Buridan's Ass

The disagreement is about what freedom of the will consists in, and the donkey was manufactured to embarrass one side of it.

Intellectualism holds that the will necessarily follows the intellect's last practical judgement. Freedom, on this view, is not the ability to act against your best judgement — it is the ability to deliberate well and to suspend action while you do. This is broadly the position associated with Buridan and, before him, with a strand of Aristotelian and Thomist psychology.

Voluntarism holds that the will has a power of its own, and can select among options the intellect has left level. Al-Ghazali argued for something like this in The Incoherence of the Philosophers, using two identical dates: if the will could not differentiate without a reason, then God could not have created a world at one moment rather than another, and the whole argument for the world's eternity would go through. The stakes were theological, not agricultural.

The donkey story is a weapon manufactured by voluntarists against intellectualists. It says: your theory implies starvation, and starvation is absurd, so your theory is false.

Buridan's actual answer is more careful than the caricature allows. He held that when the intellect finds no decisive reason, the will's proper response is to defer — to withhold assent and send the intellect back to look again. This is a real freedom: the freedom not to act yet. It is also, applied to a starving donkey with two identical bales and no further evidence to gather, exactly the behaviour the story mocks. The caricature is unfair but it is not unmotivated.

Spinoza does the unexpected thing and concedes. In the scholium to Ethics II, proposition 49, he grants that a man in perfect equilibrium between food and drink would indeed perish, and remarks that such a person should be reckoned an ass rather than a man. For Spinoza, who denies free will altogether, there is no embarrassment: a system with exactly balanced causes produces no motion, and that is simply what determinism looks like at a symmetry point.

Leibniz denies the case can arise. The principle of sufficient reason guarantees that everything has an explanation, and a perfect tie would be a state of affairs with none. He argues in the Theodicy (1710) that the universe never presents two exactly equal options, since no two things are ever exactly alike, and that the donkey is therefore an impossible object rather than a counterexample.

Modern decision theory meets the donkey as the problem of indifference. Standard axioms of preference are stated over a complete ordering, and indifference is permitted: if $a$ and $b$ are indifferent, both are optimal, and the theory says take an optimal one. That is a coherent instruction, and the donkey is not paralysed — it just has two correct answers. But this exposes what the theory cannot supply: a selection function that turns "these are optimal" into "do this one". Every real implementation needs a tie-break, and the tie-break is arbitrary by construction.

The residual philosophical question is whether an arbitrary tie-break is a rational act or merely a physical event that happens in the vicinity of a rational agent. Ullmann-Margalit and Morgenbesser's answer — that picking is a distinct and legitimate species of act — is the most widely adopted, and is essentially a proposal to stop demanding that reasons explain everything.

The honest version of this story is that almost nothing about it is what its name suggests.

c. 350 BCE — the oldest surviving version. Aristotle, On the Heavens II.13 at 295b32, describes a man who is equally hungry and thirsty and equally far from food and from drink, and who must therefore remain where he is. The context is a criticism of Anaximander, who had argued that the earth stays at the centre of the cosmos because, being equidistant from everything, it has no reason to move one way rather than another. Aristotle thinks that argument is bad, and the starving man is his illustration of how bad.

c. 1095 — the case enters the argument about the will. Al-Ghazali, in The Incoherence of the Philosophers, uses a man facing two indistinguishable dates to argue that the will genuinely can select without a differentiating reason. The Arabic tradition passes the example into Latin scholasticism, where it becomes a standard test case.

c. 1321 — Dante. Paradiso IV opens with the example in its familiar form: between two equally distant and equally attractive foods, a free man would starve before eating either. Dante's poem is finished before Buridan's career is well under way, which by itself shows the example is not Buridan's invention.

c. 1340 — Buridan, who does not tell the story. Jean Buridan was a secular master of arts at Paris, twice its rector, and the leading logician of his generation. He wrote extensively on the freedom of the will and defended the position that the will may defer choice when reason finds no decisive ground. The donkey appears nowhere in his surviving writings. Nicholas Rescher's 1959–60 study of the problem's history, which remains the standard treatment, found no such passage, and none has been produced since. Claims that Buridan told the story with a dog, or that he told it at all, do not trace to any text of his.

1597 — the name is attached. The earliest recorded text linking Buridan's name to the example is Schönlin's Logicae Assertiones. That is more than two hundred years after Buridan's death, and roughly two thousand years after Aristotle's version. The label "Buridan's ass" is therefore late, external and hostile: a nickname given by critics to a doctrine, not a title given by an author to an argument.

1677 — Spinoza concedes the case in the Ethics, and jokes about it.

1710 — Leibniz rejects the case in the Theodicy, on the grounds that perfect symmetry never occurs.

1959–60 — the history is written. Rescher's "Choice Without Preference" traces the transmission from Aristotle through the Arabic and Latin traditions, and establishes the attribution as a misattribution.

1977 — picking is separated from choosing. Ullmann-Margalit and Morgenbesser's paper gives the modern vocabulary.

1984 / 2012 — the donkey becomes a theorem. Leslie Lamport writes "Buridan's Principle", arguing that a discrete decision based on a continuous input cannot be made in bounded time, and connecting the story to arbiter metastability in digital hardware. Repeatedly rejected by reviewers who found the physical claim too strong, it was finally published in Foundations of Physics in 2012.

Nearly seven centuries of a philosopher's reputation resting on a farm animal he never mentioned is, in its own way, a better illustration of how ideas travel than anything in the story.

It found a real hole in a good theory. "Do whatever you judge best" is not a complete instruction, because it says nothing about what to do when nothing is best. Every workable account of rational action — medieval, modern, human or mechanical — has had to bolt on a rule for ties, and the bolt is always unjustifiable by the theory's own lights. That is a genuine structural finding, and it came out of a joke about a donkey.

It marks the limit of the principle of sufficient reason. If everything that happens has a reason, then the donkey cannot move. If the donkey moves, then something happened without a sufficient reason. Leibniz saw the force of this clearly enough to deny the premise, and the choice he faced — abandon the principle or deny that ties occur — is still the choice on offer.

It is why real systems have arbitrary tie-breaks written into them. Sorting algorithms specify stability. Voting systems specify how to resolve an exact tie, usually by lot, and elections have genuinely been decided by drawing names. Distributed systems break symmetry with unique identifiers, precisely so that identical processes can never face identical evidence. In each case the designer has decided, explicitly, that arbitrariness is preferable to deadlock.

It gave engineering a real constraint. Lamport's version is not a metaphor. Any device converting a continuous input into a discrete output has a set of inputs on which its decision time is unbounded, and no cleverness removes it. The practical consequence is that synchroniser circuits are designed to reduce the probability of an unresolved state to something acceptable — a mean time between failures — rather than to zero. The donkey was right that there is a problem; it was wrong only about how long the hesitation lasts.

Metastability in hardware. Every time a signal crosses from one clock domain to another, a flip-flop must decide which side of the clock edge the signal fell on. When the timing is close enough, the flip-flop can enter a metastable state whose resolution time has no upper bound. Chip designers compute a mean time between failures from the settling time they can afford and add synchroniser stages until the number is large enough. This is Buridan's ass with a datasheet.

Leader election and symmetry breaking. In a network of identical processes running identical code, no deterministic algorithm can elect a leader — the symmetry is unbreakable from inside. Real systems break it by handing every node a distinct identifier or by using randomisation. Distributed computing takes the donkey's problem as a design premise rather than a puzzle.

Recommendation and ranking systems. When two items score identically, the system must still order them, and the tie-break — item id, insertion time, alphabetical order — becomes a real and often unnoticed source of bias. Alphabetical tie-breaking in candidate lists has measurable effects on election results, which is an arbitrary rule leaking into the world.

Choice paralysis. Psychologists studying decision difficulty find that near ties, not clear differences, produce the longest deliberation and the most post-decision regret. The observed pattern is that people manufacture a differentiating reason after the fact and then report having acted on it — which is precisely the voluntarist answer, arrived at empirically.

Automated vehicles. A control system facing two options it evaluates as equally bad must still emit one command. The engineering answer is a deterministic tie-break, chosen in advance and documented, because a vehicle that hesitates is worse than a vehicle that arbitrarily picks. The donkey's field now has lane markings.