The Paradox of Buridan's Ass

Betwixt the rock and the hard place

In my post where I gave the world (you’re welcome!) the word animalisine, I referred to the French philosopher Jean Buridan, as does Sheldon in this clip from the always entertaining Big Bang Theory:

Where to start? Contrary to what Julie Andrews’ Maria in the Sound of Music suggests, let’s start at the end: 

“Should two courses be judged equal, then the will cannot break the deadlock, all it can do is to suspend judgement until the circumstances change, and the right course of action is clear. — Jean Buridan, c. 1340” 

Well, that was, as Maria did say, a very good place to start. During my investigations into the world of Buridan’s Ass, I frequently was informed of it being a philosophical paradox. OK, not unlike a donkey, I’ll bite. A philosophical paradox you say. I think I understand what philosophy is, but what is this paradox you speak of? Maria, you were right. Let’s start at the very beginning.

Paradox:

  1. a seemingly absurd or self-contradictory statement that is or may be true

  2. a self-contradictory proposition, such as: ‘I always tell lies’

  3. a person or thing exhibiting apparently contradictory characteristics

  4. an opinion that conflicts with common belief

  5. I’d also like to add that Paradox was the first database software I used back in the DOS days. I notice it is still going strong as part of Corel’s WordPerfect Office package, an alternative to Microsoft Office.

During my early secondary school education, I spent a couple of English lessons (though it could have been more as my memory of this time is selective) learning figures of speech. More on those figures as we progress through this blog journey, but I certainly recollect that we covered paradoxes as figures of speech. I would have been taught that a paradox was a statement that appears to contradict itself. Similar to an oxymoron, the paradox had more words to it and can be convoluted and hard to understand. An oxymoron can be contained within two words: clearly confusing right? We’ll have more fun with oxymorons in a later post. 

After nailing paradox as a figure of speech, a history lesson had me stumbling over this essay question:

‘The Agrarian Revolution of the 1830s was a socio-economic paradox. Explain.’

I’m sure I did explain, alas no records of that essay remain. I believe the gist of what was expected was that the revolution should have lead to better wealth distribution amongst the population which would have lifted more people off the poverty line. It did not, so I guess that’s what the paradox was. Happy to be corrected here by my loyal readership.

So armed with that knowledge, I still struggle to understand the paradox element of Buridan’s Ass. 

Some simple paradox examples which should need little in way of explanation and help our understanding:

  • I must be cruel to be kind. (From William Shakespeare’s Hamlet)

  • Please ignore the notice.

  • I can resist anything except temptation. (From Oscar Wilde’s Lady Windermere’s Fan)

  • They must go to war to make peace.

  • Deep down he’s really shallow.

  • This is the beginning of the end. (Oddly, Shakespeare uses this in his Midsummer Night’s Dream but for a different meaning.)

Some more philosophical paradoxes for your delight:

The gentleman who invented the paradox, Eubulides of Miletus, managed to give us seven examples, grouped into four themes, straight off the bat. His most famous being 'The Liar' paradox. His sôritês paradox ('The Heap') concerns the measures around language and vagueness: so what’s not to like about that? This paradox considers a heap of sand from which you remove grains of sand. If your heap starts with 10,000 grains of sand and you keep on removing one grain down to a single remaining grain of sand is that single grain of sand still a heap? If not, at which point did the heap cease to be? Now that’s a paradox I can not only get my teeth into but also understand. So perhaps it may help with Buridan and his Ass? I need a bigger heap as one cubic centimetre of sand contains approximately 8,000 grains of sand. 

Now we have a testudine paradox: Zeno’s Achilles and the tortoise:

In this paradox, Achilles races a tortoise. Achilles gives the tortoise a 100 meter head start because Achilles is an extremely cocky fast runner. In the time it takes Achilles to run the 100 meters the tortoise has majestically crawled (I think I just sneaked in an oxymoron) 10 meters. As Achilles runs those 10 meters the tortoise crawls one meter. So for any given period of time, the tortoise always covers 10 percent of the distance that Achilles does. Zeno declared: 

“By this logic, Achilles will never truly catch the tortoise. Every time he gets closer, the tortoise is always a little further ahead. Does this mean that motion itself is impossible even though we experience it daily?”

Moving on in time and to the world of game shows, we have the Monty Hall Problem. Though seemingly a paradox, it can be solved using some basic probability mathematics. The problem revolves around the show’s finale ‘Open the Door’ segment. There are three doors and only behind one of them sits the grand prize (you have a one-in-three chance of winning the top prize). The contestant picks a door to open and the presenter - Monty Hall - will open one of the other two doors always revealing a lesser prize. You’re still in with a chance to win the top prize: your odds of winning have now jumped to fifty-fifty. Right? You can now either stay with your initial door choice or select the other unopened door. If you stay put your odds of winning were one-in-three if you switch doors then it jumps to two-in-three right? Your maths skills will help answer this paradox.

A final paradox to chew over involves a cat and quantum mechanics. The simple version begins with the idea that we take a cat and place it in a soundproofed wooden box. Now, without lifting the lid to observe the cat, how do we know whether the cat is alive or dead? Physicist Erwin Schrödinger came up with this thought experiment in 1935 in response to the Copenhagen interpretation of quantum mechanics: 

‘Until we observe a particle or thing, it exists in all states possible. Our observation determines its state.’ 

Returning to our cat in a box, a more sophisticated version is to add a jar of cyanide, a hammer, and a Geiger counter along with just enough radiation so there’s a 50/50 chance of the Geiger counter being triggered within an hour, releasing the hammer to crack the jar and thus poisoning the cat. 

We can use science to tell us plenty about each particle of the cat, the box, the jar and the odds that a particle may have decayed radioactively. But science cannot tell us anything about the state of the cat until it’s actually observed. So if the hour passes without observing the cat, the animal is theoretically both alive and dead - which we all know is absurd and impossible: a paradox. 

Without observation, we can never be 100 per cent sure of a current state. Similar to those piles of sand, at what point can we assume that things we cannot directly observe actually exist in an expected state. Experience informs us of that certainty but that is not the same as empirical observation.

Some of the foregoing and further paradox examples can be found here at Mental Floss.

Hopefully, you now have, like me, a stronger understanding of paradoxes. So back to Buridan for one last time. Jean Buridan was a 14th-century French philosopher. Apocryphal stories abound (an apocryphal story is one which is probably not true or did not happen, but which may give a true picture of someone or something - talk about a word which is a paradox in itself). Whilst these stories regarded his reputed amorous affairs and adventures, he still had time in hand to teach logic and philosophy at the University of Paris. His ass thoughts were an education on free will and as Amy and Sheldon alluded to in the above clip, Buridan’s thoughts were a riff on Aristotle and al-Ghazali: 

“...a man, being just as hungry as thirsty, and placed in between food and drink, must necessarily remain where he is and starve to death. — Aristotle, On the Heavens, c. 350 BC”

“Suppose two similar dates in front of a man, who has a strong desire for them but who is unable to take them both. Surely he will take one of them, through a quality in him, the nature of which is to differentiate between two similar things. — Abu Hamid al-Ghazali, The Incoherence of the Philosophers, c. 1100”

Buridan’s Ass came much later. Not as late as the satirical cartoon above. The apostrophe s denotes possession, but Buridan’s Ass was not his to own. Buridan spoke about two courses of action judged to be morally equal. His thoughts were later satirised and an ass was used by way of example. This example then gets modified to such an extent that a donkey will die because it cannot choose between two identical piles of hay.

The paradox of Buridan’s Ass, to me, falls on its ass as no paradox exists. Buridan’s original musings are clear and non-paradoxical. If presented with two equal courses of action then more information must be received in order to choose one. This is fine. However, you do need to consider the use of language and what is meant by equal? Similarly, when the donkey analogy is rolled-out, words such as identical are also introduced. Language-wise, identical rings a little of Eubulides’ heaps of sand. At what point is a heap, linguistically or logically, no longer a heap? At what point is a pile of hay identical to another one? 

Buridan’s Ass assumes everything is identical: the distance between the donkey and the hay is identical; the terrain to each pile of hay is identical; the size and quality of the hay are identical; etc. This is never the reality, as the donkey sits and pontificates over the merits of each pile of hay, a small gust of wind blows a couple of pieces of hay from one pile. The donkey sees this and starts walking towards the other pile as it is now larger. 

At a finite point in time, the donkey was unable to choose and without observation may well have been dead (Schrödinger’s cat!). But time gallops on (much to Zeno’s Achilles’ dismay), hay piles alter and hunger pains wane. Jean Buridan’s initial contemplations were not paradoxical. Buridan’s Ass only smells a little like a paradox if we suspend our understanding on how time moves and things change. Ultimately, Buridan’s Ass and other such paradoxes enable you to get your brain into top gear and cogitate: that is an exemplary endeavour.

If you think and keep challenging with ‘Why?’ then you are well on the road to becoming a philosopher! Whilst you’re in gear to think then perhaps the more linguistically minded readership will be asking ‘Why not Buridan’s Donkey?’ and don’t get me started on why Amy is calling it an eggplant.