"[…] in the Law of Errors we are concerned only with the objective quantities about which mathematical reasoning is ordinarily exercised; whereas in the Method of Least Squares, as in the moral sciences, we are concerned with a psychical quantity - the greatest possible quantity of advantage." (Francis Y Edgeworth, "The method of least squares", 1883)
"It may be replied that the principles of greatest advantage and greatest probability do not coincide in .qeneral; that here, as in other departments of action~ when there is a discrepancy between the principle of utility and any other rul% the former should have precedence." (Francis Y Edgeworth, "The method of least squares", 1883)
"The probable error, the mean error, the mean square of error, are forms divined to resemble in an essential feature the real object of which they are the imperfect symbols - the quantity of evil, the diminution of pleasure, incurred by error. The proper symbol, it is submitted, for the quantity of evil incurred by a simple error is not any power of the error, nor any definite function at all, but an almost arbitrary function, restricted only by the conditions that it should vanish when the independent variable, the error, vanishes, and continually increase with the increase of the error." (Francis Y Edgeworth, "The method of least squares", 1883)
"Our reasoning appears to become more accurate as our ignorance becomes more complete; that when we have embarked upon chaos we seem to drop down into a cosmos." (Francis Y Edgeworth, "The Philosophy of Chance", Mind Vol. 9, 1884)
"Probability may be described, agreeably to general usage, as importing partial incomplete belief." (Francis Y Edgeworth, "The Philosophy of Chance", Mind Vol. 9, 1884)
"Observations and statistics agree in being quantities grouped about a Mean; they differ, in that the Mean of observations is real, of statistics is fictitious. The mean of observations is a cause, as it were the source from which diverging errors emanate. The mean of statistics is a description, a representative quantity put for a whole group, the best representative of the group, that quantity which, if we must in practice put one quantity for many, minimizes the error unavoidably attending such practice. Thus measurements by the reduction of which we ascertain a real time, number, distance are observations. Returns of prices, exports and imports, legitimate and illegitimate marriages or births and so forth, the averages of which constitute the premises of practical reasoning, are statistics. In short, observations are different copies of one original; statistics are different originals affording one ‘generic portrait’. Different measurements of the same man are observations; but measurements of different men, grouped round l’homme moyen, are prima facie at least statistics." (Francis Y Edgeworth, 1885)
"What is required for the elimination of chance is not that the raw material of our observations should fulfill the law of error; but that they should be constant to any law." (Francis Y Edgeworth, 1885)
"The Calculus of Probabilities is an instrument which requires the living hand to direct it" (Francis Y Edgeworth, 1887)
"The swarm of probabilities flying hither and thither, does not settle down on any particular point" (Francis Y Edgeworth, 1887)
"However we define error, the idea of calculating its extent may appear paradoxical. A science of errors seems a contradiction in terms." (Francis Y Edgeworth, "The Element of Chance in Competitive Examinations", Journal of the Royal Statistical Society Vol. 53, 1890)
"What real and permanent tendencies there are lie hid beneath the shifting superfices of chance, as it were a desert in which the inexperienced traveller mistakes the temporary agglomerations of drifting sand for the real configuration of the ground" (Francis Y Edgeworth, 1898)
"[...] the great objection to the geometric mean is its cumbrousness." (Francis Y Edgeworth, 1906)
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