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Saturday, October 21, 2023

Trilemma

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Trilemma

A trilemma is a difficult choice from three options, each of which is (or appears) unacceptable or unfavourable. There are two 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 in 1672, and later, apparently independently, by the preacher Isaac Watts in 1725.

In religion

Epicurus' trilemma

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):

  1. If God is unable to prevent evil, then he is not all-powerful.
  2. If God is not willing to prevent evil, then he is not all-good.
  3. 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 skeptic writer, possibly Carneades.

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

Apologetic trilemma

One well-known trilemma is sometimes used by Christian apologists considered a proof of the divinity of Jesus, 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:

  1. Lunatic: Jesus was not God, but he mistakenly believed that he was.
  2. Liar: Jesus was not God, and he knew it, but he said so anyway.
  3. 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.

In law

The "cruel trilemma"

The "cruel trilemma" was an English ecclesiastical and judicial weapon 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:

  1. A breach of religious oath if they lied (taken extremely seriously in that era, a mortal sin), as well as perjury;
  2. Self-incrimination if they told the truth; or
  3. 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

In the 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:

  1. 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.
  2. 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.
  3. The third horn of the trilemma is the application of a circular argument.

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) identified it as such). If free speech is suppressed, the opinion suppressed is either:

  1. True – in which case society is robbed of the chance to exchange error for truth;
  2. False – in which case the opinion would create a 'livelier impression' of the truth, allowing people to justify the correct view;
  3. 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, 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 ... 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 put powerful downward pressure on the pound sterling. Runs on the pound triggered a long series of economically and politically disruptive "stop-go" policies (deflation followed by reflation). 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. The same incompatibilities were also elaborated on in Charles E. Lindblom's 1949 book, Unions and Capitalism.

The "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.

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.

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.

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.

Holmström's theorem

In Moral Hazard in Teams, economist Bengt Holmström demonstrated a trilemma that arises from incentive systems. For any team of risk-neutral agents, no incentive system of revenue distribution can satisfy all three of the following conditions: Pareto efficiency, balanced budget, and Nash stability. This entails three optimized outcomes:

  1. 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.
  2. 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.
  3. 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.

In politics

The Brexit trilemma

Following the Brexit referendum, the 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 hard border on the island; no customs 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.

The Zionist trilemma

Zionists have often desired that Israel be democratic, have a Jewish identity, and encompass (at least) the land of Mandatory Palestine. However, these desires (or "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 Aryeh Naor [he] (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

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:

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.

In business

The project-management trilemma

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. 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 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 the three desirable value: (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 is "fast, cheap, good: choose two".

The same saying has been pastiched in 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). 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, 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. 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. 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...

In anonymous communication protocols

Anonymous communication protocols can offer two of the three desirable properties: strong anonymity, low bandwidth overhead, low latency overhead.

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.

Other (technology)

The CAP theorem, covering guarantees provided by distributed systems, and Zooko's triangle concerning naming of participants in network protocols.

Misuse of the term: "The Trilemma of the Earth"

The Trilemma of the Earth (or 3E Trilemma) is a term used by scientists working on energy and environment protection. 3E Trilemma stands for Economy-Energy-Environment interaction.

For the activation of economic development (E: Economy) to occur, we need to increase the energy expenditure (E: Energy) however this raises the environmental issue (E: Environment) of more emissions of pollutant gases.

This, however, is not an actual trilemma.(source and/or clarification needed)

Theodicy and the Bible

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Theodicy_and_the_Bible

Relating theodicy and the Bible is crucial to understanding Abrahamic theodicy because the Bible "has been, both in theory and in fact, the dominant influence upon ideas about God and evil in the Western world". Theodicy, in its most common form, is the attempt to answer the question of why a good God permits the manifestation of evil. Theodicy attempts to resolve the evidential problem of evil by reconciling the traditional divine characteristics of omnibenevolence and omnipotence, in either their absolute or relative form, with the occurrence of evil or suffering in the world.

Theodicy is an "intensely urgent" and "constant concern" of "the entire Bible". The Bible raises the issue of theodicy by its portrayals of God as inflicting evil and by its accounts of people who question God's goodness by their angry indictments. However, the Bible "contains no comprehensive theodicy".

The most common theodicy is free will theodicy, which lays the blame for all moral evil and some natural evil on humanity's misuse of its free will.

God and evil in the Bible

Barry Whitney gives the reason why a theodicy is important for those who believe in the biblical God when he observes that "it is the believer in God, more so than the skeptic, who is forced to come to terms with the problem of evil."

Biblical scholar Walter Brueggemann observes that "theodicy is a constant concern of the entire Bible" and he describes theodicy, from the biblical perspective, as a subject that "concerns the question of God's goodness and power in a world that is manifestly marked by disorder and evil." The Bible evokes a need for a theodicy by its indictments of God coupled with expressions of anger at God, both of which question God's righteousness.

The Bible contains numerous examples of God inflicting evil, both in the form of moral evil resulting from "man's sinful inclinations" and the physical evil of suffering. These two biblical uses of the word evil parallel the Oxford English Dictionary's definitions of the word as (a) "morally evil" and (b) "discomfort, pain, or trouble." The Bible sometimes portrays God as inflicting evil in the generic sense.

In other cases, the word evil refers to suffering. Suffering results from either (a) "'moral' evil, due to human volition" or (b) "'physical' evil, directly due to nature." The Bible portrays God as inflicting evil in both senses because its writers "regarded God as the ultimate Cause of evil." The Bible contains examples of suffering caused by nature that are attributed to God, as well as examples of suffering caused by humans that are attributed to God.

Biblical responses to evils

Tyron Inbody avers that "there is no biblical theodicy." However, Inbody observes that the Bible proffers "various solutions" to questions about God and the evil of human suffering. These "various solutions" to the why of suffering and other evils are delineated in the Bible's "responses" (James Crenshaw) or "approaches" (Daniel J. Harrington) or "answers" (Bart Ehrman) to evil that these biblical scholars have identified. These scholars see a range of responses including punishment for sin, teaching or testing, or the means to some greater good.

Gregory Boyd, while appreciating "expositions of various biblical motifs that explain why we suffer, goes on to warn that "none of these motifs claim to be a comprehensive theodicy." In agreement with Boyd, Milton Crum comments that although such biblical passages might lessen the weight of suffering, ad hoc interpretations of evils do not provide a blanket theodicy. N. T. Wright "reminds us" that "the scriptures are frustratingly indirect and incomplete in answering questions of theodicy."

Deuteronomic "theodic settlement"

Brueggemann observes that, while the various biblical books do not agree on a theodicy, there was a temporary "theodic settlement" in the biblical Book of Deuteronomy.

The "theodic settlement" in the Book of Deuteronomy interprets all afflictions as just punishment for sin, that is, as retribution. Brueggemann defines "the theological notion of retribution" as "the assumption or conviction that the world is ordered by God so that everyone receives a fair outcome of reward or punishment commensurate with his or her conduct." Brueggemann points to Psalm One as a succinct summary of this retribution theodicy: "the Lord watches over the way of the righteous, but the way of the wicked shall perish" (Psalm 1:6).

Deuteronomy elaborates its "theodic settlement" in Chapter 28. Verse two promises that "blessings shall come upon you and overtake you, if you obey the Lord your God." This general promise of blessings is followed by a lengthy list of fourteen specific blessings. But, on the other hand, verse fifteen warns that "if you will not obey the Lord your God ..., curses shall come upon you." This general warning of curses is followed by a list of fifty-four specific curses, all of which would fit into the biblical use of the word evil.

The Deuteronomic retribution theodic settlement interpreted whatever evils ("curses") people suffered as just retribution meted out by a just God. However, at least as early as the early 6th century BC, Jeremiah was asserting that the retribution theodicy was contrary to fact. Jeremiah upbraided God for endowing the wicked with prosperity: "Why does the way of the guilty prosper? Why do all who are treacherous thrive? You plant them, and they take root."

In John 9:1–34, Jesus dismisses this "theodic settlement" by explaining that "It was neither that [a blind] man sinned, nor his parents [that caused his infirmity]; but it was so that the works of God might be displayed in him."

The Book of Job

Brueggemann treats the biblical Book of Job as the prime example of the "newly voiced theodic challenges" to the "old [Deuteronomic] theodic settlement" Job "was blameless and upright, one who feared God and turned away from evil," but nonetheless he suffered "all the evil that the Lord had brought upon him." In the midst of his suffering, Job explicitly contradicted the Deuteronomic theodic settlement: "it is all one; therefore I say, [God] destroys both the blameless and the wicked."

Not only did Job challenge the Deuteronomic theodic settlement by the fact of his own innocent suffering and by explicit contradiction of the old settlement, he interrogated God, "Why do the wicked live on, reach old age, and grow mighty in power?" Brueggemann judges the fact that God had no answer to Job's why? to be so important that "the Book of Job turns on the refusal, unwillingness, or inability of [God] to answer" Job's query. Even worse, God says of himself: "... you [Satan] incited me against him to ruin him without any reason."

Brueggemann explains that the "turn" he sees in the Book of Job is a turn from seeing the 'right' as accepting the old theodic settlement. Now, he continues, "perhaps what is 'right' is Job's refusal to concede, and therefore what is celebrated is his entire defiant argument ... That is, what Yahweh intends as 'right' is that Job (Israel, humankind) should make a legitimate case" before God "without timidity or cowardice" to "carry the human question of justice into the danger zone of God's holiness."

Bible and free-will theodicy

A theodicy is an attempt "to reconcile the power and goodness attributed to God with the presence of evil in the human experience." The Bible attributes both "power" and "goodness" to God.

The free-will theodicy, first developed by Augustine, defends God by placing all the blame for evil on "the misuse of free will by human beings." This free-will theodicy is "perhaps the most influential theodicy ever constructed," and it is currently "the most common theodicy".

Explaining the free-will theodicy, Nick Trakakis writes that "the free will theodicist proceeds to explain the existence of moral evil as a consequence of the misuse of our freedom." Then "the free will theodicist adds, however, that the value of free will (and the goods it makes possible) is so great as to outweigh the risk that it may be misused in various ways."

In parallel with the free-will theodicy, The New Bible Dictionary finds that the Bible attributes evil "to the abuse of free-will." Others have noted the free-will theodicy's "compatibility with and reliance upon the Genesis account of creation" and the fall of Adam and Eve into sin. Because of the compatibility between the free-will theodicy and the Genesis account of the Creation and Fall of humanity "the Fall-doctrine" has been characterized as "fundamentally an exercise in theodicy-making."

Free will and freedom: definition problems

The two terms, "freedom" and "free will," are treated together (a) because, by definition, a "free will" means a "will" that possesses "freedom" and (b) because "free will" is "commonly used" as synonymous with "freedom." Likewise, Robert Kane, writing about "what is often called the free will issue or the problem of free will," says that it "is really a cluster of problems or questions revolving around the conception of human freedom"

In writing about free will, R. C. Sproul points out that "at the heart of the problem is the question of the definition of free will." Manual Vargas adds that "it is not clear that there is any single thing that people have had in mind by the term ‘free will'." Because of the confusion created when "definitions of free will are assumed without being stated," Randy Alcorn urges, "be sure to define terms."

Adler's kinds of freedom

Mortimer Adler recognized the confusion resulting from the fact that there are "several different objects men have in mind when they use the word freedom." In The Idea of Freedom, Adler resolved this confusion by distinguishing the "three kinds of freedom" that various writers have in mind when they use the word. He calls these three kinds of freedom (1) "circumstantial freedom," (2) "natural freedom," and (3) "acquired freedom." "Natural freedom" and "acquired freedom" are germane to the Bible in relation to the free-will theodicy.

"Natural freedom" and the Bible

"Natural freedom", in Adler's terminology, is the freedom of "self-determination" regarding one's "decisions or plans." Natural freedom is "(i) inherent in all men, (ii) regardless of the circumstances under which they live and (iii) without regard to any state of mind or character which they may or may not acquire in the course of their lives"

Biblical scholars find that the Bible views all humanity as possessing the "natural freedom" of the will that enables "self-determination." In this sense of the term, biblical scholars say that, although the Bible does not use the term, it assumes human "free will." For example, what Adler calls "natural freedom" matches the definition of the biblical concept of "free will" in the Westminster Dictionary of Theological Terms, namely, "the free choice of the will that all persons possess." Other scholars describe free will in the Bible as follows:

  • If the phrase "free will" be taken morally and psychologically, as meaning the power of unconstrained, spontaneous, voluntary, and therefore responsible, choice, the Bible everywhere assumes that all men, as such, possess it, unregenerate and regenerate alike. The New Bible Dictionary.
  • "Free will is clearly taught in such Scripture passages as Matthew 23:37 ... and in Revelation 22:17." Archaeology and Bible History.
  • The Bible assumes that all human beings have "free will" in the sense of "the ability to make meaningful choices," that is, "the ability to have voluntary choices that have real effects." If God Is Good.
  • We make willing choices, choices that have real effect .... In this sense, it is certainly consistent with Scripture to say that we have "free will." Bible Doctrine.

Debate on "natural freedom"

The proper interpretation of biblical passages relating to the freedom of the human will has been the subject of debate for most of the Christian era. The Pelagius versus Augustine of Hippo debate over free will took place in the 5th century. The Erasmus versus Martin Luther arguments in 16th century included disagreements about free will, as did the Arminians versus Calvinists debates in the late 16th and early 17th centuries.

There is still no resolution of the free will debate because as Robert Kane observes, "debates about free will are more alive than ever today."

"Acquired freedom" and the Bible

"Acquired freedom," in Adler's terminology, is the freedom "to live as [one] ought to live," and to live as one ought requires "a change or development" whereby a person acquires "a state of mind, or character, or personality" that can be described by such qualities as "good, wise, virtuous, righteous, holy, healthy, sound, flexible, etc."

Thus, while Adler ascribes the "natural freedom" of "self-determination" to everyone, he asserts that the freedom "to live as [one] ought to live" must be acquired by "a change or development" in a person. The New Bible Dictionary finds these two distinct freedoms in the Bible:

(i) "The Bible everywhere assumes" that, by nature, everyone possesses the freedom of "unconstrained, spontaneous, voluntary, and therefore responsible, choice." The New Bible Dictionary calls this natural freedom "free will" in a moral and psychological sense of the term.
(ii) At the same time, the Bible seems "to indicate that no man is free for obedience and faith till he is freed from sin's dominion." He still possesses "free will" in the sense of voluntary choices, but "all his voluntary choices are in one way or another acts of serving sin" until he acquires freedom from "sin's dominion." The New Bible Dictionary denotes this acquired freedom for "obedience and faith" as "free will" in a theological sense.

The Bible gives a basic reason why a person must acquire a freedom "to live as [one] ought to live" when it applies Adam and Eve's sin to all humanity: "the Lord saw that the wickedness of humankind was great in the earth, and that every inclination of the thoughts of their hearts was only evil continually" (Genesis 6:5). Or, in Paul's view, "by the one man's disobedience the many were made sinners" (Romans 5:19). Thus, the Bible describes humanity as connaturally "enslaved to sin" (Romans 6:6; John 8:34). Therefore, in biblical thinking, a freedom from being "enslaved to sin" in order to "live as one ought" must be acquired because "sin" is "the failure to live up to Jesus' commandments to love God and love neighbor."

Jesus on acquired freedom

Jesus told his hearers that they needed to be made free: "if you continue in my word, you are truly my disciples; and you will know the truth, and the truth will make you free" (John 8:32). But Jesus' hearers did not understand that he was not talking about freedom from "economic or social slavery," so they responded, "we are descendants of Abraham and have never been slaves to anyone. What do you mean by saying, ‘You will be made free'?" (John 8:33)."

To clarify what he meant by being "made free," Jesus answered them, "very truly, I tell you, everyone who commits sin is a slave to sin" (John 8:34). By his words being "made free," Jesus meant being "made free" from "bondage to sin." Continuing his reply, Jesus added, "if the Son makes you free, you will be free indeed" (John 8:36). "Free indeed [ontós]" can be more literally translated "truly free" or "really free," as it is in the following translations.

  • "If the son makes you free, you will be truly free" (John 8:36 New Century Bible).
  • "If therefore the Son shall set you free, ye shall be really free" (John 8:36 Darby Translation).

In the John 8:32–36 passage, Jesus taught that "those who sin are slaves to their sin whether they realize it or not" and "they cannot break away from their sin." The freedom of being "truly free" or "really free" had to be acquired by being made free by "the truth," John's name for Jesus in 14:6. Thus, Jesus characterized being made "truly free" as freedom from being a "slave to sin." At the same time, the Bible holds that it is freedom for righteous living because "from the very beginning God's people were taught that the alternative to servitude was not freedom in some abstract sense, but rather freedom to serve the Lord."

Paul on acquired freedom

When the New Bible Dictionary says of humanity's connatural condition that "all his voluntary choices are in one way or another acts of serving sin," it references Romans 6:17–22. In this passage, Paul depicts the connatural human condition as being "slaves of sin." To be "set free from sin," Paul told his readers that they must "become slaves of righteousness."

Regarding the transformation from being "slaves of sin" to being "slaves of righteousness," Douglas J. Moo comments that Paul uses the image of slavery to say that "being bound to God and his will enables the person to become ‘free'" – in the sense of being free "to be what God wants that person to be." The slavery image underscores, as Moo says, that what Paul has in mind "is not freedom to do what one wants, but freedom to obey God" and that the obedience is done "willingly, joyfully, naturally," and not by coercion as with literal slaves.

The Fall and freedom of the will

The Fall (sometimes lowercase) in its theological use refers to "the lapse of human beings into a state of natural or innate sinfulness through the sin of Adam and Eve." The story of the Fall is narrated in Genesis 3:1–7.

Nelson's Student Bible Dictionary describes "the fall" as "the disobedience and sin of Adam and Eve that caused them to lose the state of innocence in which they had been created. This event plunged them and all mankind into a state of sin and corruption." A Concise Dictionary of Theology provides a similar description of the Fall. In their fall, Adam and Eve "disobeyed God and so lost their innocent, ideal existence" and "brought moral evil into the world."

The Bible testifies to the deleterious impact of the Fall on all humanity. Shortly after the Fall, "the Lord saw that the wickedness of humankind was great in the earth, and that every inclination of the thoughts of their hearts was only evil continually" (Genesis 6:5). Or, in Paul's view, "sin came into the world through one man," and "by the one man's disobedience the many were made sinners" (Romans 5:12, 19).

Freedom of will given at creation

Writing about God's creation and Adam and Eve, Baker's Dictionary of Biblical Theology says that "creation is climaxed by persons who possess wills that can choose to either obey or disobey." The Book of Ecclesiasticus, which pre-Protestant Reformation churches consider part of the Bible but which Protestants classify among the Apocrypha, explicitly names freedom of the will as an element in God's creation: God "created humankind in the beginning, and he left them in the power of their own free choice" (Ecclesiasticus 15:14).

Freedom of will not given at creation

Adam and Eve were created with "free will," that is, "the ability to choose either good or evil." The Fall evidences that Adam and Eve were not created with the freedom that Paul calls being "slaves of righteousness" (Romans 6:18): a phrase that denotes "freedom to obey God – willingly, joyfully, naturally."

Critics of the free-will theodicy believe that it "fails" because "God could have created free agents without risking bringing moral evil into the world. There is nothing logically inconsistent about a free agent that always chooses the good." Relating God's creation of Adam and Eve and the Fall to theodicy, J. L. Mackie argues "there was open to [God] the obviously better possibility of making beings who would freely act but always do right." And, Mackie adds, "clearly, [God's] failure to avail himself of this possibility is inconsistent with his being both omnipotent and wholly good."

God and moral evil

The free-will theodicy justifies God by ascribing all evil to "the evil acts of human free will." At the same time, the Bible teaches that God "rules the hearts and actions of all men." The Bible contains many portrayals of God as ruling "hearts and actions" for evil. Following are a few examples:

  • God said, "I will harden [Pharaoh's] heart, so that he will not let the people go" (Exodus 4:21).
  • Isaiah asked, "Why, O Lord, do you make us stray from your ways and harden our heart, so that we do not fear you?" (Isaiah 63:17).
  • God said, "If a prophet is deceived and speaks a word, I, the Lord, have deceived that prophet" (Ezekiel 14:9).
  • John writes that those who "did not believe in [Jesus] could not believe," because, quoting Isaiah 6:10, "[God] has blinded their eyes and hardened their heart" (John 12:37–40 abr).
  • God "hardens the heart of whomever he chooses" (Romans 9:18).
  • "God sends [those who are perishing] a powerful delusion, leading them to believe what is false, so [they] will be condemned" (2 Thessalonians 2:11–12).
  • "Those who do not believe ... stumble because they disobey the word, as they were destined [by God] to do" (1 Peter 2:7–8).

Theodicy unresolved

The existence of evil in the world, in the view of Raymond Lam, "presents the gravest challenge to the existence of an all-powerful, all-knowing, all-loving God." Lam also observes that "no theodicy is easy."

Regarding theodicy and the Bible, Baker's Evangelical Dictionary of Biblical Theology concludes that "the Bible does not answer the oft-posed problem of how a just, omnipotent, and loving God could permit evil to exist in a universe he had created."

With no "definitive answer" to the theodic question, "debates about theodicy continue among believers and unbelievers alike," observes Robert F. Brown. Therefore, Brown adds, "theodicy remains a perennial concern for thoughtful religious commitment." Theodicy remains a "perennial concern" because, Brown reports, "how the divine can be compatible with the existence of evil in the world has perplexed profound thinkers and ordinary people right down to the present day."

Prism (optics)

From Wikipedia, the free encyclopedia
A plastic prism

An optical prism is a transparent optical element with flat, polished surfaces that are designed to refract light. At least one surface must be angled — elements with two parallel surfaces are not prisms. The most familiar type of optical prism is the triangular prism, which has a triangular base and rectangular sides. Not all optical prisms are geometric prisms, and not all geometric prisms would count as an optical prism. Prisms can be made from any material that is transparent to the wavelengths for which they are designed. Typical materials include glass, acrylic and fluorite.

A dispersive prism can be used to break white light up into its constituent spectral colors (the colors of the rainbow) as described in the following section. Other types of prisms noted below can be used to reflect light, or to split light into components with different polarizations.

Types

Dispersive

Comparison of the spectra obtained from a diffraction grating by diffraction (1), and a prism by refraction (2). Longer wavelengths (red) are diffracted more, but refracted less than shorter wavelengths (violet).

Dispersive prisms are used to break up light into its constituent spectral colors because the refractive index depends on wavelength; the white light entering the prism is a mixture of different wavelengths, each of which gets bent slightly differently. Blue light is slowed more than red light and will therefore be bent more than red light.

Spectral dispersion is the best known property of optical prisms, although not the most frequent purpose of using optical prisms in practice.

Reflective

Reflective prisms are used to reflect light, in order to flip, invert, rotate, deviate or displace the light beam. They are typically used to erect the image in binoculars or single-lens reflex cameras – without the prisms the image would be upside down for the user.

Reflective prisms use total internal reflection to achieve near-perfect reflection of light that strikes the facets at a sufficiently oblique angle. Prisms are usually made of optical glass which, combined with anti-reflective coating of input and output facets, leads to significantly lower light loss than metallic mirrors.

  • Odd number of reflections, image projects as flipped (mirrored)
    • triangular prism reflector, projects image sideways (chromatic dispersion is zero in case of perpendicular input and output incidence)
    • Roof pentaprism projects image sideways flipped along the other axis
    • Dove prism projects image forward
    • Corner-cube retroreflector projects image backwards
  • Even number of reflections, image projects upright (without change in handedness; may or may not be rotated)

Beam-splitting

Various thin-film optical layers can be deposited on the hypotenuse of one right-angled prism, and cemented to another prism to form a beam-splitter cube. Overall optical performance of such a cube is determined by the thin layer.

In comparison with a usual glass substrate, the glass cube provides protection of the thin-film layer from both sides and better mechanical stability. The cube can also eliminate etalon effects, back-side reflection and slight beam deflection.

  • dichroic color filters form a dichroic prism
  • Polarizing cube beamsplitters have lower extinction ratio than birefringent ones, but less expensive
  • Partially-metallized mirrors provide non-polarizing beamsplitters
  • Air gap − When hypotenuses of two triangular prisms are stacked very close to each other with air gap, frustrated total internal reflection in one prism makes it possible to couple part of the radiation into a propagating wave in the second prism. The transmitted power drops exponentially with the gap width, so it can be tuned over many orders of magnitude by a micrometric screw.
  • Biprism (or Fresnel biprism): two prisms joined at their bases, forming a wide vertex angle (~ 180°); used in common-path interferometry.

Polarizing

Another class is formed by polarizing prisms which use birefringence to split a beam of light into components of varying polarization. In the visible and UV regions, they have very low losses and their extinction ratio typically exceeds , which is superior to other types of polarizers. They may or may not employ total internal reflection;

These are typically made of a birefringent crystalline material like calcite, but other materials like quartz and α-BBO may be necessary for UV applications, and others (MgF2, YVO4 and TiO2) will extend transmission farther into the infrared spectral range.

Depolarizer

Birefringent crystals can be also assembled in a way that leads to apparent depolarization of the light.

Note that depolarization would not be observed for an ideal monochromatic plane wave, as actually both devices turn reduced temporal coherence or spatial coherence, respectively, of the beam into decoherence of its polarization components.

Others

However, prisms made of isotropic materials like glass will also alter polarization of light, as partial reflection under oblique angles does not maintain the amplitude ratio (nor phase) of the s- and p-polarized components of the light, leading to general elliptical polarization. This is generally an unwanted effect of dispersive prisms. In some cases this can be avoided by choosing prism geometry which light enters and exits under perpendicular angle, by compensation through non-planar light trajectory, or by use of p-polarized light.

Total internal reflection alters only the mutual phase between s- and p-polarized light. Under well chosen angle of incidence, this phase is close to .

  • Fresnel rhomb uses this effect to achieve conversion between circular and linear polarisation. This phase difference is not explicitly dependent on wavelength, but only on refractive index, so Fresnel rhombs made of low-dispersion glasses achieve much broader spectral range than quarter-wave plates. They displace the beam, however.
  • Doubled Fresnel rhomb, with quadruple reflection and zero beam displacement, substitutes a half-wave plate.
  • Similar effect can also be used to make a polarization-maintaining optics.

Other uses

Total internal reflection in prisms finds numerous uses through optics, plasmonics and microscopy. In particular:

  • Prisms are used to couple propagating light to surface plasmons. Either the hypotenuse of a triangular prism is metallized (Kretschmann configuration), or evanescent wave is coupled to very close metallic surface (Otto configuration).
  • Some laser active media can be formed as a prism where the low-quality pump beam enters the front facet, while the amplified beam undergoes total internal reflection under grazing incidence from it. Such a design suffers less from thermal stress and is easy to be pumped by high-power laser diodes.

Other uses of prisms are based on their beam-deviating refraction:

  • Wedge prisms are used to deflect a beam of monochromatic light by a fixed angle. A pair of such prisms can be used for beam steering; by rotating the prisms the beam can be deflected into any desired angle within a conical "field of regard". The most commonly found implementation is a Risley prism pair.
  • Transparent windows of, e.g., vacuum chambers or cuvettes can also be slightly wedged (10' − 1°). While this does not reduce reflection, it suppresses Fabry-Pérot interferences that would otherwise modulate their transmission spectrum.
  • Anamorphic pair of similar, but asymmetrically placed prisms can also change the profile of a beam. This is often used to make a round beam from the elliptical output of a laser diode. With its monochromatic light, slight chromatic dispersion arising from different wedge inclination is not a problem.
  • Deck prisms were used on sailing ships to bring daylight below deck, since candles and kerosene lamps are a fire hazard on wooden ships.

In optometry

By shifting corrective lenses off axis, images seen through them can be displaced in the same way that a prism displaces images. Eye care professionals use prisms, as well as lenses off axis, to treat various orthoptics problems:

  • Diplopia (double vision)
  • Positive and negative fusion problems

Prism spectacles with a single prism perform a relative displacement of the two eyes, thereby correcting eso-, exo, hyper- or hypotropia.

In contrast, spectacles with prisms of equal power for both eyes, called yoked prisms (also: conjugate prisms, ambient lenses or performance glasses) shift the visual field of both eyes to the same extent.

Hanging Gardens of Babylon

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This hand-coloured engraving, probably made in the 19th century after the first excavations in the Assyrian capitals, depicts the fabled Hanging Gardens, with the Tower of Babel in the background.
Timeline and map of the Seven Wonders of the Ancient World, including the Hanging Gardens of Babylon

The Hanging Gardens of Babylon were one of the Seven Wonders of the Ancient World listed by Hellenic culture. They were described as a remarkable feat of engineering with an ascending series of tiered gardens containing a wide variety of trees, shrubs, and vines, resembling a large green mountain constructed of mud bricks. It was said to have been built in the ancient city of Babylon, near present-day Hillah, Babil province, in Iraq. The Hanging Gardens' name is derived from the Greek word κρεμαστός (kremastós, lit.'overhanging'), which has a broader meaning than the modern English word "hanging" and refers to trees being planted on a raised structure such as a terrace.

According to one legend, the Hanging Gardens were built alongside a grand palace known as The Marvel of Mankind, by the Neo-Babylonian King Nebuchadnezzar II (who ruled between 605 and 562 BC), for his Median wife, Queen Amytis, because she missed the green hills and valleys of her homeland. This was attested to by the Babylonian priest Berossus, writing in about 290 BC, a description that was later quoted by Josephus. The construction of the Hanging Gardens has also been attributed to the legendary queen Semiramis and they have been called the Hanging Gardens of Semiramis as an alternative name.

The Hanging Gardens are the only one of the Seven Wonders for which the location has not been definitively established. There are no extant Babylonian texts that mention the gardens, and no definitive archaeological evidence has been found in Babylon. Three theories have been suggested to account for this: first, that they were purely mythical, and the descriptions found in ancient Greek and Roman writings (including those of Strabo, Diodorus Siculus and Quintus Curtius Rufus) represented a romantic ideal of an eastern garden; second, that they existed in Babylon, but were destroyed sometime around the first century AD; and third, that the legend refers to a well-documented garden that the Assyrian King Sennacherib (704–681 BC) built in his capital city of Nineveh on the River Tigris, near the modern city of Mosul.

Descriptions in classical literature

There are five principal writers whose descriptions of Babylon exist in some form today. These writers concern themselves with the size of the Hanging Gardens, their overall design and means of irrigation, and why they were built.

Josephus (c. 37–100 AD) quotes a description of the gardens by Berossus, a Babylonian priest of Marduk, whose writing c. 290 BC is the earliest known mention of the gardens. Berossus described the reign of Nebuchadnezzar II and is the only source to credit that king with the construction of the Hanging Gardens.

In this palace he erected very high walls, supported by stone pillars; and by planting what was called a pensile paradise, and replenishing it with all sorts of trees, he rendered the prospect an exact resemblance of a mountainous country. This he did to gratify his queen, because she had been brought up in Media, and was fond of a mountainous situation.

Hanging gardens of Semiramis, by H. Waldeck

Diodorus Siculus (active c. 60–30 BC) seems to have consulted the 4th century BC texts of both Cleitarchus (a historian of Alexander the Great) and Ctesias of Cnidus. Diodorus ascribes the construction to a Syrian king. He states that the garden was in the shape of a square, with each side approximately four plethra long. The garden was tiered, with the uppermost gallery being 50 cubits high. The walls, 22 feet thick, were made of brick. The bases of the tiered sections were sufficiently deep to provide root growth for the largest trees, and the gardens were irrigated from the nearby Euphrates.

Quintus Curtius Rufus (fl. 1st century AD) probably drew on the same sources as Diodorus. He states that the gardens were located on top of a citadel, which was 20 stadia in circumference. He attributes the building of the gardens to a Syrian king, again for the reason that his queen missed her homeland.

The account of Strabo (c. 64 BC – 21 AD) possibly based his description on the lost account of Onesicritus from the 4th century BC. He states that the gardens were watered by means of an Archimedes' screw leading to the gardens from the Euphrates river.

The last of the classical sources thought to be independent of the others is A Handbook to the Seven Wonders of the World by the paradoxographer Philo of Byzantium, writing in the 4th to 5th century AD. The method of raising water by screw matches that described by Strabo. Philo praises the engineering and ingenuity of building vast areas of deep soil, which had a tremendous mass, so far above the natural grade of the surrounding land, as well as the irrigation techniques.

Historical existence

This copy of a bas relief from the North Palace of Ashurbanipal (669–631 BC) at Nineveh shows a luxurious garden watered by an aqueduct.

It is unclear whether the Hanging Gardens were an actual construction or a poetic creation, owing to the lack of documentation in contemporaneous Babylonian sources. There is also no mention of Nebuchadnezzar's wife Amyitis (or any other wives), although a political marriage to a Median or Persian would not have been unusual. Many records exist of Nebuchadnezzar's works, yet his long and complete inscriptions do not mention any garden. However, the gardens were said to still exist at the time that later writers described them, and some of these accounts are regarded as deriving from people who had visited Babylon. Herodotus, who describes Babylon in his Histories, does not mention the Hanging Gardens, although it could be that the gardens were not yet well known to the Greeks at the time of his visit.

To date, no archaeological evidence has been found at Babylon for the Hanging Gardens. It is possible that evidence exists beneath the Euphrates, which cannot be excavated safely at present. The river flowed east of its current position during the time of Nebuchadnezzar II, and little is known about the western portion of Babylon. Rollinger has suggested that Berossus attributed the Gardens to Nebuchadnezzar for political reasons, and that he had adopted the legend from elsewhere.

Identification with Sennacherib's gardens at Nineveh

Oxford scholar Stephanie Dalley has proposed that the Hanging Gardens of Babylon were actually the well-documented gardens constructed by the Assyrian king Sennacherib (reigned 704 – 681 BC) for his palace at Nineveh; Dalley posits that during the intervening centuries the two sites became confused, and the extensive gardens at Sennacherib's palace were attributed to Nebuchadnezzar II's Babylon. Archaeological excavations have found traces of a vast system of aqueducts attributed to Sennacherib by an inscription on its remains, which Dalley proposes were part of an 80-kilometre (50 mi) series of canals, dams, and aqueducts used to carry water to Nineveh with water-raising screws used to raise it to the upper levels of the gardens.

Dalley bases her arguments on recent developments in the analysis of contemporary Akkadian inscriptions. Her main points are:

  • The name Babylon, meaning "Gate of the Gods", was the name given to several Mesopotamian cities. Sennacherib renamed the city gates of Nineveh after gods, which suggests that he wished his city to be considered "a Babylon".
  • Only Josephus names Nebuchadnezzar as the king who built the gardens; although Nebuchadnezzar left many inscriptions, none mentions any garden or engineering works. Diodorus Siculus and Quintus Curtius Rufus specify a "Syrian" king. By contrast, Sennacherib left written descriptions, and there is archaeological evidence of his water engineering. His grandson Assurbanipal pictured the mature garden on a sculptured wall panel in his palace.
  • Sennacherib called his new palace and garden "a wonder for all peoples". He describes the making and operation of screws to raise water in his garden.
  • The descriptions of the classical authors fit closely to these contemporary records. Before the Battle of Gaugamela in 331 BC Alexander the Great camped for four days near the aqueduct at Jerwan. The historians who travelled with him would have had ample time to investigate the enormous works around them, recording them in Greek. These first-hand accounts have not survived into modern times, but were quoted by later Greek writers.

King Sennacherib's garden was well-known not just for its beauty – a year-round oasis of lush green in a dusty summer landscape – but also for the marvelous feats of water engineering that maintained the garden. There was a tradition of Assyrian royal garden building. King Ashurnasirpal II (883–859 BC) had created a canal, which cut through the mountains. Fruit tree orchards were planted. Also mentioned were pines, cypresses and junipers; almond trees, date trees, ebony, rosewood, olive, oak, tamarisk, walnut, terebinth, ash, fir, pomegranate, pear, quince, fig, and grapes. A sculptured wall panel of Assurbanipal shows the garden in its maturity. One original panel and the drawing of another are held by the British Museum, although neither is on public display. Several features mentioned by the classical authors are discernible on these contemporary images.

Assyrian wall relief showing gardens in Nineveh

Of Sennacherib's palace, he mentions the massive limestone blocks that reinforce the flood defences. Parts of the palace were excavated by Austin Henry Layard in the mid-19th century. His citadel plan shows contours which would be consistent with Sennacherib's garden, but its position has not been confirmed. The area has been used as a military base in recent times, making it difficult to investigate further.

The irrigation of such a garden demanded an upgraded water supply to the city of Nineveh. The canals stretched over 50 kilometres (31 mi) into the mountains. Sennacherib was proud of the technologies he had employed and describes them in some detail on his inscriptions. At the headwater of Bavian (Khinnis) his inscription mentions automatic sluice gates. An enormous aqueduct crossing the valley at Jerwan was constructed of over two million dressed stones. It used stone arches and waterproof cement. On it is written:

Sennacherib king of the world king of Assyria. Over a great distance I had a watercourse directed to the environs of Nineveh, joining together the waters.... Over steep-sided valleys I spanned an aqueduct of white limestone blocks, I made those waters flow over it.

Sennacherib claimed that he had built a "Wonder for all Peoples", and said he was the first to deploy a new casting technique in place of the "lost-wax" process for his monumental (30 tonne) bronze castings. He was able to bring the water into his garden at a high level because it was sourced from further up in the mountains, and he then raised the water even higher by deploying his new water screws. This meant he could build a garden that towered above the landscape with large trees on the top of the terraces – a stunning artistic effect that surpassed those of his predecessors.

Plants

Date palms are a common tree species in Babylon.

The gardens, as depicted in artworks, featured blossoming flowers, ripe fruit, burbling waterfalls and terraces exuberant with rich foliage. Based on Babylonian literature, tradition, and the environmental characteristics of the area, some of the following plants may have been found in the gardens:

Imported plant varieties that may have been present in the gardens include the cedar, cypress, ebony, pomegranate, plum, rosewood, terebinth, juniper, oak, ash tree, fir, myrrh, walnut, and willow. Some of these plants were suspended over the terraces and draped over its walls with arches underneath.

The "Garden Party" relief depicting Ashurbanipal with his wife seated under a pergola of climbing grapevines with hanging grapes, also small birds, surrounded with fruiting date palms and pine trees. The head of a defeated king hangs between the 1st and 2nd figures at left. North Palace, Nineveh, c. 645 BC.

Operator (computer programming)

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