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1853 March, “Article I. The Mode of Baptism.”, in The True Baptist, volume I, number 3, Jackson, Miss.: Published by the editor, →OCLC, page 76:
With all these dilemmas and trilemmas crowding the mind, if one did not know better, one might be tempted to doubt whether any such versions were ever made at all.
A situation in which a choice must be made among three desirable options, only two of which are possible at the same time.
At the most general level, policymakers in open economies face a macroeconomic trilemma: 1. to stabilize the exchange rate; 2. to enjoy free international capital mobility; 3. to engage in a monetary policy oriented toward domestic goals. Because only two out of the three objectives can be mutually consistent, policymakers must decide which one to give up.
2018 April 18, Stephen Farry, Sorcha Eastwood, “Good Friday Agreement: why it matters in Brexit”, in (Please provide the book title or journal name), ukandeu.ac.uk:
The UK government has forced itself into a trilemma in which it has adopted three positions, only two of which can be achieved at any one time: to avoid a hard border within the island of Ireland; for the UK as whole to leave both the customs union and the single market; and to rule out any special arrangements for Northern Ireland in relation to a customs union and single market.
2023 June 2, Charles Xie, “Trilemma Trade-Offs: A New CAP Theorem For Vector Databases Has Emerged”, Forbes Technology Council, in Forbes, Forbes Media, archived from the original on 2023-06-06:
In computing, the unconquerable trilemma is embodied in the well-known CAP theorem for distributed systems, also called Brewer’s CAP theorem. This states that any distributed database can only attain two of three guarantees: consistency, availability and partition tolerance.
1851, [James William Gilbart], Logic for the Million: A Familiar Exposition of the Art of Reasoning, London: Longman, Brown, Green & Longmans, →OCLC, part IV (The Points of Reasoning), section V (Reasoning by Compound Syllogism), subsection III (The Trilemma), page 324:
It has been remarked as a characteristic of the late Sir Robert Peel, that in introducing his measures to the House of Commons, he often used the trilemma. "Three courses are before us—to go backward, to stand still, to go forward. We cannot go backward; we cannot stand still; we must, then, go forward."
1862 July 1, “Art. VII.—(1.) Kirche und Kirchen, Papstthum und Kirchenstaat. Historisch-politische Bertrachtungen von Joh. Jos. Ign. v. Döllinger. Zweiter unveränderter Abdruck. München: 1861. (2.) The Church and the Churches; or, The Papacy and The Temporal Power. An Historical and Political Review. By Dr. Döllinger. Translated by William Bernard MacCabe. London: 1862.”, in The British Quarterly Review, volume XXXVI, number LXXI, London: Jackson, Walford, & Hodder 18, St. Paul's Churchyard and Simpkin, Marshall and Co., Stationers' Hall Court; Edinburgh: W. Oliphant & Co.; Glasgow: J[ames] MacLehose; Dublin: J. Robertson, →OCLC, page 156:
And in anticipation of it, while he [Johann Joseph Ignaz von Döllinger] declares at one moment that it would be profane to limit Divine Providence to an alternative, he affirms in the next that there can be no harm whatever in shutting it up to a supposed exhaustive trilemma.
