## Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences |

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abscissa abstract Appendix articles of contract Bertrand's Theorem Calculus of Variations capacity for happiness catallactic combination conception condition consideration contract-curve contractors corresponding curve cycloid dealer deduce deductive reasoning definition demand-curve determinate differential equation diminished distribuend distribution Economics Egoistic energy equilibrium Ethics fatigue favourable field of competition final settlements force Fortnightly function given greatest possible Hedonics Herbert Spencer imperfection increase increment indefinite number indeterminate indifference indifference curves indifference-curve individual intersection J. S. Mill Jevons labour landlord less limit locus mathematical analysis mathematical psychics mathematical reasoning matical maximum means megisthedone method minimum moral negative object parties perfect competition perhaps physical Political Economy positive postulate precise premisses present principle problem Professor Jevons's pure utilitarianism quantity rate of exchange recontract remuneration sense sentient Sidgwick sort species suppose tenant tends theorem theory tion Todhunter's Trades Unions utilitarian utility variable wage-fund Walras zero

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Page 2 - there are data which, though not numerical are quantitative—for example, that a quantity is greater or less than another, increases or decreases, is positive or negative, a maximum or minimum,, —there mathematical reasoning is possible and may be indispensable. To take a trivial instance : a is greater than b, and b is ' greater than c, therefore a is greater than c. Here is

Page 30 - says with reference to a similar case, ' Such a transaction must be settled upon other than strictly economical grounds. . . . The art of bargaining consists in the buyer ascertaining the lowest price at which the seller is willing to part with his object, without disclosing, if possible, the highest price which he, the buyer, is willing to give.

Page 84 - are manifestly inapplicable where the causes on which any class of phenomena depend are so imperfectly accessible to our observation, that we cannot ascertain by a proper induction their numerical laws.

Page 15 - II. SUCH are some of the preliminary considerations by which emboldened we approach the two fields into which the Calculus of Pleasure may be subdivided, namely Economics and Utilitarian Ethics. The Economical Calculus investigates the equilibrium of a system of hedonic forces each tending to maximum individual utility ; the Utilitarian Calculus, the equilibrium of a system in which each and all tend to maximum

Page 35 - it will in general be possible for one of the Ys (without the consent of the other) to recontract with the two Xs, so that for all those three parties the recontract is more advantageous than the previously existing contract. For the right line joining the origin to (the neighbourhood of)

Page 1 - salient feature. (1) The science of quantity is not alien to the study of man, it will be generally admitted, in so far as actions and effective desires can be numerically measured by way of statistics—that is, very far, as Professor Jevons 2 anticipates. But in so far as our data may consist of > 1

Page 50 - the foundations of the uniformities of Physics; if competition is found wanting, not only the regularity of law, but even the impartiality of chance—the throw of a die loaded with villainy—economics would be indeed a ' dismal science,' and the reverence for competition would be no more.

Page 16 - first principle of Economics 2 is that every agent is actuated only by self-interest. The workings of this principle may be viewed under two aspects, according as the agent acts without, or with, the 1 See Appendix IV.

Page 17 - of his sacrifice. The articles of contract are in this case the amount of sacrifice to be made by each, and the principle of distribution. ' Is it peace or war ? ' asks the lover of ' Maud,' of economic competition, and answers hastily : It is both, pax or pact between contractors during contract, war, when some of the contractors without the

Page 127 - To treat variables as constants is the characteristic vice of the unmathematical economist. Many of the errors criticised by M. Walras are of this character. The predeterminate Wage-fund is a signal instance.