Editing Trilemma

{{Short description|Difficult choice from three options}}
{{Multiple issues|
{{Unfocused|date=March 2024}}
{{Original research|date=March 2024}}
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A '''trilemma''' is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two [[Logical equivalence|logically equivalent]] ways in which to express a trilemma: it can be expressed as a choice among three unfavourable options, one of which must be chosen, or as a choice among three favourable options, only two of which are possible at the same time.

The term derives from the much older term ''[[dilemma]]'', a choice between two or more difficult or unfavourable alternatives. The earliest recorded use of the term was by the British preacher [[Philip Henry (clergyman)|Philip Henry]] in 1672, and later, apparently independently, by the preacher [[Isaac Watts]] in 1725.<ref>{{cite book |first=Allan A. |last=Metcalf |title=Predicting New Words: The Secrets of Their Success |publisher=Houghton Mifflin Reference |year=2004 |pages=106–107}}</ref>

== In religion ==
=== Epicurus' trilemma ===
{{see also|Epicurean paradox}}
One of the earliest uses of the trilemma formulation is that of the Greek philosopher [[Epicurus]], rejecting the idea of an [[omnipotent]] and [[omnibenevolent]] God (as summarised by [[David Hume]]):<ref>{{cite book |last=Hume |first=David |author-link=David Hume |title=Dialogues Concerning Natural Religion |publisher=Penguin Books, Limited |year=1779 |quote=Is God willing to prevent evil, but not able? Then is He impotent. Is He able but not willing? Then is He malevolent. Is He both able and willing? Whence then is evil? |url=https://archive.org/details/bub_gb_E7dbAAAAQAAJ|page=[https://archive.org/details/bub_gb_E7dbAAAAQAAJ/page/n189 186] }}</ref>

# If God is unable to prevent evil, then he is not all-powerful.
# If God is not willing to prevent evil, then he is not all-good.
# If God is both willing and able to prevent evil, then why does evil exist?

Although traditionally ascribed to Epicurus and called [[Epicurus' trilemma]], it has been suggested that it may actually be the work of an early [[Philosophical skepticism|skeptic]] writer, possibly [[Carneades]].<ref>{{cite book |first=Mark Joseph |last=Larrimore |title=The Problem of Evil: a reader |publisher=Blackwell |year=2001}}</ref>

In studies of philosophy, discussions, and debates related to this trilemma are often referred to as being about the ''[[problem of evil]]''.

===Apologetic trilemma===
{{main|Lewis's trilemma}}
One well-known trilemma is sometimes used by [[Christian apologetics|Christian apologists]] considered a proof of the divinity of [[Jesus]],<ref>{{cite book |first=Steven T. |last=Davis |chapter-url=https://books.google.com/books?id=zsqAx7B_TJIC&pg=PA166 |chapter=Was Jesus Mad, Bad or God? |editor=Michael C. Rea |title=Oxford Readings in Philosophical Theology |volume=1: Trinity, Incarnation, and Atonement |publisher=Oxford University Press |year=2009 |page=166|isbn=9780199237470 }}</ref> and is most commonly known in the version by [[C. S. Lewis]]. It proceeds from the premise that Jesus claimed to be God, and that therefore one of the following must be true:<ref>{{cite book |last=Lewis |first=C.S. |year=1952 |title=Mere Christianity |pages=54–56 |chapter=Chapter 3: The Shocking Alternative |location=London |publisher=Collins|title-link=Mere Christianity }}</ref>

# ''Lunatic'': Jesus was not God, but he mistakenly believed that he was.
# ''Liar'': Jesus was not God, and he knew it, but he said so anyway.
# ''Lord'': Jesus is God.

The trilemma, usually in Lewis' formulation, is often used in works of popular apologetics, although it is almost completely absent from discussions about the status of Jesus by professional theologians and biblical scholars.<ref>{{cite book |chapter=Was Jesus Mad, Bad, or God? |first1=Stephen T. |last1=Davis |first2=Daniel |last2=Kendall |first3=Gerald |last3=O'Collins |title=The Incarnation: an interdisciplinary symposium on the Incarnation of the Son of God |publisher=Oxford University Press |year=2004 |pages=222–3}}</ref>

== In law ==

=== The "cruel trilemma" ===
{{main|Ex officio oath}}
The "cruel trilemma"<ref name="rubenfeld">{{cite book|last=Rubenfeld|first=Jed|title=Revolution by Judiciary: the structure of American constitutional law|year=2005|publisher=Harvard University Press|isbn=9780674017153|pages=33–35|url=https://books.google.com/books?id=4slwLg-8VLcC&q=%22cruel+trilemma%22+oath&pg=PA34}}</ref> was an [[English nation|English]] ecclesiastical and judicial weapon<ref name="fellman">{{cite book|last=Fellman|first=David|title=Defendants Rights Today|year=1979|publisher=University of Wisconsin Press|isbn=9780299072049|pages=304–306|url=https://books.google.com/books?id=6BOD1Lg1YYAC&q=%22ex+officio+oath%22+-wikipedia&pg=PA305}}</ref> developed in the first half of the 17th century, and used as a form of coercion and persecution. The format was a religious oath to tell the truth, imposed upon the accused prior to questioning. The accused, if guilty, would find themselves trapped between:
# A breach of religious oath if they lied (taken extremely seriously in that era, a [[mortal sin]]),<ref name="rubenfeld" /> as well as [[perjury]];
# [[Self-incrimination]] if they told the truth; or
# [[Contempt of court]] if they said nothing and were silent.

Outcry over this process led to the foundation of the right to not incriminate oneself being established in [[common law]] and was the direct precursor of the [[right to silence]] and non-self-incrimination in the [[Fifth Amendment to the United States Constitution]].

== In philosophy ==

=== The Münchhausen trilemma ===
{{main|Münchhausen trilemma}}
In the [[epistemology|theory of knowledge]] the Münchhausen trilemma is an argument against the possibility of proving any ''certain'' truth even in the fields of logic and mathematics. Its name is going back to a logical proof of the German philosopher [[Hans Albert]].
This proof runs as follows: All of the only three possible attempts to get a certain justification must fail:
# All justifications in pursuit of ''certain'' knowledge have also to justify the means of their justification and doing so they have to justify anew the means of their justification. Therefore, there can be no end. We are faced with the hopeless situation of an [[infinite regression]].
# One can stop at self-evidence or common sense or fundamental principles or speaking ''[[ex cathedra]]'' or at any other evidence, but in doing so the intention to install ''certain'' justification is abandoned.
# The third horn of the trilemma is the application of a [[circular argument]].

=== {{anchor|Censorship}} The trilemma of censorship ===
In [[John Stuart Mill]]'s ''[[On Liberty]]'', as a part of his argument against the suppression of free speech, he describes the trilemma facing those attempting to justify such suppression (although he does not refer to it as a trilemma, Leo Parker-Rees (2009){{Citation needed|reason=What is the '2009' referring to?|date=August 2018}} identified it as such).
If free speech is suppressed, the opinion suppressed is either:<ref>{{cite book |last=Mill |first=John Stuart |author-link=John Stuart Mill |year=1869 |title=On liberty |chapter-url=http://www.bartleby.com/130/2.html |location=London |publisher=Longman, Roberts & Green |isbn=1-58734-034-8 |edition=4th |orig-year=1859 |access-date=10 September 2014 |chapter=Chapter II: Of the Liberty of Thought and Discussion |quote=(§1).. If the opinion is right, they are deprived of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error. .. (§34) .. But there is a commoner case than either of these; when the conflicting doctrines, instead of being one true and the other false, share the truth between them; and the nonconforming opinion is needed to supply the remainder of the truth, of which the received doctrine embodies only a part.}}</ref>
# True – in which case society is robbed of the chance to exchange error for truth;
# False – in which case the opinion would create a 'livelier impression' of the truth, allowing people to justify the correct view;
#Half-true – in which case it would contain a forgotten element of the truth, that is important to rediscover, with the eventual aim of a synthesis of the conflicting opinions that is the whole truth.

===Buddhist Trilemma===
The Buddhist philosopher [[Nagarjuna]] uses the trilemma in his ''[[Verses on the Middle Way]]'',<ref>{{Cite book |last=Nāgārjuna |first=activend century |url=https://www.worldcat.org/oclc/642693197 |title=The fundamental wisdom of the middle way : Nāgārjuna's Mūlamadhyamakakārikā |date=1995 |publisher=Oxford University Press |others=Jay L. Garfield |isbn=978-0-19-509336-0 |location=New York |oclc=642693197|page=262}}</ref> giving the example that:

* a cause cannot follow its effect
* a cause cannot be coincident with its effect
* a cause cannot precede its effect

== In economics ==

=== "The Uneasy Triangle" ===
In 1952, the British magazine ''The Economist'' published a series of articles on an "Uneasy Triangle", which described "the three-cornered incompatibility between a stable price level, full employment, and&nbsp;... free collective bargaining". The context was the difficulty maintaining external balance without sacrificing two sacrosanct political values: jobs for all and unrestricted labor rights. Inflation resulting from labor militancy in the context of full employment had put powerful downward pressure on the pound sterling. Runs on the pound then triggered a long series of economically and politically disruptive "stop-go" policies (deflation followed by reflation).<ref>Editorial, "The Uneasy Triangle," ''The Economist,'' August 9, 16, and 23, 1952.</ref> [[John Maynard Keynes]] had anticipated the severe problem associated with reconciling full employment with stable prices without sacrificing democracy and the associational rights of labor.<ref>John Maynard Keynes, ''The General Theory of Employment, Interest and Money'' (London: Macmillan, 1936), 267; "The Objective of International Price Stability," Economic Journal (June–September, 1943).</ref> The same incompatibilities were also elaborated upon in [[Charles E. Lindblom]]'s 1949 book, ''Unions and Capitalism''.<ref>Charles E. Lindblom, Unions and Capitalism (New Haven: Yale University Press, 1949).</ref>

=== The "impossible trinity" ===
{{main|Impossible trinity}}
In 1962 and 1963, a trilemma (or "impossible trinity") was introduced by the economists [[Robert Mundell]] and [[Marcus Fleming]] in articles discussing the problems with creating a stable international financial system. It refers to the trade-offs among the following three goals: a [[fixed exchange rate]], national independence in [[monetary policy]], and capital mobility. According to the [[Mundell–Fleming model]] of 1962 and 1963, a small, open economy cannot achieve all three of these policy goals at the same time: in pursuing any two of these goals, a nation must forgo the third.<ref>{{Cite journal |doi = 10.1162/0034653054638300|title = The Trilemma in History: Tradeoffs Among Exchange Rates, Monetary Policies, and Capital Mobility|journal = Review of Economics and Statistics|volume = 87|issue = 3|pages = 423–438|year = 2005|last1 = Obstfeld|first1 = Maurice|last2 = Shambaugh|first2 = Jay C.|last3 = Taylor|first3 = Alan M.|s2cid = 6786669|url = https://www.dnb.nl/binaries/sr094_tcm46-146871.pdf}}</ref>

=== Wage policy trilemmas ===
In 1989 Peter Swenson posited the existence of "wage policy trilemmas" encountered by trade unions trying to achieve three egalitarian goals simultaneously. One involved attempts to compress wages within a bargaining sector while compressing wages between sectors and maximizing access to employment in the sector. A variant of this "horizontal" trilemma was the "vertical" wage policy trilemma associated with trying simultaneously to compress wages, increase the wage share of value added at the expense of profits, and maximize employment. These trilemmas helped explain instability in unions' wage policies and their political strategies seemingly designed to resolve the incompatibilities.<ref>Peter A. Swenson, Fair Shares: Unions, Pay, and Politics in Sweden and West Germany (Ithaca NY: Cornell University Press, 1989).</ref>

=== The Pinker social trilemma ===
[[Steven Pinker]] proposed another social trilemma in his books ''[[How the Mind Works]]'' and ''[[The Blank Slate]]:'' that a society cannot be simultaneously "fair", "free", and "equal". If it is "fair", individuals who work harder will accumulate more wealth; if it is "free", parents will leave the bulk of their inheritance to their children; but then it will not be "equal", as people will begin life with different fortunes.{{citation needed|date=March 2023}}

=== The political trilemma of the world economy ===
Economist [[Dani Rodrik]] argues in his book, ''The Globalization Paradox'', that democracy, national sovereignty, and global economic integration are mutually incompatible. Democratic states pose obstacles to global integration (e. g. regulatory laws, taxes and tariffs) to protect their own economies. Therefore, if we need to achieve complete economic integration, it is necessary to also remove democratic nations states. A government of some nation state could possibly pursue the goal of global integration on the expense of its own population, but that would require an authoritarian regime. Otherwise, the government would be likely replaced in the next elections.<ref>{{cite web |last1=Rodrik |first1=Dani |title=The inescapable trilemma of the world economy |url=https://rodrik.typepad.com/dani_rodriks_weblog/2007/06/the-inescapable.html |website=Dani Rodrik's weblog |access-date=9 June 2019}}</ref>

=== Holmström's theorem ===
{{main|Holmström's theorem}}
In ''Moral Hazard in Teams'',<ref>{{cite journal |last1=Holmström |first1=Bengt |title=Moral Hazard in Teams |journal=The Bell Journal of Economics |volume= 13 |issue = 2 |pages=324–340 |year=1981 |doi=10.2307/3003457 |url=https://www.econstor.eu/bitstream/10419/220831/1/cmsems-dp0471.pdf |jstor=3003457}}</ref> economist [[Bengt Holmström]] demonstrated a trilemma that arises from [[incentive system]]s. For any team of [[risk neutral preferences|risk-neutral agents]], no incentive system of revenue distribution can satisfy all three of the following conditions: [[Pareto efficiency]], [[balanced budget]], and [[Nash equilibrium|Nash stability]]. This entails three optimized outcomes:
# Martyrdom: the incentive system distributes all revenue, and no agent can improve their take by changing their strategy, but at least one agent is not receiving reward in proportion to their effort.
# Instability: the incentive system distributes all revenue, and all agents are rewarded in proportion to their effort, but at least one agent could increase their take by changing strategies.
# Insolvency: all agents are rewarded in proportion to their effort, and no shift in strategy would improve any agent's take, but not all revenue is distributed.

=== Arrow's impossibility theorem ===
{{Main article|Arrow's impossibility theorem}}
In [[social choice theory]], economist [[Kenneth Arrow]] proved that it is impossible to create a social welfare function that simultaneously satisfies three key criteria: [[Pareto efficiency]], [[Dictatorship mechanism|non-dictatorship]] and [[independence of irrelevant alternatives]].

== In politics ==
===The Brexit trilemma===
{{Main|Brexit|Northern Ireland protocol}}
Following the [[Brexit referendum]], the [[first May ministry|first May government]] decided that not only should the United Kingdom leave the European Union but also that it should leave the [[European Union Customs Union]] and the European Single Market. This meant that a customs and regulatory border would arise between the UK and the EU. Whilst the sea border between Great Britain and continental Europe was expected to present manageable challenges, the UK/EU border in Ireland was recognised as having rather more intractable issues. These were summarised in what became known as the "[[Brexit trilemma]]", because of three competing objectives: no [[Brexit and the Irish border#Hard border|hard border on the island]]; no customs [[Irish Sea border|border in the Irish Sea]]; and no British participation in the European Single Market and the European Union Customs Union. It is not possible to have all three.<ref>{{Cite web |last=Springford |first=John |date=7 March 2018 |title=Theresa May's Irish trilemma |url=https://www.cer.eu/insights/theresa-mays-irish-trilemma |access-date=17 June 2019 |publisher=Centre for European Reform}}</ref>

=== The Zionist trilemma ===

[[Zionists]] have often desired that Israel be [[Democracy|democratic]], have a [[Jewish identity]], and encompass (at least) the land of [[Mandatory Palestine]]. However, these desires (or "[[wikt:desiderata|desiderata]]") seemingly form an [[inconsistent triad]], and thus a trilemma. Palestine has an Arab majority, so any democratic state encompassing all of Palestine would likely have a [[binational]] or [[Arab identity]].

However, Israel could be:

* Democratic and Jewish, but not in all of Palestine. 
* Democratic and in all of Palestine, but not Jewish.
* Jewish and in all of Palestine, but not democratic.

This observation appears in "[[From Beirut to Jerusalem]]" (1989), by [[Thomas Friedman]], who attributes it to the political scientist {{ill|Aryeh Naor|he|אריה נאור}} (historically, the 'trilema' is inexact since early Zionist activists often (a) believed that Jews would migrate to Palestine in sufficiently large numbers; (b) proposed forms of bi-national governance; (c) preferred forms of [[communism]] over democracy).

=== The Žižek trilemma ===
[[File:Communist 3lemma.svg|thumb|The Zizek Trilemma illustrates the impossibility of demonstrating loyalty to the Communist regime while also being honest and intelligent.]]
The "Žižek trilemma" is a humorous formulation on the incompatibility of certain personal [[virtues]] under a constraining [[ideological]] framework. Often attributed to the philosopher [[Slavoj Žižek]], it is actually quoted by him as the product of an anonymous source:
<blockquote>
One cannot but recall here a witty formula of life under a hard [[Communist regime]]: Of the three features—personal honesty, sincere support of the regime and intelligence—it was possible to combine only two, never all three. If one were honest and supportive, one was not very bright; if one were bright and supportive, one was not honest; if one were honest and bright, one was not supportive.<ref>Slavoj Žižek [http://www.inthesetimes.com/article/3183/ "The Dreams of Others"] {{Webarchive|url=https://web.archive.org/web/20141121104328/http://www.inthesetimes.com/article/3183/ |date=2014-11-21 }} In These Times, May 18, 2007</ref>
</blockquote>

== In business ==

=== The project-management trilemma ===
[[File:Project management triangle - fast cheap good.pdf|thumb|The [[project management triangle]] as a "pick any two" [[Euler diagram]]]]
[[Arthur C. Clarke]] cited a management trilemma encountered when trying to achieve production quickly and cheaply while maintaining high quality.<ref>Arthur C. Clarke, The Ghost from the Grand Banks, (Gollancz, London, 1990), page 73.</ref> In the [[software]] industry, this means that one can pick any two of: fastest time to market, highest software quality (fewest defects), and lowest cost (headcount). This is the basis of the popular [[project management]] aphorism "Quick, Cheap, Good: Pick two," conceptualized as the [[project management triangle]] or "[[quality, cost, delivery]]".

=== The trilemma of an encyclopedia ===
The ''[[Stanford Encyclopedia of Philosophy]]'' is said<ref>{{cite web|url=http://scroll.in/article/757969/this-free-online-encyclopedia-has-achieved-what-wikipedia-can-only-dream-of|title=This free online encyclopedia has achieved what Wikipedia can only dream of|date=September 26, 2015|author=Sonnad, Nikhil|work=Scroll.in}}</ref> to have overcome the trilemma that an encyclopedia cannot be authoritative, comprehensive and up-to-date all at the same time for any significant duration.

== In computing and technology ==

===In data storage===
The [[RAID]] technology may offer two of three desirable values: (relative) inexpensiveness, speed or reliability ([[RAID 0]] is fast and cheap, but unreliable; [[RAID 6]] is extremely expensive and reliable, with correct performance and so on). A common phrase in data storage, which is the same in project management, is "fast, cheap, good: choose two".

The same saying has been [[pastiche]]d in [[Quiet PC|silent computing]] as "fast, cheap, quiet: choose two".

In researching magnetic recording, used in [[hard drive]] storage, a trilemma arises due to the competing requirements of readability, writeability and stability (known as the Magnetic Recording Trilemma).  Reliable data storage means that for very small bit sizes the magnetic medium must be made of a material with a very high [[coercivity]] (ability to maintain its magnetic domains and withstand any undesired external magnetic influences).<ref name="backblaze_dec_2017">{{Cite web | url=http://www.guru3d.com/news-story/backblaze-on-hamr-hdd-technology.html |title = Backblaze on HAMR HDD Technology| date=18 December 2017 }}</ref>  But this coercivity must be overridden by the drive head when data is written, which means an extremely strong magnetic field in a very tiny space,<ref name="backblaze_dec_2017" /><ref name="Seagate_HAMR_technical">{{Cite web|url=https://www.seagate.com/www-content/ti-dm/tech-insights/en-us/docs/TP707-1-1712US_HAMR.pdf|title=Seagate HAMR technical brief}}</ref> but the size occupied by one [[bit]] of data eventually becomes so small that the strongest magnetic field able to be created in the space available, is not strong enough to allow data writing.<ref name="backblaze_dec_2017" />  In effect, a point exists at which it becomes impractical or impossible to make a working disk drive because magnetic writing activity is no longer possible on such a small scale.<ref>{{Cite journal|url=https://ieeexplore.ieee.org/document/824422/;jsessionid=P12MczFuLo_0cMH_GYjBrXj1SEzzegHPeL7Kg7sfzqivLvZyGh2f!-1598427568|title=The feasibility of magnetic recording at 1 Terabit per square inch|first=R.|last=Wood|date=January 11, 2000|journal=IEEE Transactions on Magnetics|volume=36|issue=1|pages=36–42|via=IEEE Xplore|doi=10.1109/20.824422|bibcode=2000ITM....36...36W |url-access=subscription}}</ref><ref name="backblaze_dec_2017" /> [[Heat-assisted magnetic recording]] (HAMR) and Microwave Assisted Magnetic Recording (MAMR) are technologies that aim to modify coercivity during writing only, to work around the trilemma<ref>{{Cite journal|url=https://ieeexplore.ieee.org/document/5257351|title=Future Options for HDD Storage|first1=Y.|last1=Shiroishi|first2=K.|last2=Fukuda|first3=I.|last3=Tagawa|first4=H.|last4=Iwasaki|first5=S.|last5=Takenoiri|first6=H.|last6=Tanaka|first7=H.|last7=Mutoh|first8=N.|last8=Yoshikawa|date=October 11, 2009|journal=IEEE Transactions on Magnetics|volume=45|issue=10|pages=3816–3822|via=IEEE Xplore|doi=10.1109/TMAG.2009.2024879|bibcode=2009ITM....45.3816S |s2cid=24634675 |url-access=subscription}}</ref>..

=== In anonymous communication protocols ===
[[Anonymous communication]] protocols can offer two of the three desirable properties: strong anonymity, low [[bandwidth (computing)|bandwidth]] overhead, low [[network latency|latency]] overhead.<ref>{{Cite web|url=https://eprint.iacr.org/2017/954|title=Strong Anonymity, Low Bandwidth Overhead, Low Latency — Choose Two.|date=2017 }}</ref>

Some anonymous communication protocols offer anonymity at the cost of high bandwidth overhead, that means the number of messages exchanged between the protocol parties is very high. Some offer [[anonymity]] with the expense of latency overhead (there is a high delay between when the message is sent by the sender and when it is received by the receiver). There are protocols which aims to keep the bandwidth overhead and latency overhead low, but they can only provide a weak form of anonymity.<ref>{{Cite web|url=https://blog.torproject.org/blog/one-cell-enough|title=One cell is enough to break Tor's anonymity.|access-date=2018-07-17|archive-date=2010-09-20|archive-url=https://web.archive.org/web/20100920113629/http://blog.torproject.org/blog/one-cell-enough|url-status=dead}}</ref>

=== In clustering algorithms ===
Kleinberg demonstrated through an axiomatic approach to clustering that no clustering method can satisfy all three of the following fundamental properties at the same time:<ref>{{Cite conference |last=Kleinberg |first=Jon |year=2002 |title=An Impossibility Theorem for Clustering |url=https://proceedings.neurips.cc/paper_files/paper/2002/file/43e4e6a6f341e00671e123714de019a8-Paper.pdf |conference=Advances in Neural Information Processing Systems |publisher=MIT Press |volume=15 |book-title= |editor=}}</ref>

# '''Scale Invariance''': The clustering results remain the same when distances between data points are proportionally scaled.
# '''Richness''': The method can produce any possible partition of the data.
# '''Consistency''': Changes in distances that align with the clustering structure (e.g., making closer points even closer) do not alter the results.

===Other (technology)===
The [[CAP theorem]], covering guarantees provided by [[distributed database management system|distributed systems]], and [[Zooko's triangle]] concerning naming of participants in [[Communication protocol|network protocols]], are both examples of other trilemmas in technology. 

== See also ==
* [[Ternary plot]]
* [[Trichotomy (philosophy)]]
* [[Inconsistent triad]]
* [[Condorcet paradox]]
* [[Tetralemma]]

== References ==
{{Reflist}}

== External links ==
{{Wiktionary}}
* {{cite EB1911 |wstitle = Trilemma }}

[[Category:Lemmas]]
[[Category:Rhetoric]]