Buridan's Ass Paradox
For those who are unfamiliar with the paradox it's about a hungry ass being placed in the exact middle of two identical stacks of grass. Having no reason to choose one over the other (since they're identical) the ass is paralyzed into indecision and eventually dies of starvation.
How do we solve this paradox?
The odd thing that strikes me is that the scenario is exactly like as if there were not a single stack of grass. In both situations the ass starves to death. This implies that in the paradox, choice, as commonly understood, is an illusion. The presence of two stacks of grass is identical to there being not a single stack of grass. The ass, for all practical purposes, doesn't have a choice at all (as usually understood).
However let us re-examine the ass's predicament. As I demonstrated above there's no difference between 2 identical stacks of grass and zero stack of grass. Both result in starvation and death. It then becomes obvious that the real options for the ass are life or death. It then follows that he must choose one of the stacks (to stay alive). He may then, upon his whim, choose one, eat and live. I italicized ''whim'' because there is a reason to being whimsical.
In conclusion, reason can still guide the ass to make an appropriate response to the scenario. The only random element (which stack to eat) is also a rational decision and so is NOT random as random really is.
Your thoughts.
How do we solve this paradox?
The odd thing that strikes me is that the scenario is exactly like as if there were not a single stack of grass. In both situations the ass starves to death. This implies that in the paradox, choice, as commonly understood, is an illusion. The presence of two stacks of grass is identical to there being not a single stack of grass. The ass, for all practical purposes, doesn't have a choice at all (as usually understood).
However let us re-examine the ass's predicament. As I demonstrated above there's no difference between 2 identical stacks of grass and zero stack of grass. Both result in starvation and death. It then becomes obvious that the real options for the ass are life or death. It then follows that he must choose one of the stacks (to stay alive). He may then, upon his whim, choose one, eat and live. I italicized ''whim'' because there is a reason to being whimsical.
In conclusion, reason can still guide the ass to make an appropriate response to the scenario. The only random element (which stack to eat) is also a rational decision and so is NOT random as random really is.
Your thoughts.
Comments (63)
If we leave the example scenario as an ass and hay, it opens the door to all kinds of cheap tricks to solve the problem, using the mechanics/determinism of the universe, biology, etc. The same applies to any "practical" scenario; you can always find a fudge somewhere in the reality of the situation.
To avoid that, I like to reduce the problem down to an isolated, logical system. There exists (in conceptual/mathematical space) an entity which is driven to "eat" cells to avoid death. It will always "eat" the cell closest to it, It's placed at a coordinate on a unit grid (i.e. we're agreed that this space is not infinitely divisible, etc) and two identical cells are placed at equal distances from the entity.
The question now becomes about the process by which a) the entity becomes aware of cells (i.e. how it knows they're there, how it calculates the distance, whether and how it stores this knowledge, etc) and b) how it makes the decision to approach a cell.
These processes need to be further refined. For example, the entity could be programmed to approach the first cell that qualifies as being the closest cell (i.e. it keeps an internal database sorted by distance and just chooses the first), but this solution is conditional; it depends on the assumption that the entity is a) programmed and b) programmed in this way.
So I imagine the solution comes subsequent to identifying a situation where the conditions and processes are disconnected from the scenario/situation.
Any thoughts?
I don't think this really addresses the problem, which is that the decision to choose one over the other isn't a rational decision. Although there might be a reason to pick one, there isn't a reason to pick this one. The decision, then, over which to choose is random. Whether or not a random decision counts as having free will is then an issue. Although, if random decisions like this are impossible in nature then in such a scenario any action would be impossible.
A real world application of this is metastability in electronics. The circuit is unable to make a decision and so something else (an arbiter circuit) makes the decision for it. The circuit "knowing" that it has to pick one doesn't help.
What I'm saying is:
1. The real options are life or death. NOT the two stacks (as explained above).
2. The random element of actually choosing one particular path is actually guided by the realization that not making a choice is going to be harmful/fatal. So it's not really random
Yes, but there are two ways to avoid death, and no reason to pick one over the other. That's where the decision-making halts. Simply knowing that you have to live doesn't help you choose which life-saving option to choose. Does my realization push me to pick A or B? Given that there are no reasons to prefer one over the other, any decision is random (assuming that random decisions are even possible).
Hmmmm...
I already explained above that 2 stacks of grass is the same as NO stack of grass. Therefore the choice at that level is an illusion. There is NO choice.
The real choices are LIFE or DEATH. The choice is clear here - life. The next obstacle, as you've pointed out, is the juncture where we actually choose between the rwo stacks. In the original paradox it says that there's no reason to choose one over the other. Hence the paradox. However I've shown in my analysis that the ass having chosen life must be compelled (logically) to make a random choice between the two stacks. Therefore the ass has a reason to make a random (if you can call it that) selection.
All you've explained here is that when given the three options of a) eat the hay on the left, b) eat the hay on the right, and c) do nothing, we have a reason to dismiss c) as an option. The problem is that we have no reason to then dismiss either a) or b). So, as you say, the decision over which to choose is random. But given that it's a random decision it isn't a rational decision. And if random decisions are impossible – if every decision must be rational – then no decision can be made.
So rather than solve the problem you've just tried to hide it behind a false dichotomy (or maybe misleading dichotomy is the better term).
It seems to me that any such scenario which posits that, in a deterministic universe, the ass physically couldn't select one of the hay bales to eat (and therefore must starve to death) must assume that the universe is (and has always been, at least within the light cone of the ass) perfectly symmetrical, with a perfect counterbalance of forces. (The universe, of course, includes the ass himself.)
In order for the paradox to obtain, there can be no physiological (or otherwise physical) bias towards one side or the other for the ass (e.g. we cannot assume that his left eye works slightly better than the right). Otherwise, even the smallest difference might suffice to break the symmetry and allow the ass to choose one bale of hay to the exclusion of the other.
But, such "cheap tricks," aside, I understand that the classical paradox is about decision-making and ratiocination, and that, as you say, all else can be (and perhaps should be) abstracted away.
I have shown you how, in fact, the ass must (has a reason) choose (random or otherwise).
You've only explained that it has a reason to pick either a) or b) over c). You haven't explained that it has a reason to pick a) over b) or b) over a). That's the choice that leads to the paradox. As above, your proposed dichotomy is a misleading one. There are three options and no rational reason to pick one (only a rational reason to not pick one).
It's like saying that I have a rational reason to choose to play football over choosing not to play football, but ignoring the fact that I have no rational reason to choose amongst the various positions. Do I choose striker or keeper? Knowing that I have to pick one doesn't help me choose which to pick.
It's erroneous to simply think that the only two elements in this problem/paradox are the grass and the ass. There's a third: the process by which the ass makes decisions. Again, how that process works is integral.
First, it's unlikely, if not impossible, that there will ever be two identical stacks of grass.
Second, it's unlikely, if not impossible, that these two stacks of grass, even if they are identical duplicates, will be perceived as identical.
Third, it seems to me that if the ass really, really needed food, the preference for obtaining this goal would over-ride any hypothetical hesitation. Subconscious thoughts might come into play and start to make one of the stacks appear more preferable than the other, even if they are (objectively) identical.
In fact without any sub/unconscious motivation, it appears that basically nothing would be preferable at all. That we are given a choice in the first place depends on previous unknown manipulations.
I understand what you mean. So you agree that I've demonstrated that the ass has to choose between the two stacks of grass. This wasn't part of the original paradox.
If you will allow an analogy to describe your objection to my ''solution''. It's like having a reason to go to the hospital but not having reason to choose between two routes. If I am right then...
Well, once the ass is logically compelled to make a choice it now has to analyze the options it has. Since both choices are equally acceptable it doesn't matter which is its choice - he may choose randomly. In other words the choice is no longer relevant to the problem. It chooses one and lives.
Of course this choice is relevant to the problem. This choice is the problem. The problem isn't the choice between eating or not eating or the choice between going to the hospital or not going to the hospital; the problem is the choice between eating the hay on the left or eating the hay on the right or the choice between taking the first route or taking the second route.
You say that the answer is "the choice is random" but this is the problematic answer. If random choices are impossible – if every choice must be rational – then the ass cannot choose randomly, in which case the ass is incapable of making a choice at all. And even if random choices are possible, a case can be made that random choices aren't actually free choices.
So, again, you're not solving the problem. You're just hiding it behind a misleading dichotomy.
Well, in my humble opinion, as I've shown above, choosing randomly IS the rational choice.
Sorry for being dense, but what do you mean by solving? Are you hoping to find an explanation of why such a situation couldn't occur, or an explanation of what would be required for it to occur, or something else?
An ass wouldn't actually die of starvation in front of two stacks of grass. However, there could conceivably be an organism which would, and of course similar problems regularly manifest in other information-processing systems such as computer software. What more is there to say about it?
That it's rational to choose a) or b) over c) is not that the random decision to choose a) over b) or b) over a) is rational. And if it's impossible to randomly choose a) over b) or b) over a) then the ass cannot choose a) or b). That's the problem.
The stacks must by necessity be different in some respect, and it is this difference which makes the left one prettier. Just the fact that one is on the right, and the other on the left gives reasons, many many reasons to employ. The pigs left leg hurts and turning right is easier. It chose right last time and wants to keep things fair so goes for left. It's left hoofed, so it goes left. It's father told it on his death bed to always go down the right path, and interprets this literally, etc.
In the disreputable field of psychology (according to Un) Buridan's ass illustrates the 3 basic choice situations:
Attraction / attraction
Attraction / repulsion
Repulsion / repulsion
It's easy for an ass to choose when the choice is between nice fresh grass and a pile of sand. The other two are more difficult, and they illustrate a common enough human situation. Two good job offers or two bad job offers. At least with the two good job offers, you won't loose no matter which one you choose, and in the case of two bad job offers, you won't win, regardless of which you choose.
In real life, the outcome is often enough NO DECISION. One dithers too long about which of two cars to buy, and when you finally make up your mind a week later, both have been sold. Is there a solution? In balanced win/win or lose/lose situations, there isn't, if you don't find a way to tip the scale.
Reasonably intelligent people call in somebody else to help. If a second ass had come along, Buridan's ass would have lived to face even worse choices.
This raises an interesting point. I have to brush up on my readings on the identity of indiscernibles (was that one "Leibniz's Law"?), but I seem to recall similar thought experiments involving, say, two identical spheres symmetrically distributed in a symmetrical universe which contains no other objects. Given that there is nothing that could be predicated of the one sphere which could not predicated of the other (including their relational properties, which in this case would amount to "being located such-and-such distance from a sphere with such-and-such characteristics"), in what sense would they be distinct (clearly, they are numerically distinct, as a potential observer could easily see that there are two separate spheres)?
From the fact that the decision is irrational it does not follow that it is random. The ass must choose, and who knows why she chooses one over the other. Who knows what transpires in the ass-mind; perhaps the landscape is more appealing behind the one than the other; or it is due to the position of the sun in the sky, the direction of the breeze, the proximity of a copse of trees, a cloud in the sky, a wafting scent, or perhaps the ass just chooses regardless. Free will consists only in the fact (if it is indeed a fact) that the ass could equally have chosen the other pile of hay.
I always thought it is a ridiculous, archly reductionist thought experiment, because two piles of hay could never be exactly equal. Even if they were exactly the same size down to the straw, one might appear slightly bigger than the other, or a more appealing colour, there are a million other possibilities if you exercise your imagination.
I only want to say that the alleged random choice the ass has to make is based on rationality. There's no paradox.
In the original paradox the ass was paralyzed because it didn't have a reason to make a random choice between two identical stacks
I have shown and you've agreed that the rational choice is to make a random selection.
The ass now makes a random choice and lives. What's the difficulty here?
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The difficulty here is that you haven't explained how the ass can choose a) over b) or b) over a). You've only explained how the ass has a rational reason not to choose c). Your answer "it is rational to make a random choice" isn't an answer as it doesn't explain how the random choice is made. How does one make a random choice? And does this conflict with having free will?
Again, you're just disguising the problem behind the misleading dichotomy "life or death". The actual options are "eat hay on left, eat hay on right, or do nothing". That two of the options lead to the same outcome isn't that we can pretend that they're just one option.
Indiscernability of identicals (if I'm remembering right... too lazy to look up...). As in, if two things are identical, they share all of the same properties, and there aren't two things there is one thing. Identicality of indiscernables is that if two things share all of the same properties, then they're identical. This second one is less obvious, and doesn't seem necessary.
I think that in stipulating that two things are identical, you either mean in some respect, but distinct in others, or you are stipulating that there aren't two things at all. That's just what identical means. Two things can be completely indistinguishable, indistinct, but not be identical if you reject the IOD, but stipulating that they're identical does necessitate that they share all of the same properties, and are actually the same thing.
I think this misses the point. Obviously the two stacks of hay are different in that they're two stacks of hay, located in different places and being constituted of different instances of matter. But the premise is just that there's nothing about either of them for there to be a rational preference for one over the other. It's not that one's closer, or safer, or tastier, or more nutritious. So how does one choose which to eat? Is it possible to make a random decision, or would we end up like the circuit in metastability? And if we can make a random decision, is this actually something that we choose, or is it just something that happens to us, like the circuit being influenced by an arbiter?
I don't think so, I realize that the point is that because they're identical, that it is impossible to rationally preference one over the other, because what could be said of one, can be said of the other as well -- but I'm saying, and you're agreeing that this obviously isn't so. One can actually come up with a bunch of things that would be true of one and not the other. Say the wind is coming in from the left, and the pig smells that one but not the one on the right (not to mention the other reasons I've given).
The premise is that there isn't anything about either that provides for a rational preference – or at least nothing that the ass is aware of.
So, assuming that there is no (known) reason to prefer one over the other, what does the ass do? Is it incapable of acting, or can it make a random decision? And if it's capable of making a random decision, would the decision actually count as a free choice?
I know that, and I'm saying that that can't be because it doesn't make any sense for the reasons I've given.
If you want to be pedantic, you could start arguing that there's no such thing as a "pile of grass" and maybe even throw in some Sorites paradox for added awkwardness. Maybe throw in some Buddhist koans about how the ass doesn't eat the grass, but the grass does in fact eat the ass.
This is partly also why it's beneficial to abstract away the problem. Keep the focus on what is important so that you don't get distracted by things that are ultimately irrelevant.
This is no longer a problem. In the paradox the ass has NO reason to make a choice.
As I've explained the ass HAS a reason to make a choice.
Either the decision is logical or it is random. It can't be logical as you've already explained and I agree. However it can be random but with the added qualification that there IS a reason to being random.
Yes, your summary is accurate, as far as I recall.
From Wiki:
[quote=wiki]The indiscernibility of identicals
For any x and y, if x is identical to y, then x and y have all the same properties.
? x ? y [ x = y ? ? P ( P x ? P y ) ]
The identity of indiscernibles
For any x and y, if x and y have all the same properties, then x is identical to y.
? x ? y [ ? P ( P x ? P y ) ? x = y ]
https://en.wikipedia.org/wiki/Identity_of_indiscernibles
[/quote]
But, I believe the point is that the hay bales are not numerically identical, even if they are identical in all of their relevant properties (indeed, even if they are identical in all of their properties, period).
In any event, some forms of this paradox invoke an ass who is equally hungry and thirsty, and is placed equidistant from a bale of way and a bowl of water, each of which are equally desirable to him. So, if this identicality issue presents a serious impediment to anyone's considering the paradox, then they should feel free to think about this version, instead.
You keep missing the point. Given that it has to pick either a) or b), how does it actually make the random decision to pick one over the other? And is this random decision, if even possible, a free choice?
All you're saying is that it has a reason not to pick c). But there are still two options left to it – a) or b) – and you haven't addressed that decision. That it has a reason to pick one isn't that it has a reason to pick this particular one. And it's picking this particular one that is the problem.
Knowing that I have to play football doesn't help me decide which position to play. Knowing that I have to go to the hospital doesn't help me decide which route to take. Knowing that I have to eat some hay doesn't help me decide which bale to eat.
At the moment your answer is akin to saying that because I have a reason to escape the burning building I should just do it, without explaining how to escape the burning building, or even if it's possible. So saying that I have a reason to make a random decision doesn't explain how a random decision is made, or even if it's possible.
And maybe the only way to escape the building is if a Fireman rescues me, in which case I'm not the one doing the escaping. So maybe the only way to make a "random" decision is if something else makes the decision for me, in which case I'm not exercising free will.
What I've shown is that rationality can still guide the ass - it is rational to choose. How it does that is immaterial. If you want to know well, either the actual choosing is rational or random. We already know it can't be rational (isn't that why we have the pardox). So the ass has to make a random choice.
And the problem is that random choices might not actually be possible (e.g. hard determinism) or that random choices aren't actually choices but things that happen to us.
But say instead that the ass isn't driven to survive, but is instead motivated purely by a desire to eat. What then?
This is the trap I was hoping to avoid by abstracting away the problem. We're now talking very specifically about a donkey that we have decided has a desire to live and is capable of tossing a coin. Everything about the essence of the problem has just been left behind.
That's another story isn't it. Also my response to this is to observe how we behave. In a lifetime we face many situations that are similar to this. Do we behave like the ass and well, starve ourselves? No we do not. We simply make a random choice and get on with it. Fact seems to contradict your hypothesis.
Yes I could've entirely missed the point of the paradox. However I focussed on how a rational being can be stumped by such a scenario - as per the paradox. I showed that rationality can still be used to come to a decision.
I'm curious as to what you think is the main ossue here. I'd be grateful if you could clarify. Please dumb it down as I'm not so bright (perhaps you already got that from my posts). Thanks.
Forget the ass. Forget the grass. Forget life and death. When presented with two options and the outcome of either choice would be equally beneficial and equally harmful - i.e. there is no clear reason to choose one over the other - how does a decision get made?
I don't intend to eventually push any particular opinion; I just think there's more interesting ground to be covered if you can look beyond the donkey.
However my particular solution (if you agree) can be generalized. The choice is not between two things of equal appeal. The choice is between loose and win. This is the real issue and it compells us to make the choice.
To expand on the "win and lose" point: You're taking the original problem - which is how to reach a decision - and hiding it behind this idea of there being an objective to achieve. That is to say, rather than solving the problem of how the donkey decides between two identical piles of grass, you've changed the problem into, how does the donkey take a course of action that keeps it alive. The original problem goes unsolved.
I explained in my previous posts that there being 2 stacks of grass is equivalent to there being no stack of grass, as far as logic is concerned. The ass cannot decide - two identical choices is equivalent to there being no choice. Here, again as far as logic is concerned, choice is simply an illusion.
Then I explained that the real choice here is between satisfying hunger or going hungry. These choices are the real choices available to the ass. I'm sure this approach can be generalized as I think that's what you have in mind. Rationality is now applicable to the problem now. The ass has a logical reason to make a choice. However as explained above the act of choosing between the two stacks of grass cannot be rational. It has to be random - that is the only option available.
In summary I've shown how the ass can still be guided by rationality to make a decision, given the circumstances.
No, you have not. Read the replies again. They explain the issue the thought experiment brings up: how do we choose between two equal choices when we have no reason to choose one over the other? You are getting caught up on the details of thought experiment itself. You are like the person who hears the trolley problem and tries to find some reason to stop the trolley without killing anyone, when the real point is asking whether it is better to kill one person or let five people die.
Sometimes in such thought experiments or problems it is difficult to know which aspects we can safely abstract away, and which we can sensibly retain. Like those problems concerning how to figure out which light switch controls which light bulb in a room we can only view once. The solutions often concern feeling light bulbs to see if they're warm and such.
Obviously, it would defeat the purpose of the problem if we say we will set up a surveillance camera in the room: such solutions leave us too much latitude. On the other hand, if we got too abstraction-crazy and claimed that the fact that the problem involves light bulbs in particular is of no consequence to the logical structure of the problem, we would have abstracted ourselves right out of a valid and legitimate solution.
And I've explained that this is an illusion of choice. There's no way reason and logic can solve this conundrum. It has to be a random selection.
Quoting Chany
Wouldn't saving everybody be the best solution?
Or it could be that the ass cannot make a decision or its mind has a built-in deterministic way of dealing with situations like this.
Quoting TheMadFool
Trolley problems are set up so that way you are faced with a dilemma: you must either kill one person or let five people die. We would like to save everyone, but the thought experiment says we cannot and that we have to make a decision between the two options. Any attempt to weasel your way out by creating some scenario in which everyone lives will be explained away in the thought experiment.
The fact is that we do make random choices in our lives. We never get stuck like the ass. I'm sure if you were ever hungry you wouldn't get paralyzed between two boxes of cereals. [B]Fact[/b] shows that we are capable of making random choices.
We make choices between competing options and sometimes those choices are extremely difficult. It does not follow from this fact alone that we have observed an actual situation of two equally compelling choices that Buridan's Ass describes. Nor has it been demonstrated that, even in the hypothetical case it has been shown, the mechanism that does the choice is actually random and not deterministic.
I'll offer you conclusive proof. Please invent a situation that accurately captures Burridan's Ass' situation. I'll be happy to take the role of the ass (X-) ). You can observe what I do.
I can't. That's my point. There is no way (at least based in modern science and human ability) to set up a real world Buridan's Ass scenario that is not open to criticism. I would have to set up two exactly compelling options, but I have no way of knowing if anything I present is actually equally compelling. I would need to ensure they remain equal until you make your choice, which is practically, if not actually, impossible. If you think I can, then you misunderstand the words "equally compelling".
How can I ensure the case to pick each can is perfectly symmetrical and equally appealing in your mind and remains that way as you go through the decision making process?
Just holding the two cans in each hand suffices as equality in all respects to me.
But its not. You have to set up controls for the experiment to eliminate variables that could make the can unequal. If not, there is always a way for me to criticize the exercise and claim the two cans were not equal in your mind. I am saying it is impossible to account for all the control variables in this case, which is required for the experiment to work.
I'm saying I can make a random choice. I'll flip a coin and choose. That removes the difficulty of making things equal in all respects.
This doesn't mean that there are not important issues similar to this in computer programming, but there are ways to avoid a program getting stuck between two options.
You cannot solve it, but nature might solve it through chaos - meaning that eventually one stack of grass (I've heard the donkey and two carrots) will drift closer, thereby stimulating a decision (one way or the other, for the ass may prefer the further stack of grass on pure principle).