1. Solution: A rock ends where the minerals that compose end and other materials, such as the atmosphere, begin. There is no clean line to draw describing where the minerals end because the surface of the rock is fractal – the closer you look the more bumps and dents you will see. Still, the fact that it is hard to describe where the rock’s surface is doesn’t mean that it is impossible, and as our tools improve a better and better measure of where exactly the rock ends can be obtained.
Evaluation: This is the scientific answer to the question, and in scientific terms there is nothing to find fault with. Still, the response can be pushed at a number of points on the philosophical level. For example, we can ask what the difference is between the minerals that make up the rock and the air around it. The answer to that question that can be given in terms of molecules and atoms. And if we ask what the difference between atoms is an answer can be given by appealing to their composition of protons and neutrons or how they interact with various measuring devices. Again, these are valid scientific answers. However, there are also differences along these lines within the rock. The rock is not composed of exactly the same thing, and so there are also differences between the atoms and molecules that make up the rock, although these differences are less extreme, by some measure, than those between the rock and the surrounding air. The question to ask now is why do we draw the line that puts the differences between the components of the rock on one side and the differences between the components and the air on the other. Why not accept larger differences as still counting as being part of the rock, and thus end up including some air as well? Or why not make the division more sensitive to those differences and conclude that really there are a number of rocks, not just one? No purely scientific answer can be given to those questions, which shows one weakness in the purely scientific approach.
2. Solution: Fundamentally there is no difference between the rock and the rest of the world. Thus it makes no sense to ask where the rock ends and the world begins – the rock and the world are one. Of course the rock appears to be distinct from the remainder of the world. This appearance does not contradict the idea that the rock and the world are one, because supposing that the world is not everywhere the same does not contradict the idea. The fact that we experience the rock as being a distinct object is thus merely a product of our own minds and the way that they interpret variation in the world.
Evaluation: The best way to press such a solution is simply to ask: what do you mean? If everything is really unified then what distinguishes unity from separation? To understand what unity is we usually point to some things that are unified and contrast them with others that aren’t, and through those differences come to understand the idea. But if everything is unified then there is nothing to point out as lacking unity, and so there is no way to understand that unity. Of course you might say that you already understand unity, inasmuch as you conceive of the world as consisting of some unified parts and some separate parts. Simply take that idea, grounded in a misperception of the world, and apply it to the whole universe, you might say. But that doesn’t make the problem go away. If the whole world really is unified then the idea of unity you had previously, when you thought some things were distinct from others, must be a flawed idea since it was developed on the basis of flawed comparisons. Thus, if this claim was correct, trying to understand what it means to say that the whole world was unified by extending our ordinary idea of unity to encompass the whole world would be to extend a flawed idea, and thus not to really understand the actual unity that the world does possess.
Perhaps it is best to try a different approach to this solution. Why not simply grant that, if the world is unified, we have no idea what that unity is like? Thus to say that the world is unified is really to say that our ideas of unity and separation don’t apply to the world – they are faulty ideas. That position, at least, is consistent. With that resolved another problem appears. What is the point of looking at the world in this way? How does rejecting the idea of unity and separation help us lead better lives? I can think of several metaphorical ways to take the assertion that make it useful, but none that encompass the original solution to the question “where does a rock end and the rest of the world begin?” Perhaps that is this solution’s greatest weakness.
3. Solution: The rock and the world are products of our consciousness. Thus the distinction between the rock and the world, as well as the rock and the world itself, are in our minds.
Evaluation: This is the radical idealist solution to the problem that solves the difficulty of finding an external criterion to divide the rock from the world by locating the rock, along with everything else, in the mind. There are a number of ways to challenge radical idealism. We could ask why the world remains constant when we aren’t thinking about it, why it doesn’t respond to our wishes directly if it is part of our mind, and why it is able to surprise us. Answers can be given to these questions, but ultimately they all take the form of “that’s just the way things are”. Perhaps the contrived nature of the answers may make us suspicious of idealism, but its inability to give truly satisfying answers to these questions isn’t necessarily a mark against it. No matter what perspective on the world you take some lines of questioning will exhaust your ability to provide reasons and you will be forced to say “that’s just they way things are”. Indeed such answers are necessary because reasons must either come to an end or be circular. A better way to challenge radical idealism is to ask what is accomplished by moving everything into the mind. Since the mind is apparently unable to affect the world, except though our bodies in the normal way, it doesn’t seem that adopting the perspective of idealism opens up any new avenues of insight or new approaches to problems. Obviously it can answer certain questions such as the one posed here, but answering the question isn’t really the point of these solutions, since the question is a pointless one.
4. Solution: There is no division between the rock and the world because both are nothing, and nothing is not distinct from nothing. Of course we can’t deny our experience of the rock and the world, but, by calling them nothing, the idea that the world and the rock are an illusion in some way is expressed. How might that be the case? Well everything that is is always in the process of changing. And change is an illusion. Really everything exists at once, but since our perspectives are embedded within the universe we only see a piece of it at a time and thus perceive it as changing. Now if everything is changing and change is an illusion then everything is an illusion, and behind that illusion is some fixed and eternal reality.
Evaluation: The logic embedded in this solution is faulty. Even if we grant that change is an illusion it doesn’t follow that everything that is changing is an illusion. However, the idea being developed may have some merit on its own, even though the argument for it isn’t sound. It is true that the universe exists “all at once”, at least as far as we know. But because we are stuck within it, and specifically stuck with a perspective that moves constantly though time, we can’t see the universe “all at once”. Indeed it is difficult for us to even conceive of the universe “all at once” except through abstractions. If we take the universe as it exists “all at once” to be reality then, in comparison, the universe as we perceive it is a kind of an illusion, inasmuch as it fails to capture the universe “all at once”, and perhaps could therefore be called nothing in a metaphorical way of speaking (although it certainly is something to us). Although we might challenge that view by arguing that our perspective is not an illusion but accurately captures one slice of the universe. What would embracing such a perspective entail? Well it might imply a kind of stoicism, where we reject the value of external things because we deem them to be nothing. And we could challenge this stoicism by pointing out that it presupposes that an illusion has no value. Is an illusion without value? Since others and ourselves are affected by that illusion it might seem as much a candidate for being valuable as anything else.
5. Solution: It can’t be denied that there are objective facts about the rock and the world, as described in solution 1. However, where the rock ends and the world begins is not among those facts, as was revealed by the shortcomings of solution 1. Thus we might understand the situation as follows: We decide what we call “rock” and “not-rock”, and to that extent where the rock ends and the world begins, is a product of our own minds. However, there is also a set of objective facts, the facts captured by science, that these invented distinctions lay on top of. The best way to divide the world is thus an interplay between the facts we are laying the divisions on top of and considerations of which divisions are conceptually convenient, as discussed in the evaluation of 2:1.
Evaluation: This solution is a kind of combination of solution 1 and solution 2. It accepts that there may be relevant scientific facts, following solution 1, but it also accepts that where to divide rock from world is a product of our mind, following solution 2. Of course, as with all these solutions, we should ask what embracing this perspective gives us. The value of this perspective is that it cleanly distinguishes matters of fact from matters of opinion, and possibly philosophy. Thus we can use this perspective to untangle other issues in which sometimes we become confused and start mixing together facts and our own invented distinctions. I suggest that philosophy is like deciding on where to separate the rock from the world because philosophy is in the business of helping us conceptualize the world, either in a clearer way or a better way. As with separating the rock from the world there isn’t really a right or wrong answer in philosophy, as long as we don’t miss the facts completely. However, there may be better or worse answers, and which is which depends on what use we are trying to put them to.
6. Solution: It is impossible to determine where the rock ends and the rest of the world begins because the rock and the rest of the world are the same. This is not to say that they are one thing, as in solution 2, but rather that the rest of the world contains the rock and the rock also contains the rest of the world. Consider the rock first. Any fact about the world can be expressed in terms of the rock. Napoleon’s defeat at Waterloo can be located in terms of a number of rock lengths from the current position of the rock and as a point in time during the duration of the rock. The number of Napoleon’s troops can be counted as a multiple of the rock and the weight of Napoleon himself can be expressed in terms of the rock’s weight. In this way every fact about the world is in the rock. And though those same relationships every part of the world expresses a fact about the rock.
Evaluation: One way to understand this solution is as expressing the idea that there is no fixed or absolute standard with which to express the world. We could just as easily describe the facts in terms of the rock as we do in terms of meters and years. Of course there is no denying that the facts are the facts, and are in a sense the same no matter how they are expressed. However, we only have access to those facts via some standard, and the standard itself is completely up to us.
Another way to understand the solution is as expressing the interconnectedness of all things, which is known in modern times as the butterfly effect. The butterfly effect is the observation that even small changes in insignificant objects, such as a butterfly flapping its wings, propagate causally (i.e. which causes a disturbance in the air, which changes the direction of a breeze slightly, etc), and can possibly have significant long-term consequences, such as a hurricane. Obviously it is beyond the ability of any human being to predict the consequences of these small changes, and so we can’t harness butterflies to control the weather. But when we express the interconnectedness of all things we mean to point out that little things can be important to, and shouldn’t be ignored just because we can’t see how they might one day be significant. There is, however, one problem with this moral: the changes that are propagated through the butterfly effect do not respect the original intent. So it is possible that by giving some money to a homeless person you will set into motion a chain of events that will make the world a significantly better place. But it is also possible that by giving money to that homeless person you will set into motion a chain of events that leads to the destruction of the world. So it is true that everything is connected, and that little things can in the long run make a big difference, but it requires foresight to exploit those connections; blindly making little changes is just as likely to be bad as to be good. (On the other hand, doing small amounts of good may be worth it simply because they are small amounts of good.)
7. Interpretation: The question itself is a meaningless metaphysical puzzle. It serves as a trap for the philosophically unwary, as well as a lesson for them. If you take the puzzle seriously it is possible to spend a lifetime trying to answer it. Every time a solution is reached the principles underlying that solution will themselves turn out to be subject to question, and in this way new problems will emerge that need to be addressed before the original question can really be answered. That there is no end to such questions is the trap. However, unlike many other metaphysical puzzles, this one doesn’t appear to be intrinsically “deep”. And yet it is just as hard to answer as the deep questions. Thus we may be brought to the realization that there is a problem with metaphysical questions, deep and trivial alike. And that problem is that the answers have no value. We can puzzle over where the rock ends and the world begins forever, but the answer to the question will never do us any good. Thus metaphysical puzzles are best set aside completely.
Evaluation: I can’t deny that the answers to metaphysical questions are often useless. Solutions 2 and 3 ran into this problem; the question was answered but it was hard to see how knowing that answer benefited us. However, in contrast, a number of solutions have also contained within them interesting ideas that may indeed be useful, at least from some perspectives. So I think that rejecting metaphysical questions out of hand is too hasty. Rather what we need to reject is an obsession with metaphysics, one that would take the point of metaphysical speculation to be answers to metaphysical questions. What we need to do is keep our metaphysical speculation grounded by connecting it to other issues and by constantly questioning how it can help us with those issues.