevons covered a breadth of concepts on energy depletion that have recently been revisited by writers covering the subject of peak oil.
For example, Jevons explained that improving energy efficiency typically reduced energy costs and thereby increased rather than decreased energy use, an effect now known as the Jevons paradox. The Coal Question remains a paradigmatic study of resource depletion theory. Jevons's son, H. Stanley Jevons, published an page follow-up study in in which the difficulties of estimating recoverable reserves of a theoretically finite resource are discussed in detail. In a relatively minor work, "Commercial Crises and Sun-Spots",  Jevons analyzed business cycles, proposing that crises in the economy might not be random events, but might be based on discernible prior causes.
To clarify the concept, he presented a statistical study relating business cycles with sunspots.