Beyond Sense and Nonsense

Personally I am an advocate of the idea that the universe is essentially a meaningless place, onto which we impose meaning. We create significance, we constitute it – we don’t find it. However, there is a dangerous ambiguity lurking in this brief description. I said that the universe is meaningless – the events in it are without significance – without us. But what does it mean to say that something is meaningless? To call something meaningless is not to leave it exactly as it was, it is to look at it in a certain way. It is to deny the existence of meaningful relationships between it and other things. This looks very much like giving meaning to it, like taking up an attitude towards it, like interpreting it. In other words, “meaningless” is itself a meaning that can be given to things. To say that something is meaningless is not to deny it meaning, it is to give it a meaning – albeit a rather empty one. Nihilism is simply one way of constituting the world, not a refusal to constitute the world at all.

This raises the question of what things are like then before we give them meanings. In a way the question cannot be properly answered. We cannot say that they have significant relationships to other things, because that is to say they have meaning intrinsically. But neither can we assert that they lack such relationships, because that is a significant fact on its own, which is also to say that they have meaning intrinsically (the meaning of being “meaningless”). Perhaps weak souls may simply give up at this point and conclude that on the basis of this dilemma that meanings of some kind must be intrinsic after all. The problem, however, stems not from the fact that meanings are really intrinsic, but that to describe something, to understand it, we have to take up an attitude towards it. In other words, if we think about it we can hardly help but give some meaning to it. The apparent contradiction arose then because we were trying to explain what a thing is like outside all attitudes towards it, while at the same time taking up such an attitude. What we are left with are things-in-themselves, noumena, beings-in-themselves. This are all labels for the unthinkable that sits outside, and in a sense “behind”, of the domain of meaning.

This is more of a terminological clarification than anything, the idea of the noumena has already been done to death by Kant. And besides, what can you say about things of which you cannot think? The interesting lesson is not that noumena pop up, but that meaninglessness is a kind of meaning. One immediate consequence of this is that there are two kinds of nihilists, where nihilists are characterized by the slogan “it’s all meaningless”. On one hand we have the hypocritical nihilist. The hypocritical nihilist goes around labeling things as meaningless without realizing that in doing so they are giving them meaning. Thus the hypocritical nihilist is constantly in the business of contradicting themselves. On the other hand we have the catatonic nihilist. The catatonic nihilist avoids self-contradiction by actually refusing to give things meanings, and the only way to do that is to refuse to interact with them. Thus the catatonic nihilist must curl into a ball and shut out the world.

This is why nihilism is an absurd position. Are there ways for the nihilist to be consistent? Yes. The nihilist could embrace the terminological clarification we have made here and run around saying “it’s all noumena”. But this would hardly be shocking, because the claim that noumena exist and in some way lie behind the world we experience in no way contradicts our ability to find meaning in the world. Or the nihilist may admit that they had something more traditional in mind when they made their claim. Perhaps they meant only to deny the existence of absolute meanings or divinely ordained meanings. But is there really anything shocking about that these days? We are well aware that most meanings, and most values, vary from culture to culture. We would hardly be shocked if we ran into a culture that thought gold was worthless, even though our culture values it highly.

If it is at all bothersome it must be because we are attached to some small set of meanings that we hold to be above this. Ethical values, perhaps, or the significance of life. But I would say that there is nothing contradictory about denying absolute meanings while still holding on to an absolutist system of ethics. In fact the absolutist must affirm this. From the absolutist perspective an ethical fact is not something that exists because we constitute it. Rightness and wrongness are independent of people and their opinions about rightness and wrongness. Thus, so conceived, rightness and wrongness are not a meaning. Rightness and wrongness are as much a fact as the hight of the desk or the weight of the lamp. They are something that belongs to the noumena; they are something that we give a meaning to. Just as we give a meaning to the weight of the lamp (heavy enough to serve as a paperweight) so too would we give meaning to ethical facts. Thus the absolutist position, if it is indeed correct, is in no way threatened by the denial of absolute meanings. Nor is the relativist for that matter.

Perhaps I have once again made a straw man out of the nihilist’s position. Can’t the nihilist simply accompany their denial of absolute meanings with the additional assertion that ethical values are meaning and not facts? Perhaps they could, and this would threaten the absolutist conception of ethics. However, it is also to beg the question against the absolutist, and thus isn’t much of an argument. We can borrow an argument from the Euthyphro here, and ask why we constitute something as good or bad, if ethical values are meanings we give things. It it an arbitrary choice, or do we constitute it as good because it is good? The second creates a paradox – if good is nothing but our constitution of something as good, then this is to say that we constitute it as good because we constitute it as good, which says nothing. Thus it must be the first – it is an arbitrary choice. But this is nothing more, and nothing less, than relativism. And relativism is the denial of absolutism. So to tell the absolutist that ethical values are meanings and not facts is simply to assert that absolutism is false. Which is not much of an argument against it. The absolutist’s position presupposes that ethical values are facts and not meanings that we assign.

This digression into ethics, while not helping the nihilist look like less of a fool, has touched upon an interesting question, namely how to decide what is a “fact” and thus part of the noumenon, and what is part of the meaning that we give to the noumenon. Given that we can’t conceive of noumena I would say that it is impossible to know the answer to this question; we can’t look at the noumena as they are in themselves and see what we find there. But this is philosophy, the fact of the matter isn’t our concern here. On the philosophical level we are still free to hypothesize about what is and isn’t a noumenal property, on the same basis which we do all philosophy, namely that some ways of looking at the world are better than others. In simpler terms: the world makes more sense if we conceive of some properties as belonging to the noumenal, regardless of what the noumena is “really” like. This is why I think we can describe the size and mass of an object as “facts”, as properties that are what they are independent of us. It’s not that these properties couldn’t be understood as something we are projecting onto the world – they certainly could. We could point out that length is only something that comes into existence for us through our interactions with the world and through our interpretations of our experiences. This is why things shrank as we grew up, although since we are invested in the idea that length is an objective fact we describe that experience as the size of objects seeming to shrink.

But isn’t it absurd to say that length is merely a meaning that we impose on the world, and not a fact? It certainly seems absurd to me. The question is why. What’s so wrong about taking length to be something imposed on the world when it is perfectly acceptable to say it about the aesthetic value of the same item? One distinguishing feature is that we accept that judgments about aesthetic value can vary without indicating that some of them are in error, but we don’t say the same about length. If someone disagrees with us that the ruler is longer than the pencil after we place them side by side we conclude that their vision must be distorted, or that they have misunderstood the word. But if they disagree with our judgment that the pencil is more beautiful than the ruler we shake our heads and accept that they just see things differently than us.

The point is that we take uniformity concerning judgments about length very seriously, and judgments about beauty less so. A lot can hang on getting length “right”. We desire to communicate accurately and clearly about length, and we can only do that if length isn’t up for grabs. Much less hangs on beauty, and so it simply doesn’t pay to worry about having a single aesthetic standard. But I can imagine a situation where things are reversed. Imagine a culture with only a very primitive level of technology. Because they don’t have much in the way of technology they have no need for precise measurements. Indeed they don’t even have words for length specifically. Instead they have words for vaguely defined shapes each of which has a characteristic general size. In this culture there are valid disagreements about whether the ruler is “longer” than the pencil. One person might group the pencil under “A” and the ruler under “B”, which is characteristically larger. But another might classify the pencil under “C”, which is characteristically larger than “B”. Because these notions are vaguely defined, and they accept that there is no “right” way to classify shapes, both answers are equally valid. But, on the other hand, certain aesthetic values might play a large role in their lives. So large that they have developed a complicated numerical system for measuring beauty in its many different forms. They consider it to be an objective matter of fact that the ruler is 5.6 units in the R-h axis, while the pencil is only 3 units in the G-m axis. Thus the ruler has objectively greater aesthetic value than the pencil. If we disagreed with them about this they would conclude that somehow our perceptions were in error or that we didn’t properly understand what beauty means. Thus for them aesthetic value is properly placed in the noumena while length/size/shape is merely an interpretation of the world.

Now it is easy to object to this example by saying that,as I have described them, these people aren’t talking about length and beauty; the words they use simply don’t mean the same thing, so there can be no comparison. And that the words they use to describe shapes do not capture facts, as we take judgments about length to, thus says nothing about whether those judgments actually capture facts. This is a valid criticism. The reason I gave the example I did was because we are so set in our ways that we simply can’t conceive of using “length” in a way that isn’t factual. Thus I described a language that used non-factual shape words to describe something we normally think is factual, namely shape and size, to make plausible the possibility that the same could hold for length, that there might be ways of using length words and length concepts that isn’t factual either. At best this is an illustration, not an argument – and I’m perfectly happy with that because of my metaphilosophical commitments.

Let me finally get back to the point. The point of this lengthy digression is to show that what we choose to see as a noumenal property, and what we decide isn’t a noumenal property, depends on what we, collectively, consider important to communicate about in a clear, unambiguous, standardized, and objective way. We put length, charge, mass, etc into the noumena because they are part of our scientific and technological apparatus where all of the elements on the list are extremely important. It doesn’t matter if they are “really” – whatever that could possibly mean in this context – meanings projected out onto the world, so long as we are all projecting the same ones. Since beauty is not part of this or some similar apparatus we are free to leave it up for grabs.

So now let me tie this back into ethics and hopefully get some closure on this wandering mess. As I mentioned earlier, whether absolutism in ethics make sense under this worldview (where we project meanings onto a meaningless world) depends on whether right and wrong are facts – part of the substratum for interpretation, the noumena – or whether they are meanings. And that, if the second part of this piece is on the right track, depends on whether clarity, unambiguity, standardization and objectivity are things we want ethics to display. Whether they are things we need ethics to display. Obviously that is a philosophical argument in its own right. But I think the answer is yes; given what we do with ethics those features are features it needs to have, and thus we make better sense of the world we are in by placing ethical facts along with length and mass in the noumena (and let us leave questions of whether they reduce to some of those other properties to philosophers with more time on their hands).

Addendum: First Order Logic Without Objects

One argument for keeping the properties + objects model around (versus the bundle of properties model) is that it is integrated into first order logic. However, it is relatively simple to construct a logical system with the same expressive power as first order logic without that model.

The system is as follows:

All rules of syntax are the same as first order logic, except that instead of atomic formulae of the form Px we instead have property bundles of the form {A, B, C, D …}. And quantifiers range over properties; i.e. members of bundles. Later we may treat these bundles in the same way as sets (using some of the same notation), and like sets their members should be considered unordered. However, unlike sets, the expression of a property bundle of the form {A, B, C} does not mean that it is necessarily limited to those three properties; it may contain additional, unlisted, properties. If necessary a property bundle can be named with a subscript, such as {A, B}_a.

The following rules of inference are also permitted (in addition to the usual ones)
X_a → Y_a, where Y ⊆ X
P₁ = P₂ → ({P₁, A, B, …}_a → {P₂, A, B, …}_a)
X_a & Y_a → X∪Y_a (although this isn’t very useful until the second-order version of the system)

This has the same expressive power as first order logic, which can be demonstrated as follows:
Anything that can be expressed in first order logic can be expressed within this system via property bundle pairs (of the form {A, B}), and turn both designations for properties and objects under the old systems into properties under the new system. For example, ∀x(Fx → Px) becomes ∀x({F, x} → {P, x}). Likewise anything expressible under the new system can be expressed in the old system by treating each property as an object and taking being a member of a particular property bundle to be a unique predicate. For example ∀x({x, A, B}_y → {x, C}_z) becomes ∀x((Yx & Ya & Yb) → (Zx & Zc)).

Of course the system, as described, can’t express some ideas, such as the idea that if a property bundle has a certain property that it must also have a second property. ∀x({F, x} → {P, x}) only expresses the idea that if a property bundle with F and x exists that a second with P and x must also exist, not that the first bundle contains F, P, and x. A partial solution is to designate some properties as uniquely identifying a particular “object” (the property of being a particular person, for example), such that they exist only in a single bundle because, in a way, they describe the bundle itself. A stop-gap way to express such properties is to say that, for them, the following rule of inference holds:
({z, A_1,1, A_1,2, …} & {z, A_2,1, A_2,2, …} & … & {z, A_n,1, A_n,2, …}) → {z, A_1,1, A_1,2, …, A_2,1, A_2,2, …, …, A_n,1, A_n,2, …}, where z is a unique identifier
However, this simply guarantees that there is some bundle with all the properties associated with z, which is not quite what we wanted.

To really express the idea (as well as dependant properties, and other such things), we need to move to a second order logic, one where bundles can be quantified over as well (this is why I introduced the idea of naming them previously.)
Then we could define a unique identifier as follows:
∀x∀y({u}_x & {u}_y → ∀z({z}_x ↔ {z}_y)), making u a unique identifier
Also we could express the idea that property Y depends on property X (i.e. any bundle that has Y must have X) as follows:
∀x({Y}_x → {X}_x)

Properties In Context

I claim that any theory of properties should aim primarily to be a useful intellectual tool; to be an abstraction that covers up the messy details of the world. That there is no one best theory about properties for all people and in all situations is one consequence of that claim. However, it remains to be shown exactly how a theory about properties can be a useful intellectual tool, and the burden of proof rests on me to demonstrate that it can serve as such a tool. Below are some of my notes about how a theory about properties may find applications outside of philosophy, and where one theory may be more useful than another.

1. Properties themselves can be attributed to our need to abstract details from specific situations in order to reason about things in general, and to communicate without each other. Perhaps in the experience of infants, before the conceptual apparatus of language is developed (which brings properties with it in the form of adjectives), objects and events are experienced as unified wholes – without parts and thus without properties. But, as mentioned, without breaking the experience of an object or event up into properties you can’t talk about it (except, perhaps, by pointing), or reason about it, because each experience is wholly unique. Thus the idea of properties itself is a useful abstraction that permeates almost our entire intellectual life. I’d say that’s a pretty useful piece of philosophy.

2. One of the rare cases where we may explicitly invoke the idea of properties outside philosophy is when trying to define something. In attempting to come up with a good definition we self-consciously think about the properties a thing has that makes it unique. Consider a general definition, one that picks out a class of things rather than a particular object. Specifically consider a definition/description of a regular monopoly board, in general. It is reasonable to include “has a space labeled ‘Boardwalk’” as part of our description of what a monopoly board is. But what about a damaged monopoly board, one that is missing Boardwalk? Does it cease to be a monopoly board? The fact that we refer to it still as a monopoly board, albeit a damaged one, strongly implies that it should still count. But yet it is still valid to describe a monopoly board in general as having Boardwalk. When we run into a case such as this having a theory about properties and what they are properties of may come in handy. If the theory you are working with asserts that properties must apply to objects you may be faced with a dilemma. Either you accept that there is some abstract “monopoly board in general” object that has these properties, which is unpalatable, or the properties of monopoly boards in general are properties of each monopoly board, which creates problems in the case of the damaged board. Now these “problems” can be resolved. You could say, for example, that the properties of a monopoly board in general are only properties that most, but not all, monopoly boards have. But then to a question such as “do monopoly boards include Boardwalk?” you must answer “the majority have Boardwalk but a minority may not” when what you want to be able to say is “yes”. Again, the theory is defective here not because we can’t make it do what we want, but because instead of being a useful tool it makes us adopt unusual and unhelpful ways of thinking to make it work. Alternately, if we still want to hold on to the idea that all properties are properties of objects, we could treat “monopoly boards” as a list of properties that individual game boards can fall under – in other words a complicated property that we define in terms of other properties. Again though this leads to the need to jump though hoops to make this approach work in certain situations. Instead of being able to say that monopoly boards are game boards (fall under a more general category), we would have to say that all the individual boards that fall under the category “monopoly board” fall under the category “game board”. There is nothing wrong with this, but it’s not a convenient or particularly useful way of thinking about the situation. Finally, we come to the theory best suited to this situation: properties simply clump together; there are no objects, just property clumps. Under this theory we can take the idea of a monopoly board in general to be its own clump of properties, which is not an object in any normal sense because it lacks properties such as a location in time and space, individual existence, and so on. The relation of particular, possibly defective, boards, to this clump of properties representing the abstraction of a monopoly board in general can de described in one word: “approximates”. Obviously in this case the last approach is far superior to the rest – it provides a consistent framework that allows us to talk about monopoly boards in general, the category’s relation to particular boards, and its relation to larger categories in exactly the way we want, all without committing us to any metaphysical extravagance. Of course that’s just what’s right in this extended example; it may not always be the best approach.

3. The properties-as-clumps versus properties-as-attached-to-objects distinction may also come up when how the properties are related to each other is at issue. The properties-as-clumps picture promotes a view where the properties in the clump are connected to each other, and possibly depend on each other. In contrast the properties-as-attached-to-objects picture promotes a view where the properties are like tags that are stuck to the object, and which can be added or removed without substantially affecting each other. I can think of situations where both perspectives are appropriate. When thinking about a case where the properties in question are closely connected to each other, such as the properties that define someone’s personality, thinking of them as linked together is helpful. It is not the case that you can simply switch off one aspect of someone’s personality or add something new in isolation. The manifestations of an individual personality are interconnected at a deep level, and any change in one aspect is going to have an effect elsewhere as well. And the properties-as-attached-to-objects theory may lead us to think, contrary to this, that we could simply swap out greed for altruism without other changes resulting from the switch. On the other hand, there are cases where properties are like tags stuck to an object – easily added and removed without affecting each other – perhaps literally. In a case like that it would be foolish dwelling on the interconnectedness of properties when they simply aren’t.

4. Another difference between theories about properties is whether different objects can have the same properties. Most theories do provide some way in which the properties of different objects can be described as literally the same. However, there are also approaches in which the properties that are found in individual objects are not the same, at least not in a normal sense; the best that can be said is that they are similar. In most cases the former sort of theories are preferable to the latter. After all the whole point of the abstraction of properties is to abstract and communicate, which would seem to necessitate thinking of properties found in different objects as the same. However, there are cases where we want to emphasize that there are subtle differences, even when the objects in question are described as having the “same” properties, in which case the latter sort of theory is superior. For example, we may be classifying people by personality but at the same time want to keep in mind that Bob’s pacifism is not exactly the same as Charlie’s pacifism.

5. Cases where we need to demonstrate that two objects do in fact have the same property (or where questions of how we know that two properties are the same come up) need a specific kind of approach to properties as well. Any theory that takes the sameness of properties in different objects to be a bare fact will not be helpful. In such cases theories that take the properties found in each object to be essentially distinct and attempt to explain how properties in different objects are similar or fall under the same category are more useful. Because, in doing so, those theories usually outline tests or methods by which the properties of different objects can be compared to see whether they are similar or whether they fall under the same category. And that is exactly what is needed.

6. But what’s wrong with flying by the seat of our pants? Obviously there is an intuitive conception of properties that most people, not having extensive training in philosophy, get by with just fine. Well, there’s nothing inherently wrong about it. I often compare philosophical theories to tools. Using an intuitive conception of properties is like using a rough and unrefined tool – it may get the job done but it isn’t optimal. Generally the rough and ready tool is unsystematic. If we were to analyze it as a philosophical theory it would look like a combination of approaches, each of which is deployed in specific situations. The problem with this is that it may lead to internal contradictions. If you hammer with your tool in one place and it leaves a certain kind of mark and you hammer in another and it leaves a different kind of mark then if you try to put the two together they may not fit. Again, this isn’t an fatal defect, we are always free to fiddle with the results of our unrefined tool to make them fit together, but it is an example of how the unrefined tool can occasionally get in the way. Another, larger, problem with sticking with an intuitive conception of properties is that it simply may not be the right tool for the job. As illustrated above, which approach is best varies from situation to situation. If we are masters of a number of different theories then we are free to pick the one that best suits the task at hand, which will yield the best results more often than always trusting whatever approach we intuitively find ourselves using.

Properties and Universals

Theories about properties generally come in two varieties. First we have the theories that explain properties by appeal to universals (or forms). The idea of a universal, in this context, is that of something that exists in addition to the object. All objects that have a particular property are related to a single universal in some way, and in virtue of that relationship possess the property in question. (I know that not all theories that use the term “universals” describe them in this way, but it’s the kind of theory that springs to mind for me when I consider the term, so I’m sticking with it here.) Other theories describe properties as part of the object. They claim that if we have two white books there is a property of whiteness in one and a property of whiteness in the other, and that these two properties are numerically distinct. What exactly these properties are and how they are embedded in the object varies from theory to theory naturally. (On a previous occasion I outlined a theory about properties of the second sort, which defined them as patterns of (causal) effects that the object was responsible for.)

Both approaches have their strengths and weaknesses. Let’s begin with the universals approach. The strength of the universals approach is that it can easily explain how two objects have the same properties, and thus how they are similar to each other, by pointing to the fact that they are related to one and the same universal. Why are these two white books similar? Because they participate in the same form of whiteness – end of story. The problem with this approach is, first, that it is metaphysically loaded, and, secondly, that it leaves a good deal unexplained when it comes to the relationship between objects and universals. The theory is metaphysically loaded because it introduces new objects: universals and their relations, which are distinct from the existing objects, and which some new place must be found for. I’ll ignore that problem here, at least for the moment. The second set of issues, those stemming from the relationship between universals and objects, often comes from integrating this theory with other theories, such as those about change or essential properties. Under this approach every property of the object is pulled off of it, and becomes a relationship and a universal. This creates problems because it means that we are left with an object that is bare – an object that has no properties of its own. If every object is bare it would seem that they are indistinguishable from one another. So what makes one object related to a particular universal while its identical twin is related to a different universal? Or, in other words, why is an object related to the universals that it is? It’s hard to connect a theory that appeals to universals with other philosophical positions without raising these issues. For example, if you were a substance dualist, and you appealed to universals, you would have to answer the question: why can’t one and the same object be related to both mental and physical universals?

Taking the position that properties are in the objects themselves turns the weakness of the universals position into strengths, but unfortunately also turns its strengths into weaknesses. If properties are explained as being part of objects then the question of why an object has them essentially disappears. You wouldn’t, for example, be stumped by the question “why is page 5 part of this book?”, you could appeal to the book’s history whereby various parts became stuck together. Similarly, you can tell a story about properties where various properties become bound up and dislodged from each other (making an object a properties bundle in essentially the same way a book is a pages bundle). This makes talking about change, for example, extremely easy. And it also resolves the problems that arise from treating objects as additional bare particulars. However, solving these problems comes at a cost. Now it is difficult to describe how two objects can be similar or have the same properties. Consider our two white books. Under this theory they both have a whiteness part. But what makes those whiteness parts the same property of whiteness? Nothing, it would seem. The fact that we talk about them as both being whiteness parts does not mean that there is any grounding in the theory for doing so. Now it is not impossible to tack on a solution to this problem. We could, for example, say that these property-parts are both related to the same universal of whiteness (raising for property-parts the same problems that solution raised for objects). But, unfortunately, these solutions tend to be extremely complicated and metaphysically loaded.

Either way we go, then, there are problems. Of course these problems have solutions – many solutions in fact. Many have attempted to tack on more complicated frameworks to these initially simply solutions in an attempt to bury the problems mentioned above. These solutions are not successful. Some simply raise new problems as they deal with the existing ones. Others become so baroque and metaphysically loaded that they defeat the point of having a metaphysical theory about properties and objects in the first place. And, to refresh your memory, the point of such a theory is to be a useful tool for thought; to a guide that allows us to deal with properties and object in other contexts cleanly and smoothly, allowing us to focus on the issues at hand rather than problems arising from wrestling with properties and objects. A theory that is too complicated defeats that purpose. It is not a convenient tool for thought; it becomes a system that uses us rather than allowing us to use it. By being metaphysically loaded it has the tendency to decide issues for us, rather than allowing us to decide them. And by being baroque it means that to invoke the system is to spend as more time working with it than with the issues we invoked it to assist us with. Thus such solutions fail us as philosophy, even if they have consistent answers to all the questions we might pose to them.

Let’s consider a third approach. We’ll start with the same basic idea as the properties-as-parts approach: each object is a collection of properties, each of which is a part of the object, and which collectively are the object. This leaves us with the problem of explaining how objects can be said to share the same properties. Here is where we can take a different path: let’s simply bite the bullet and assert that they simply share the same properties. That’s right, whiteness is a part of a book, and if we have two white books whiteness is a part of both of them, and, perhaps counter-intuitively, the same whiteness part is in both. I say this is counter-intuitive because if we have two white books it seems quite clear that they don’t overlap, and that each is independent of the other. But this intuitive sense in which they don’t overlap is only a spatiotemporal one. Instead of thinking of objects as sitting in space-time think of them as sitting in property space. For the sake of simplicity think of property space as a big sheet of paper, on which are written the names of different properties. (And if you want to be fancy you can think of these properties as organized such that the property of being a cat is a large region, inside of which are the smaller regions that correspond to being a particular species of cat.) And think of an object as a loose loop of string. The string lies on top of property space, and all the properties that fall within that loop are properties the object has. Our two white books are two such loops of string. Now, for the most part, these loops don’t overlap; they don’t surround the same spatial location, for example. However, when it comes to the property of being white they do; they both include the same region of property-space. And in that way they share the same part. Of course just because they share the same part in this sense doesn’t mean that one white book can influence another in some spooky way. An object under this view is a division in property-space. The object, the division, is mutable, but property-space is not. So even though they share a part in common, whiteness, whiteness itself is immutable (although whether an object is white is mutable), and thus they cannot be influenced by their part in common.

I won’t pretend that the above is beyond our ability to pose problems for it. For example, this view can pose difficulties when trying to explain how all properties ultimately reduce to physical properties. At the very least this introduces complexities such as a mapping between physical space and property-space and the necessity of dealing with a structure of property space such that not all divisions of it are admissible as objects. (Clearly such a structure is necessary, otherwise you could have an object that had the property of being a white-book without having the property of being white.) Another problem that has to go unaddressed is that of how the world is divided into objects. This is the problem of saying why the four pennies on the table form a group with the property of four-ness and why they aren’t considered to be part of a larger group that contains the penny in my pocket as well (manifesting five-ness), the one stuck under the table (manifesting six-ness), and so on. Obviously any solution to that has consequences for which properties there are and which objects have them. But since the best solution is generally to admit that how the world is divided into object is conventional this makes all of the schemes discussed here for explaining properties and objects unworkable (since they must all be relativized to the mind in some way while at the same time explaining how it is an objective fact that this book is white; not an easy task).

But the purpose of a philosophical theory (or perspective, as I like to call them) is not to answer every question that can be raised; it is to be a useful intellectual tool. In this specific case the point of the tool is to cleanly handle properties and objects whenever they arise. I submit that the position described here is genuinely useful in this capacity since issues of reduction and the relativity of objects don’t come up that often (outside of contexts that are heavily philosophical) and that it is more useful than the first two approaches described because it is roughly as simple as they are and works in all the situations they do, as well as some in which they don’t (such as when they lead to questions about why an object has the properties it does or in what way two objects have the same properties).

6: Where Does A Rock End And The Rest Of The World Begin?

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.