Buridan's ass
Encyclopedia
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
in philosophy in the conception of free will
Free will
"To make my own decisions whether I am successful or not due to uncontrollable forces" -Troy MorrisonA pragmatic definition of free willFree will is the ability of agents to make choices free from certain kinds of constraints. The existence of free will and its exact nature and definition have long...
.
It refers to a hypothetical situation wherein an ass
Donkey
The donkey or ass, Equus africanus asinus, is a domesticated member of the Equidae or horse family. The wild ancestor of the donkey is the African Wild Ass, E...
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 will die of both hunger and thirst since it cannot make any rational decision to choose one over the other. The paradox is named after the 14th century French
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
philosopher Jean Buridan
Jean Buridan
Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
, whose philosophy of moral
Moral
A moral is a message conveyed or a lesson to be learned from a story or event. The moral may be left to the hearer, reader or viewer to determine for themselves, or may be explicitly encapsulated in a maxim...
determinism
Determinism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...
it satirises.
History
The paradox did not originate in Buridan's time; it dates to antiquity, being first found in AristotleAristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
's De Caelo, where Aristotle mentions an example of a man who makes no move because he is as hungry as he is thirsty and is positioned exactly between food and drink.
Buridan nowhere discusses this specific problem, but 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. Buridan allowed that the will could delay the choice to more fully assess the possible outcomes of the choice. Later writers satirised this view in terms of an ass
Donkey
The donkey or ass, Equus africanus asinus, is a domesticated member of the Equidae or horse family. The wild ancestor of the donkey is the African Wild Ass, E...
which, confronted by both food and water must necessarily die of both hunger and thirst while pondering a decision.
A common variant substitutes two identical piles of hay for both hay and water and advances that the ass, unable to choose between the two, dies of hunger alone.
Discussion
Some proponents of hard determinismHard determinism
Hard determinism, or Metaphysical determinism, defends the strongest version of Determinism: the world is a mechanism, and all events and choices have been determined by earlier conditions. Particularly, they accept Causal Determinism and Logical Determinism. Faced with the Standard argument...
have granted the unpleasantness of the scenario, but have denied that it illustrates a true paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
, since one does not contradict
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...
oneself in suggesting that a man might die between two equally plausible routes of action. For example, Baruch Spinoza
Baruch Spinoza
Baruch de Spinoza and later Benedict de Spinoza was a Dutch Jewish philosopher. Revealing considerable scientific aptitude, the breadth and importance of Spinoza's work was not fully realized until years after his death...
in his Ethics
Ethics (book)
Ethics is a philosophical book written by Benedict de Spinoza. It was written in Latin. Although it was published posthumously in 1677, it is his most famous work, and is considered his magnum opus....
, suggests that a person who sees two options as truly equally compelling cannot be fully rational:
Other writers have opted to deny the validity of the illustration. A typical counter-argument is that rationality
Rationality
In philosophy, rationality is the exercise of reason. It is the manner in which people derive conclusions when considering things deliberately. It also refers to the conformity of one's beliefs with one's reasons for belief, or with one's actions with one's reasons for action...
as described in the paradox is so limited as to be a straw man
Straw man
A straw man is a component of an argument and is an informal fallacy based on misrepresentation of an opponent's position, twisting his words or by means of [false] assumptions...
of the real thing, which does allow the consideration of meta-arguments. In other words, it's entirely rational to recognize that both choices are equally good and arbitrarily (randomly
Randomness
Randomness has somewhat differing meanings as used in various fields. It also has common meanings which are connected to the notion of predictability of events....
) pick one instead of starving. This counter-argument is sometimes used as an attempted justification for faith
Faith
Faith is confidence or trust in a person or thing, or a belief that is not based on proof. In religion, faith is a belief in a transcendent reality, a religious teacher, a set of teachings or a Supreme Being. Generally speaking, it is offered as a means by which the truth of the proposition,...
or intuitivity (called by Aristotle noetic or noesis). The argument is that, like the starving ass, we must make a choice in order to avoid being frozen in endless doubt. Other counter-arguments exist.
Buridan's principle
The situation of Buridan's ass was given a mathematical basis in a paper by Leslie LamportLeslie Lamport
Leslie Lamport is an American computer scientist. A graduate of the Bronx High School of Science, he received a B.S. in mathematics from the Massachusetts Institute of Technology in 1960, and M.A. and Ph.D. degrees in mathematics from Brandeis University, respectively in 1963 and 1972...
, in which Lamport presents an argument that, given certain assumptions about continuity
Continuity
Continuity may refer to:In mathematics:* The opposing concept to discreteness; common examples include:** Continuous probability distribution or random variable in probability and statistics...
in a simple mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
of the Buridan's ass problem, there will always be some starting conditions under which the ass will starve to death, no matter what strategy it takes.
Lamport calls this result Buridan’s principle, and states it as:
- A discrete decision based upon an input having a continuous range of values cannot be made within a bounded length of time.
Application to digital logic: metastability
A version of Buridan's principle actually occurs in electrical engineeringElectrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
. Specifically, the input to a digital logic gate must convert a continuous voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
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
Comparator
In electronics, a comparator is a device that compares two voltages or currents and switches its output to indicate which is larger. They are commonly used in devices such as Analog-to-digital converters .- Input voltage range :...
. The voltage value can then be likened to the position of the ass, and the values 0 and 1 represent the bales of hay. Like the situation of the starving ass, there exists an input on which the converter cannot make a proper decision, resulting in a metastable
Metastability in electronics
Metastability in electronics is the ability of a digital electronic system to persist for an unbounded time in an unstable equilibrium or metastable state....
state. Having the converter make an arbitrary choice in ambiguous situations does not solve the problem, as the boundary between ambiguous values and unambiguous values introduces another binary
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...
decision with its own metastable state.
See also
- Catch-22Catch-22 (logic)A Catch-22, coined by Joseph Heller in his novel Catch-22, is a logical paradox arising from a situation in which an individual needs something that can only be acquired with an action that will lead him to that very situation he is already in; therefore, the acquisition of this thing becomes...
- Dining philosophers problemDining philosophers problemIn 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....
- EntropyEntropyEntropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
- Hobson's choiceHobson's choiceA Hobson's choice is a free choice in which only one option is offered. As a person may refuse to take that option, the choice is therefore between taking the option or not; "take it or leave it". The phrase is said to originate with Thomas Hobson , a livery stable owner in Cambridge, England...
- Jean BuridanJean BuridanJean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. Although he was one of the most famous and influential philosophers of the late Middle Ages, he is today among the least well known...
- Metastability in electronicsMetastability in electronicsMetastability in electronics is the ability of a digital electronic system to persist for an unbounded time in an unstable equilibrium or metastable state....
- Morton's forkMorton's ForkA Morton's Fork is a choice between two equally unpleasant alternatives , or two lines of reasoning that lead to the same unpleasant conclusion...
- Spontaneous symmetry breakingSpontaneous symmetry breakingSpontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....