Definition of "ratiocination"

But it will be apparent from the refutation of the ſecond Falſification, wherewith you charge the Author of the Letters, that theſe miſchievous conſequences are rightly drawn from the wicked principle layd down by Vaſquez [Gabriel Vásquez] in the ſame place, and accordingly, that that Jeſuit hath not done violence to the rules of ratiocination, but to thoſe of the Goſpel.

1658, [Blaise Pascal], transl. sometimes attributed to John Evelyn, “The Answer of a Certain Apologist for the Jesuits to the XII. Letter, Refuted”, in Les Provinciales, or, The Mystery of Jesvitisme. Discovered in Certain Letters, Written upon Occasion of the Present Differences at Sorbonne, between the Jansenists and the Molinists: Displaying the Pernicious Maximes of the late Casuists, 2nd corrected edition, London: Printed for Richard Royston, and are to be sold by Robert Clavell, at the Stags-Head neer St. Gregories Church in St. Pauls Church-yard, page 196

He'd run in Debt by Diſputation, / And pay with Ratiocination. / All this by Syllogiſm, true / In Mood and Figure, he wou'd do.

1663, Samuel Butler, Hudibras. The First Part. Written in the Time of the Late Wars, London: Printed by J. G. for Richard Marriot [...]; republished as Hudibras. In Three Parts. Written in the Time of the Late Wars. Corrected and Amended: with Additions. To which is Added Annotations, with an Exact Index to the Whole. Adorn’d with a New Set of Cuts, from the Designs of Mr. [William] Hogarth, Dublin: Printed by S. Powell, for R. Gunne, G. Risk, G. Ewing, and W. Smith, 1732, canto I, page 20, lines 77–80

Reasoning, in the extended sense in which I use the term, and in which it is synonymous with Inference, is popularly said to be of two kinds: reasoning from particulars to generals, and reasoning from generals to particulars; the former being called Induction, the latter Ratiocination or Syllogism. […] The meaning intended by these expressions is, that Induction is inferring a proposition from propositions less general than itself, and Ratiocination is inferring a proposition from propositions equally or more general.

1843, John Stuart Mill, “Of Inference, or Reasoning, in General”, in A System of Logic, Ratiocinative and Inductive, being a Connected View of the Principles of Evidence, and the Methods of Scientific Investigation. […], volume I, London: John W[illiam] Parker, […], § 3, page 223

It is hard to follow the kinks of woman suffrage ratiocination.

1916 June 8, “Suffrage at Chicago”, in The New York Times‎

As the requirements of mass democracy forced the gentleman intellectual from the political scene, the new style political leaders felt the need to flatter the electorate by stressing the superiority of inborn, natural, intuitive and folkish wisdom and to devaluate the ratiocinations of the cultivated.

1965, Lewis A. Coser, The Nation, volume 201, New York, N.Y.: J. H. Richards, page 166, column 2; republished as “Anti-intellectualism”, in A Handful of Thistles: Collected Papers in Moral Conviction, New Brunswick, N.J.: Transaction Books, 1988, page 149

Finally Tao comes to possess the meaning of “rational speech” or “word,” and in this sense it closely resembles the Greek Logos, for in addition to its philosophical significance the term Tao touches a religious chord in the souls of the Chinese just as did the word Logos among the Platonists and the Greek Christians. […] The Tao of man, jan tao [footnote: 人道], is the process of ratiocination, and as such it is fallible; but there is an Eternal Reason, ch‘ang tao [footnote: 常道], also called t‘ien tao [footnote: 天道], “Heaven’s Reason,” i.e., the world-order which shapes all things, and the burden of Lao-tze’s message is to let this Heaven’s Reason or Eternal Reason prevail.

1913, Paul Carus, “Introduction”, in Lao-tze, translated by Paul Carus, The Canon of Reason and Virtue: 老子 道德經: Being Lao-tze’s Tao Teh King: Chinese and English, Chicago, Ill.: Open Court Publishing Company, pages 14–15

Where the Qur’an has not been explicit, the Hadith has often supplied guidance, providing an intermediate source of knowledge between the text of the Holy Book itself and the ratiocinations of the religious lawyers, the fuqaha’, who had recourse, when all else failed, to such principles as analogical reasoning and personal judgement.

1975, C[lifford] E[dmund] Bosworth, “Foreword”, in Imam Nawawi, translated by Muhammad Zafrulla Khan, Gardens of the Righteous: Riyadh as-Salihin, Abingdon, Oxon.: Published with the permission of Routledge by Islam International Publications Limited, published 2007, page vii