Buridan's ass

Political cartoon ca. 1900, showing the United States Congress as Buridan's ass, hesitating between a Panama route or a Nicaragua route for an Atlantic-Pacific canal.

Buridan's ass is an illustration of a paradox in philosophy in the conception of free will.

It refers to a hypothetical situation wherein an ass 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 philosopher Jean Buridan, whose philosophy of moral determinism it satirizes. A common variant of the paradox substitutes two identical piles of hay for the hay and water; the ass, unable to choose between the two, dies of hunger.

History

The paradox did not originate in Buridan's time; it dates to antiquity, being first found in Aristotle'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 which, confronted by both food and water must necessarily die of both hunger and thirst while pondering a decision.

Discussion

Some proponents of hard determinism have granted the unpleasantness of the scenario, but have denied that it illustrates a true paradox, since one does not contradict oneself in suggesting that a man might die between two equally plausible routes of action. For example, Baruch Spinoza in his Ethics, suggests that a person who sees two options as truly equally compelling cannot be fully rational:

[I]t may be objected, if man does not act from free will, what will happen if the incentives to action are equally balanced, as in the case of Buridan's ass? [In reply,] I am quite ready to admit, that a man placed in the equilibrium described (namely, as perceiving nothing but hunger and thirst, a certain food and a certain drink, each equally distant from him) would die of hunger and thirst. If I am asked, whether such a one should not rather be considered an ass than a man; I answer, that I do not know, neither do I know how a man should be considered, who hangs himself, or how we should consider children, fools, madmen, &c.

— Baruch Spinoza, Ethics, Book 2, Scholium

Other writers have opted to deny the validity of the illustration. A typical counter-argument is that rationality as described in the paradox is so limited as to be a straw man 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. This counter-argument is sometimes used as an attempted justification for faith 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 Lamport, in which Lamport presents an argument that, given certain assumptions about continuity in a simple mathematical model 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

Main article: Metastability in electronics

A version of Buridan's principle actually occurs in electrical engineering. Specifically, the input to a digital logic gate must convert a continuous voltage 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. Like the situation of the starving ass, there exists an input on which the converter cannot make a proper decision, resulting in a metastable 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 decision with its own metastable state.

See also

• Analysis paralysis
• Catch-22
• Dining philosophers problem
• Entropy
• Hobson's choice
• Metastability in electronics
• Morton's fork
• Spontaneous symmetry breaking

Bibliography

• The Columbia Encyclopedia (6th ed.). 2006. 
• Knowles, Elizabeth (2006). The Oxford Dictionary of Phrase and Fable. 
• Mawson, T.J. (2005). Belief in God. New York, NY: Oxford University (Clarendon) Press. p. 201. 
• Rescher, Nicholas (1959/60). "Choice Without Preference: A Study of the History and of the Logic of the Problem of “Buridan’s Ass”". Kant-Studien 51: 142–75. 
• Zupko, Jack (2003). John Buridan: Portrait of a Fourteenth-Century Arts Master. Notre Dame, Indiana: University of Notre Dame Press. pp. 258, 400n71. 

• E. Ullmann-Margalit and S. Morgenbesser, "Picking and Choos- ing," Social Research, XLIV (1977), 757-785.

External links

• Vassiliy Lubchenko (August 2008). "Competing interactions create functionality through frustration". Proc. Natl. Acad. Sci. U.S.A. 105 (31): 10635–6. doi:10.1073/pnas.0805716105. PMC 2504771. PMID 18669666. http://www.pnas.org/content/105/31/10635.full. 
• Definition of term at wordsmith.org