What Is Philosophy, And What Can It Do For You?

If there is one thing philosophers agree about it is that philosophers don’t agree about what philosophy is. You might think that philosophers would limit themselves to disagreeing with each other’s theories. But no, they go farther than that, and claim that other philosophers have not only reached the wrong conclusions, but that they have been going about philosophy itself in the wrong way. The best way describe what philosophy is, then, is not to present a single definition, but rather to treat the issue itself as a philosophical problem. In other words we will begin by thinking about intuitive or common sense answers to the question, and, on the basis of problems arising for those answers, motivate some of the more theoretical solutions that have been proposed.

Perhaps the simplest, and least helpful, answer to the question “what is philosophy?” is to point at famous philosophers – to say that it is whatever Plato, Aristotle, Kant, and so on did. And what did they do? Well they did ethics, epistemology, and metaphysics, to name the big three categories. And maybe that could serve to answer our question: philosophy is anything that deals with ethics, epistemology, or metaphysics. But things are never so simple. The big three don’t exhaust the topics philosophers deal with. Logic, language, truth, mind, consciousness, aesthetics, the good life, ontology, politics, and culture are also topics that one philosopher or another has turned their attention to. And surely even that list isn’t complete; even if it covers everything philosophers have written about so far there it is likely that new philosophical topics will appear in the future.

But, for the sake of being charitable to this definition, let’s simply assume that we could list all the topics philosophy covers. Even so, it still wouldn’t be satisfactory. Consider the following: what makes religion distinct from philosophy? Religion covers many of the same topics as philosophy. The big three, for example, all find some reflection in religion. Ethics is clearly central to many religions, and inasmuch as they endorse faith and the existence of god they contain claims about epistemology and metaphysics, respectively. But clearly (or at least this is clear to philosophers, if not to the man on the street) philosophy is not religion and religion is not philosophy. The difference, to put it succinctly, is that religion is built on faith and dogma while philosophy is not. Philosophy embraces the idea that claims are to be argued for, or at least motivated in some way, and that every theory is subject to criticism and revision. Any satisfactory definition of philosophy will at least rule out faith and authority as a source of philosophical theories.

This motivates us to look for an understanding of philosophy that describes what it does rather than simply lists the topics it studies. This brings us the one of the oldest answers the question: philosophy studies the essence of things. Essence, in this context, is a fancy word to describe “what something is”, and explaining the essence of something often looks a lot like a definition. For example, a philosopher might describe the essence of a chair as “a thing that is for sitting on”. Essences have also been called forms, and occasionally concepts. But, whatever they are called, the idea is that they are abstract objects – they aren’t part of the physical world that science studies. Instead of having physical access to them we have intellectual access to them, it is claimed; we come to know the essence of a thing by reflection, by considering different examples, and by argument. This all sounds good in theory, but in practice problems arise. The theory implies that there is some one essence that all philosophers investigating a particular topic, such as justice, should be describing. However, there is widespread disagreement, not agreement, about what justice is among philosophers. This implies that, at the very least, our intellectual access to these essences is unreliable, and sometimes leads us astray. And, worse, since we have no other way of getting access to an essence, there is no way to tell which philosophers are successfully describing it and which are mistaken. And so the unfortunate consequence of this theory about philosophy is that, while we now know what philosophy is, we also realize that we don’t have any reliable way to pursue a philosophical inquiry or settle a philosophical dispute.

Obviously that’s not a happy situation for philosophy to be in, and wresting with such problems has motivated other understandings of philosophy. Some have seen the problems with the previous approach as stemming primarily from the way essences are disconnected from the physical world. Realizing that philosophy aimed at describing essences produces results that look a good deal like definitions, they suggest that philosophy is really about studying language and clearly defining terms of philosophical interest. This alleviates worries about the unreliability of our intellectual access to the subject matter, because it is clear that we can observe how words are used in a very mundane and ordinary ways. It also solves problems arising from disagreement among philosophers. That disagreement, they might say, is simply a sign that how words are used varies from person to person. But, ideally, the philosopher aims to give a definition that reflects the common understanding of the term; and there is only one right way to do that. Of course this approach is easily mocked by pointing out that under it Webster is the best philosopher, or at least the most comprehensive. Now that is not really a fair attack, there is room for those who subscribe to this approach to argue that the philosophically interesting terms are complex and that Webster’s simple and intuitive definitions miss how the words are actually used. However, when I entertain the idea that the goal of philosophy as being to write a better dictionary with respect to certain terms, it is not clear to me why we should care. People get along just fine without these precise definitions; and it is not clear to me how giving them a precise definition would affect their lives in any way besides changing how they use a term.* The end result of this theory then is that, while it is clear what the task of philosophy is and how it can be accomplished, it is no longer clear why we should bother.

Fortunately that’s not the only way to improve on the idea that philosophy studies essences or concepts. Another way to revise the theory is to move essences or concepts into the mind. Under the modified theory, then, philosophy studies essences (or concepts) that are revealed to us in experience. Again, this resolves both of the major problems facing the previous approach. It should be uncontroversial now how we have intellectual access to essences, since it is uncontroversial that we have access to our own experience. And it also explains why philosophers disagree: how we experience the world varies from person to person. As with the view that philosophy is all about language, the idea that some philosophy is better than others can be preserved under the assumption that the philosopher’s target should be a common form of experience, and not merely a reflection of their own idiosyncrasies. However, we also run into some of the same problems facing the view that philosophy is primarily about language, namely that it is not clear how it matters. It is true that how we experience the world does matter in some contexts: in understanding consciousness, in trying to communicate, and in producing art. However, it seems far too narrow for philosophy. And it also seems like a retreat from several important philosophical questions. For example, explaining why consulting a magic 8 ball is an objectively bad method for forming beliefs seems like the kind of question that philosophy should answer. However, if we confine ourselves to studying only our own experiences (or common forms of experience) the best we can say is that the magic 8 ball is not experienced as or conceived of as having the right qualities to serve as evidence. But this says nothing about why it really, objectively, is a bad idea.

I consider the three previous approaches to be failures in one way or another, as I have described, although this is far from a universally held judgment, and there are many philosophers who are willing to defend them and work under that conception of philosophy. What I see as the fundamental problem with those approaches, behind the specific problems with them, is their fixation on the idea that there is a right answer in philosophy, or at the very least that some philosophy is objectively better than others. If that is true then there must be something that philosophy aims to reflect or describe, such that it can capture it in a better or worse way. Essences, language, and experience are three possible such subjects. The problem with this, however, is that, if there is something worth studying that can be studied in a relatively objective** manner then science has probably gotten there first. Because that is what science does, it studies things in an objective manner as possible. This leaves philosophy either with subjects that no one cares to do a scientific study of (how words are used, the exact structure of experience) or with subjects that can’t be studied in an objective way (essences). Neither is any good.

But if we give up on right/wrong or better/worse in a universal sense then what is left? Wouldn’t moving away from these ideas leave us with an anything-goes approach to philosophy, where every theory, no matter how absurd or new-age, would have to be treated as equally worthy? Consider two hammers. Is there a sense in which one hammer is right and the other wrong, or a sense in which one is universally better than another? No. It is possible, for example, for one hammer to be better at hammering nails while the other is better at being a decorative item. One hammer may be more durable, the other may be a better prop for a movie. But, even so, it is not the case that simply everything is a worthy hammer. My shoe, for example, is not a suitable hammer in any way – of the things we expect of hammers the shoe is always the worse choice. My suggestion then is that we look at philosophy like a tool. Not a physical tool, like a hammer, but an intellectual tool.

But what is an intellectual too, exactly? This brings me to the second question: what can philosophy do for you? In the broadest sense philosophy is a tool for thinking – for thinking clearly and precisely, for drawing helpful distinctions, and for connecting different ideas via chains of argument. Of course while that is generally useful is also very broad, so broad that such skills could probably be learned by other means as well. To be more specific we would have to get into each of the specific topics that philosophers think about, and this isn’t the right place for that. Instead allow me to give just one example. A question that everyone thinks about, or at least should think about is: “what is a good life?”, where good ranges from ethical, to meaningful, to simply pleasurable. Only philosophy really addresses itself to such questions, and this is one way that philosophy can be useful. Many philosophical theories provide a perspective on what the good life is. And we can see that a particular perspective may be better or worse for someone, depending on the values they have, the situation they are in, and culture they are part of. Now you could read philosophy book after philosophy book to find the perspective on what makes a good life that is best for you. That’s probably better than not thinking about the issue at all. However, situations change, as do what people value. And so, just as one perspective on the good life won’t suit everyone, a single perspective on the good life won’t suit someone forever. And so what’s really important to take away from this class is not, for example, Plato’s opinion on how to live, but rather an understanding of how Plato addressed such questions, so that you have the ability to tackle such issues for yourself, as many times as you need to.

* Even when it comes to ethics. If you tell some authoritatively “this is what other people mean by the term ‘right’” and they accept that, and modify their usage of the term to comply, that doesn’t meant that they will also alter their internal measure of right and wrong that guides them, nor does presenting them with this definition give them any reason to do so. In other words, changing how people use terms does not necessarily change how they think about thing, nor is their reason to believe that correcting small deviations from the norm in the way a term is used is beneficial.

** By objective here I mean only that it is possible to come to an agreement, at least in the long run, about which theories are better and worse (i.e. as Peirce would have it).

Adapted from a presentation on 9/26

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).

The Big Picture