Meaning and origin of the Ceteris Paribus term

Maybe Aristotle was the first to state it:

ἔστω γὰρ αὕτη ἡ ἀπόδειξις βελτίων τῶν ἄλλων τῶν αὐτῶν ὑπαρχόντων, ἡ ἐξ ἐλαττόνων αἰτημάτων ἢ ὑποθέσεων ἢ προτάσεων...:  We may assume the superiority ceteris paribus (other circumstances being similar) of the demonstration which derives from fewer postulates or hypotheses — in short from fewer premisses; for, given that all these are equally well known, where they are fewer knowledge will be more speedily acquired, and that is a desideratum. Posterior Analytics, I, 25.

Some say that the term was coined by Cicero:

Cicero (44BC) De Officiis I, xv: si cetera paria sunt: if other matters are equal.

Cicero (44BC) De Officiis I, xxiii: Quid si haec paria in utroque?: What if these are equal in both?

Seneca, De Beneficis (62), IV, 35, 3: Omnia esse debent eadem, quae fuerunt (rebus sic stantibus)

Nicolai de Oresme, Quaestiones Animam II, 17: quia cetera non sunt paria:

Nicolai de Oresme, Quaestiones Physicam 7, 10: ceteris omnibus paris:

Bernardino Telesio, De rerum natura, Pro., ...naturam... quae summe sibi ipsi concors idem semper et eodem agit modo atque idem semper operatur.

Ulloa, J. (1711) Prodromus, caetera non sunt paria (266); concede si caetera sint paria, nega si disparia (166) ...quando caetera fuerint paria, neganda vero quando fuerint imparia (424).

George Campbell (1776), Phil Rhet, 76: "This is the ordinary course of nature." "Such an event may reasonable be expected, when all the attendant circumstances be similar."

Lainez, J. (1886) Disputationes, v.2, II, I,, 2. p.229: si caetera paria sint.

An interesting definition by G. Reed Thesaurus, (1891) p.35 : Quando in una re a similitudine argumentamur ad aliam; v.g. sicut se habet genus ad speciem; sic se habet materia ad compositum; ergo sicut genus in recto praedicatur de specie, etiam materia praedicabitur de composito. Resp. negando consequen. quia cetera non sunt paria: disparitas est in hoc, quia genus est totum potentiale, et ut totum significatur, materia vero semper est pars. Et huc venit illud; «est par, vel est dispar ratio »; nam ubi cetera non sunt paria, debet disparitas, aut dispar ratio assignari. Also, ceteris vel omnibus paribus.

One of the most authoritative statements comes from Jakob Bernoulli who was the pioneer of Probability:

Jakob Bernoulli, Ars Conjectandi, 224: in simili rerum statu (in a similar state of affairs [of things]) clearly denoting a systems view. The complete quotation is very clear: Quandoquidem praesumi debet, tot casibus unumquodque posthac contingere et non contingere posse, quoties id antehac in simili rerum statu contigisse et non contigisse fuerit deprehensum. (For it should be presumed that each event will occur or not occur in the future as many times as it has been observed, in a similar state of affairs, to have occurred or not occurred in the past.) From Adams, W. (1974) The Life and Times of the CLT, 10.

No comments:

Post a Comment