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Buridan's ass is an illustration of a
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictor ...
in
philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
in the conception of
free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...
. It refers to a hypothetical situation wherein an
ass Ass most commonly refers to: * Buttocks (in informal American English) * Donkey or ass, ''Equus africanus asinus'' **any other member of the subgenus ''Asinus'' Ass or ASS may also refer to: Art and entertainment * Ass (album), ''Ass'' (albu ...
(or
donkey The donkey or ass is a domesticated equine. It derives from the African wild ass, ''Equus africanus'', and may be classified either as a subspecies thereof, ''Equus africanus asinus'', or as a separate species, ''Equus asinus''. It was domes ...
) that is equally hungry and thirsty is placed precisely midway between a stack of hay and a pail of water. Since the paradox assumes the ass will always go to whichever is closer, it dies of both hunger and thirst since it cannot make any rational decision between the hay and water. A common variant of the paradox substitutes the hay and water for two identical piles of hay; the ass, unable to choose between the two, dies of hunger. The paradox is named after the 14th-century French
philosopher Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
Jean Buridan Jean Buridan (; ; Latin: ''Johannes Buridanus''; – ) was an influential 14thcentury French scholastic philosopher. Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and ...
, whose philosophy of moral
determinism Determinism is the Metaphysics, metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes ov ...
it satirizes. Although the illustration is named after Buridan, philosophers have discussed the concept before him, notably
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
, who put forward the example of a man equally hungry and thirsty, and
Al-Ghazali Al-Ghazali ( – 19 December 1111), archaically Latinized as Algazelus, was a Shafi'i Sunni Muslim scholar and polymath. He is known as one of the most prominent and influential jurisconsults, legal theoreticians, muftis, philosophers, the ...
, who used a man faced with the choice of equally good dates. A version of this situation appears as
metastability In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...
in
digital electronics Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. It deals with the relationship between Binary number, binary inputs and outputs by passing electrical s ...
, when an electric circuit must decide between two states based on an input that is in itself undefined (neither zero nor one). Metastability becomes a problem if the circuit spends more time than it should in this "undecided" state, which is usually set by the speed of the clock the system is using.


History

The paradox predates Buridan; it dates to antiquity, being found in
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
's ''
On the Heavens ''On the Heavens'' (Greek: ''Περὶ οὐρανοῦ''; Latin: ''De Caelo'' or ''De Caelo et Mundo'') is Aristotle's chief cosmological treatise: written in 350 BCE, it contains his astronomical theory and his ideas on the concrete workings o ...
''. Aristotle, in ridiculing the
Sophist A sophist () was a teacher in ancient Greece in the fifth and fourth centuries BCE. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics and mathematics. They taught ''arete'', "virtue" or "excellen ...
Anaximander Anaximander ( ; ''Anaximandros''; ) was a Pre-Socratic philosophy, pre-Socratic Ancient Greek philosophy, Greek philosopher who lived in Miletus,"Anaximander" in ''Chambers's Encyclopædia''. London: George Newnes Ltd, George Newnes, 1961, Vol. ...
's idea that the Earth is stationary simply because it is spherical and any forces on it must be equal in all directions, says that is as ridiculous as saying that However, the Greeks only used this paradox as an analogy in the context of the equilibrium of ''physical'' forces. The 12th-century Persian scholar and philosopher
Al-Ghazali Al-Ghazali ( – 19 December 1111), archaically Latinized as Algazelus, was a Shafi'i Sunni Muslim scholar and polymath. He is known as one of the most prominent and influential jurisconsults, legal theoreticians, muftis, philosophers, the ...
discusses the application of this paradox to human decision making, asking whether it is possible to make a choice between equally good courses without grounds for preference. He takes the attitude that free will can break the stalemate. Andalusian philosopher
Averroes Ibn Rushd (14 April 112611 December 1198), archaically Latinization of names, Latinized as Averroes, was an Arab Muslim polymath and Faqīh, jurist from Al-Andalus who wrote about many subjects, including philosophy, theology, medicine, astron ...
(1126–1198), in commentary on Ghazali, takes the opposite view. Although Buridan nowhere discusses this specific problem, its relevance is that he did advocate a moral determinism whereby, save for ignorance or impediment, a human faced by alternative courses of action must always choose the greater
good In most contexts, the concept of good denotes the conduct that should be preferred when posed with a choice between possible actions. Good is generally considered to be the opposite of evil. The specific meaning and etymology of the term and its ...
. In the face of equally good alternatives Buridan believed a rational choice could not be made. Later writers satirised this view in terms of an ass which, confronted by both food and water, must necessarily die of both hunger and thirst while pondering a decision. Many later philosophers have addressed this problem of "choice without preference". In his ''
Ethics Ethics is the philosophy, philosophical study of Morality, moral phenomena. Also called moral philosophy, it investigates Normativity, normative questions about what people ought to do or which behavior is morally right. Its main branches inclu ...
'' (), Baruch de Spinoza accepts that his determinist philosophy implies that such a state of indecision could happen, but that this should be classed with other irrational behavior:Clemens, Justin, "Spinoza's Ass", in
Pierre Bayle Pierre Bayle (; 18 November 1647 – 28 December 1706) was a French philosopher, author, and lexicographer. He is best known for his '' Historical and Critical Dictionary'', whose publication began in 1697. Many of the more controversial ideas ...
(1647–1706) in his ''Dictionnaire'' authored some of the most comprehensive discussions of the problem. He recognized explicitly that if humans have the ability to make a decision between choices with no reason for preference, this means that humans have
free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...
, and bears on man's rationalization of God's choices. He regarded the previous examples of the ass or dates as artificial, and pointed out there are many real instances in everyday life in which a person must make a choice in which the choice doesn't matter to him, and that this presents no problem.
Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...
(1646–1716) believed, from his
principle of sufficient reason The principle of sufficient reason states that everything must have a Reason (argument), reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by ...
, that if a person's preferences were really balanced no decision could be made, but that ''petites perceptions'', small perceived preferences below the threshold of consciousness that are always present, explains why people are able to make such a choice.


Discussion

Some proponents of hard determinism such as Spinoza have granted the unpleasantness of the scenario, but have denied that it illustrates a true
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictor ...
, since one does not contradict oneself in suggesting that a man might die between two equally plausible routes of action. Other writers have opted to deny the validity of the illustration. A typical counter-argument is that
rationality Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do, or a belief is rational if it is based on strong evidence. This quality can apply to an ab ...
as described in the paradox is so limited as to be a straw man version of the real thing, which does allow the consideration of meta-arguments. In other words, it is entirely rational to recognize that both choices are equally good and arbitrarily ( randomly) pick one instead of starving; although the decision that they are sufficiently the same is also subject to Buridan's ass. The idea that a random decision could be made is sometimes used as an attempted justification for
faith Faith is confidence or trust in a person, thing, or concept. In the context of religion, faith is " belief in God or in the doctrines or teachings of religion". According to the Merriam-Webster's Dictionary, faith has multiple definitions, inc ...
or intuitivity (called by Aristotle noetic or noesis). The argument is that, like the starving ass, we must make a choice to avoid being frozen in endless doubt. Other counter-arguments exist. According to Edward Lauzinger, Buridan's ass fails to incorporate the latent biases that humans always bring with them when making decisions. Social psychologist Kurt Lewin's field theory treated this paradox experimentally. He demonstrated that lab rats experience difficulty when choosing between two equally attractive (approach–approach) goals. The typical response to approach–approach decisions is initial ambivalence, though the decision becomes more decisive as the organism moves towards one choice and away from another.


Buridan's principle

The situation of Buridan's ass was given a mathematical basis in a 1984 paper by American computer scientist Leslie Lamport, in which Lamport presents an argument that, given certain assumptions about continuity in a simple
mathematical model A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical m ...
of the Buridan's ass problem, there is always some starting condition under which the ass starves to death, no matter what strategy it takes. Original December 1984 version published by Digital Equipment Corp
archived here
/ref> He further illustrates the paradox with the example of a driver stopped at a
railroad crossing A level crossing is an intersection where a railway line crosses a road, path, or (in rare situations) airport runway, at the same level, as opposed to the railway line or the road etc. crossing over or under using an overpass or tunnel. The ...
trying to decide whether he has time to cross before a train arrives. He proves that regardless of how "safe" the policy the driver adopts, because indecision can cause an indefinite delay in action a small percentage of drivers will be hit by the train. Lamport calls this result "Buridan’s principle": :A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time. He points out that just because we do not see asses or people starving to death through indecision, or other examples of Buridan's undecided states in real life, does not disprove the principle. The persistence of a Buridan's undecided state for a perceptible length of time may just be sufficiently improbable that it has not been observed.


Application to digital logic: metastability

A version of Buridan's principle occurs in
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
. Specifically, the input to a
digital logic A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for ...
gate must convert a continuous
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
value into either a 0 or a 1, which is typically sampled and then processed. If the input is changing and at an intermediate value when sampled, the input stage acts like a comparator. The voltage value can then be likened to the position of the ass, and the values 0 and 1 represent the bales of hay. As in the situation of the starving ass, there exists an input on which the converter cannot make a proper decision, and the output remains balanced in a
metastable In chemistry and physics, metastability is an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is onl ...
state between the two stable states for an undetermined length of time, until random noise in the circuit makes it converge to one of the stable states. The metastability problem is a significant issue in
digital circuit design Integrated circuit design, semiconductor design, chip design or IC design, is a sub-field of electronics engineering, encompassing the particular Boolean logic, logic and circuit design techniques required to design integrated circuits (ICs). A ...
, and metastable states are a possibility wherever
asynchronous Asynchrony is any dynamic far from synchronization. If and as parts of an asynchronous system become more synchronized, those parts or even the whole system can be said to be in sync. Asynchrony or asynchronous may refer to: Electronics and com ...
inputs (digital signals not synchronized to a
clock signal In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') is an electronic logic signal (voltage or current) which oscillates between a high and a low state at a constant frequency and ...
) occur. The ultimate reason the problem is manageable is that the probability of a metastable state persisting longer than a given time interval ''t'' is an exponentially declining function of ''t''. In electronic devices, the probability of such an "undecided" state lasting longer than a matter of nanoseconds, while always possible, can be made negligibly low. In asynchronous system design, arbiter circuits have been developed to make such decisions. They can reduce to insignificance the probability that a metastable state occurs, at the cost of increased decision time.


In popular culture

* ''Buridan's Donkey'', a 1932 French comedy film, is named after the paradox. *
Lewis Cass Lewis Cass (October 9, 1782June 17, 1866) was a United States Army officer and politician. He represented Michigan in the United States Senate and served in the Cabinets of two U.S. Presidents, Andrew Jackson and James Buchanan. He was also the 1 ...
, the Democratic candidate for the U.S. presidency in 1848, was contrasted with Buridan's ass by
Abraham Lincoln Abraham Lincoln (February 12, 1809 – April 15, 1865) was the 16th president of the United States, serving from 1861 until Assassination of Abraham Lincoln, his assassination in 1865. He led the United States through the American Civil War ...
: "Mr. Speaker, we have all heard of the animal standing in doubt between two stacks of hay, and starving to death. The like would never happen to General Cass; place the stacks a thousand miles apart, he would stand stock still midway between them, and eat them both at once, and the green grass along the line would be apt to suffer some too at the same time." Carl Sandburg (1954), ''Abraham Lincoln: The Prairie Years'', 1960 reprint, New York: Dell, Vol. 1, Ch. 7, "Congressman Lincoln", p. 173. (This being a reference to Cass's support for "popular sovereignty" in the run-up to the Civil War.) * In the ''
Doctor Who ''Doctor Who'' is a British science fiction television series broadcast by the BBC since 1963. The series, created by Sydney Newman, C. E. Webber and Donald Wilson (writer and producer), Donald Wilson, depicts the adventures of an extraterre ...
'' novel ''
The Eight Doctors ''The Eight Doctors'' is a BBC Books original novel written by Terrance Dicks and based on the long-running British science fiction on television, science fiction television series ''Doctor Who''. It was the first of the Eighth Doctor Adventure ...
'', the Fifth and Eighth Doctors are confronted by a Raston Warrior Robot. The Doctors stand exactly the same distance away from the Robot as it approaches them; unable to decide which to attack first (since the Robot attacks by sensing brain patterns, which are identical in the two Doctors), the Robot shuts down. * In episode 7 of the 10th season of ''
The Big Bang Theory ''The Big Bang Theory'' is an American television sitcom created by Chuck Lorre and Bill Prady for CBS. It aired from September 24, 2007, to May 16, 2019, running for 12 seasons and 279 episodes. The show originally centered on five charact ...
'', Sheldon and Amy discuss the history of Buridan's ass (renamed donkey), and its application to their lives. Amy resolves the paradox (of Sheldon desiring to live in different apartments) by creating a more desirable option by engaging Sheldon in a discussion of the theory and its history.


See also

*
Analysis paralysis Analysis paralysis (or paralysis by analysis) describes an individual or group process where overanalyzing or overthinking a situation can cause forward motion or decision-making to become " paralyzed", meaning that no solution or course of acti ...
* Catch-22 *
Dining philosophers problem In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them. It was originally formulated in 1965 by Edsger Dijkstra ...
* Fredkin's paradox * Hobson's choice *
Lagrangian point In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium (mechanics), equilibrium for small-mass objects under the gravity, gravitational influence of two massive orbit, orbiting b ...
* Morton's fork * * Search cost *
Spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion o ...


References


Bibliography

* * * * * *


External links

* {{Decision theory paradoxes Decision-making paradoxes Fictional donkeys Thought experiments in philosophy