I wouldn't count this as a paradox, but it is an interesting problem.

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?

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. — TheMadFool

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.

I thought the core issue was some kind of breakdown in rationality: the ass can find no reason to choose one stack over the other and thus will starve itself despite there being given TWO choices.

The decision, then, is random. Whether or not a random decision can be considered an application of free will is then an issue. — Michael

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

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 — TheMadFool

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).

Are you accounting for the mechanism behind rationality, though? Whether a brain, a computer, whatever - there are processes which inform how a decision gets made. How those processes work is directly related to how those processes react in the example scenario.

Yes, but there are two ways to avoid death, and no reason to pick one over the other — Michael

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.

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. — TheMadFool

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).

The mechanism of rationality? What do you mean?

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. — Efram

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.

In the original paradox there was no reason to make a choice (random or otherwise).

I have shown you how, in fact, the ass must (has a reason) choose (random or otherwise).

In the original paradox there was no reason to make a choice (random or otherwise).

I have shown you how, in fact, the ass must (has a reason) choose (random or otherwise). — TheMadFool

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.

When the donkey is given the choice, a process is involved in making a decision. For sake of example, we assume that this process is physical - the chemical and electrical processes of the brain.

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.

Ok. The way I see it decision making processes involve maximizing positive outcomes for the decision maker. Is this too simplistic a conception for the purpose of dealing with the paradox?

I think this is an example of a philosophical thought experiment that seems to be legitimately problematic, but in reality is actually not an issue at all.

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.

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. — Michael

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.

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. — TheMadFool

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.

– 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. — Michael

Well, in my humble opinion, as I've shown above, choosing randomly IS the rational choice.

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? — TheMadFool

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?

Well, in my humble opinion, as I've shown above, choosing randomly IS the rational choice. — TheMadFool

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.

They can't be identical, or they couldn't be two things. Two things that are identical are the same thing, and one thing. Like superman and Clark Kent. You can't stand one over here, and one over there.

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.

The ass should do what a person would do - if you can't decide, flip a coin and go with what that says.

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.

They can't be identical, or they couldn't be two things. Two things that are identical are the same thing, and one thing. Like superman and Clark Kent. You can't stand one over here, and one over there. — Wosret

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)?

Whether or not a random decision counts as having free will is then an issue. — Michael

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.

Sorry for being dense, but what do you mean by solving? — zookeeper

I only want to say that the alleged random choice the ass has to make is based on rationality. There's no paradox.

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. — Michael

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?

.

Consider it a parable, not a paradox, that you shouldn't be an indecisive ass.

I have shown and you've agreed that the rational choice is to make a random selection. — TheMadFool

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.