Mathematical psychics: An essay on the application of mathematics to the moral sciences

F. Y. Edgeworth

London, 1881

Abstract

In Mathematical Psychics (1881), F. Y. Edgeworth investigates the application of mathematical methods—particularly the calculus of variations and dynamical maximum principles—to the moral sciences, dividing the field into an economical calculus and a utilitarian calculus. He argues that mathematical reasoning does not require precise numerical data to be valid, demonstrating that deductive analysis can proceed from general quantitative properties such as diminishing marginal utility and increasing fatigue, analogous to maximum energy principles in physics. In the economical section, Edgeworth models bargaining and exchange between self-interested individuals using indifference curves and introduces the concept of the contract curve. He demonstrates that whereas contract in a perfect market with an indefinite multiplicity of competitors is determinate, contract under conditions of imperfect competition—such as limited numbers of dealers, trade combinations, or collective associations—is indeterminate, yielding multiple possible final settlements and creating deadlocks that necessitate principles of arbitration. In the utilitarian calculus, Edgeworth proposes the maximization of aggregate happiness across sentients as the rational basis for resolving this indeterminateness. Treating pleasure as a measurable quantity across intensity, time, and number, he examines the optimal distribution of means, labor, and population. From these models, he deduces that the greatest total utility requires assigning resources and work according to differing individual capacities for pleasure and effort, concluding that utilitarianism does not inherently mandate equal distribution among sentients who differ in their capacity for happiness. – AI-generated abstract.

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‘Méchanique Sociale’ may one day take her place along with ‘Mécanique Celeste’, throned each upon the double-sided height of one maximum principle, the supreme pinnacle of moral as of physical science. As the movements of each particle, constrained or loose, in a material cosmos are continually subordinated to one maximum sum-total of accumulated energy, so the movements of each soul, whether selfishly isolated or linked sympathetically, may continually be realizing the maximum energy of pleasure, the Divine love of the universe.

hedonium
p. 12

[T]he general term [‘pleasure’] does not appear to call up with equal facility all the particulars which are meant to be included under it, but rather the grosser feelings than for instance the ‘joy and felicity’ of devotion.

pleasure
pp. 56-57

[L]et there be granted to the science of pleasure what is granted to the science of energy ; to imagine an ideally perfect instrument, a psychophysical machine, continually registering the height of pleasure experienced by an individual, exactly according to the verdict of consciousness, or rather diverging therefrom according to a law of errors. From moment to moment the hedonimeter varies; the delicate index now flickering with the flutter of the passions, now steadied by intellectual activity, low sunk whole hours in the neighbourhood of zero, or momentarily springing up towards infinity. The continually indicated height is registered by photographic or other frictionless apparatus upon a uniformly moving vertical plane. Then the quantity of happiness between two epochs is represented by the area contained between the zero-line, perpendiculars thereto at the points corresponding to the epochs, and the curve traced by the index; or, if the correction suggested in the last paragraph be admitted, another dimension will be required for the representation.

hedonimetry
p. 101