Property

A property is an attribute that isn’t a relation.

Simple and Complex Properties

Some properties are simple. All simple properties can be exemplified by definition. (A philosopher of religion might wonder if there is a property of being maximal that entails necessary existence, and if so, whether it is simple.)  

Some properties are complexes of attributes—properties and sometimes relations, too. See comments about complex attributes in general.

Relational and Non-relational Properties

If there are five people behind the couch, they each exemplify being behind the couch (that’s just what it means to say that each is behind the couch). The property of being behind the couch is a complex property that contains the property of being the couch (which is an individual essence) and the relation of behind. Relational properties are ones that contain relations as parts. Non-relational properties are ones that do not contain any relations.

Extrinsic and Intrinsic Properties

It’s tempting to say that extrinsic properties just are relational ones. However, some philosophers have thought that some relational properties, like having longer legs than arms, are intrinsic. Examples of relational properties that might still be considered intrinsic seem to have the following feature: the relational part holds among the parts of any exemplifier of the property in question. Given this fact, we could say that an intrinsic, relational property is a property P, such that at least one part of P is a relation and there is no relation R, such that R is part of P and it is not necessary that if P is exemplified by x, then x or its parts stand in R. An intrinsic, non-relational property is just a non-relational property. An intrinsic property, then, is a property that is non-relational or intrinsic, relational (as defined above). An extrinsic property is one that is not intrinsic.

Conjunctive and Disjunctive Properties

A conjunctive property of the form A and B is a property that contains A and B as parts.

What about disjunctive properties like being red or round? How do they fit in? I don’t deny their existence because it does seem as though they can be exemplified—things can be red or round, for example. (I didn’t always used to think this. In the past, I thought I might be able to do away with disjunctions altogether. But I’ve become skeptical that there is a principled way to do that.) My answer is to analyze disjunctive properties as conjunctive relational ones: e.g., being red or round becomes lacking (lacking redness and lacking roundness).

Notice: disjunctive properties not only have simple properties and relations as parts, but they also have at least three complex properties as parts. For example, lacking (lacking A and B roundness) has these three complex parts: the property of lacking A and lacking B, the property of lacking A, and the property of lacking B. It’s important to realize that these are all distinct parts. It would be a mistake to think that the only parts are simple properties and relations, such as A, B, and the lacking relation.

Propositional Properties

Is there a property of being such that 2+2=4? I’m not sure. If there is, then I’d think that it would have the proposition that 2+2=4 as a part. The same goes for any propositional property—any property of the form, being such that P, for some proposition P.

Chisholm thought that propositions could themselves be analyzed as propositional properties. This option is ruled out, though, by my account of propositions as ordered complexes and properties as unordered ones.

It might be worth appending to our definition of ‘intrinsic property’ a clause stipulating that no intrinsic property has a proposition as a part.  

Grue and Logically Equivalent Attributes

Many logically equivalent properties are distinct from one another. Consider an example. Grue is the complex property of being green before 2010 or blue after 2010, and bleen is the property of being blue before 2010 or green after 2010. Now consider the property crazy-green which is this: being grue before 2010 or bleen after 2010. Crazy-green is pretty clearly equivalent to plain old green:  necessarily, green is exemplified if and only if crazy-green is exemplified. But we should not thereby conclude that crazy-green just is green. These are distinct properties because they have different parts. Indeed, green seems to have no parts at all. To see what parts crazy-green has, it will help to convert the disjunction into its proper conjunctive form:

            crazy-green = lacking (lacking (being grue and being before 2010) and lacking (being bleen and after 2010)), where

            grue = lacking (lacking (greenness and being before 2010) and lacking (blueness and after 2010)), and

            bleen = lacking (lacking (blueness and being before 2010) and lacking (greenness and after 2010)).

So crazy-green is quite complicated. (For this reason, its prior probability is low. I suspect that this explains why the hypothesis that all emeralds are green is a much preferable explanation of the fact that all emeralds before 2010 are green [and of the fact that all the ones observed before 2010 are green] than the hypothesis that all emeralds are grue. Both equally entail the data, but one has a vastly higher prior probability.)

Essential and Accidental Properties

There is no such thing as being essential. Rather, there is the relational property of being essential to such and such. A property is essential to x if and only if necessarily, if x exists, then x exemplifies that property. For example, it is essential to me that I am possibly conscious because it’s not possible for me to exist without having that property. But being possibly conscious isn’t of itself an essential property. A property is accidental to a thing if it isn’t essential to it. In many cases, a property that is essential to one thing could be accidental to something else. For example, it might be essential to a being like God to be conscious, but it is not essential to me to be conscious. Or to use an equally controversial example, a cup-shaped arrangement is essentially cup-shaped, whereas as mass of clay might be accidentally cup-shaped.

If a property P is essential to anything that might have it, then we might call P, ‘strongly essential’.

Kinds and Properties

Some philosophers (e.g., Aristotle, contemporary philosopher, E. J. Lowe) make a distinction between properties and kinds. Kinds are supposed to be what things are, as opposed to how they are. For example, the kind, Man, is what Socrates is, whereas the property of being snubnosed is how he is. I do not draw this distinction because I don’t understand the distinction between what something is and how it is. Or if I do understand it, I understand it to be a distinction between strongly essential properties and ones that are not strongly essential. Or it might even be that an Aristotelian kind is strongly essential property and simple (if Man is simple, then being rational and being animal would not be parts of Man, though they may be entailed by it). At any rate, I do not recognize a fundamental distinction between kind properties and non-kind properties, unless the distinction between being strongly essential and not being strongly essential is considered a fundamental distinction.  

There is a linguistic difference between the kind, Man, and the property, being a man. But I suspect that the difference is merely linguistic. Man is identical to being a man: ‘Man’ and ‘being a man’ express one and the same property.  

Categories of Properties

Just as there are many ways one might categorize beings into most general categories, there are many ways one might categories properties. That isn’t to say that categories are themselves “arbitrary constructions” that lack genuine reality. On the contrary, the categories are themselves properties (they can be exemplified, or have parts that can be), and properties are as real as anything (as any being). I suggest the following categories of properties that are especially worthy of investigation: Category, Shape, Color, Sound, Quantity, Aesthetic, Moral, Phenomenal, and Dispositional.

The Problem of Non-Self-Exemplification

Here’s a famous paradox of properties. Observe that some properties exemplify themselves. For example, lacking red exemplifies lacking red. But most properties don’t exemplify themselves. For example, being red does not exemplify being red. Consider, then, the property of lacking exemplifying oneself. Call this property, non-E. Does non-E exemplify non-E? Well, if it does, then it would lack exemplifying itself, which means that non-E would not exemplify non-E. On the other hand, if non-E lacks non-E, then non-E lacks lacking exemplifying oneself, which entails exemplifying oneself. Therefore, non-E exemplifies non-E if and only if non-E lacks non-E, which is absurd. It follows that there is no such thing as non-E.

This is a paradox because it seems true of many different things that they do not exemplify themselves. They seem to have non-E in common. So it looks like non-E should exist, yet non-E cannot exist without absurdity.

Let’s take a step back and consider the slightly simpler property, E, which is the property of exemplifying oneself. Ask: does E exemplify E? Suppose not. Then, E lacks E. That is, E lacks exemplifying oneself, which entails that E lacks E. That might sounds a little fishy maybe, but I see nothing absurd here. The same goes for the proposal that E exemplifies E. E exemplifies E entails that E exemplifies exemplifies oneself, which entails that E exemplifies E. This isn’t an absurd result, but there does seem to be something fishy going on. It’s fishy that we have no way to see whether E exemplifies E or whether E lacks E. This is strange because E’s definition is supposed to give us direct insight into E, and if we have direct insight into a thing, I think we should be able to tell whether that thing exemplifies itself or not. I think the problem is that we don’t have direct insight into E because we don’t have a clear definition of E. And the reason we don’t have a clear definition of E is because the definition contains the term, ‘oneself’. But what does ‘oneself’ mean?

The term, ‘oneself’ is a context sensitive term. Its meaning is always borrowed from its context. It’s like the term, ‘it’. In the sentence, “John picked up the ball and then threw it,” Here, ‘it’ refers to the ball, and the meaning of ‘it’ is the same as the meaning of ‘the ball’. But in the sentence, “Sally picked up the vase and then threw it”, ‘it’ refers to the vase. It would be meaningless to say that Sally and John both throw it unless there is a context to tell us what ‘it’ means. The term, ‘oneself’ works the same way: it borrows its meaning from the context. But when we say that a bunch of things all exemplify oneself, we haven’t specified what ‘oneself’ means. There is an illusion that we know what ‘oneself’ means there, but I suspect that this illusion arises from the fact that one and the same word is being used in each of the example cases. We think there is a common property because we use a common word, i.e. ‘oneself’ in our description of each thing. But in reality, there isn’t a common property being ascribed because the word, ‘oneself’, means something different in each case. So, I’ve come to think that the expression ‘exemplifies oneself’ is meaningless without context because ‘oneself’ is meaningless without context.

At this point, we might consider the property of being such that the predicate ‘exemplifies oneself’ correctly applies to it. After all, isn’t it true that ‘exemplifies oneself’ does correctly apply to many things? But this is just to make the same mistake again, only this time with the term ‘it’. What do we mean when we say without context that the predicate ‘exemplifies oneself’ applies to it. What does ‘it’ mean here? I suspect it is meaningless.

I’ve discussed this with Peter van Inwagen, and his response was to point out a connection between ‘it’ and variables in quantificational logic: e.g. there is an x, such that it exemplifies itself = there is an x, such that x exemplifies x. So as long as ‘it’ is bound by quantificational operators, we can understand it. But my reply is that such expressions in quantificational logic are meaningless for the same reason: the variables do not mean anything unless they can be interpreted. I realize this is a bold claim, but I believe it is the sober truth. Before you completely write me off here, I should say that although I think that some quantificational sentences are strictly speaking meaningless, I do think that the vast majority of quantificational sentences successfully convey the propositions we wish to convey. That is, I think that we normally understand the intended meaning of a sentence in quantificational logic but only because we’ve learned to instinctively interpret the variables in a way that allows us to grasp the intended proposition: for example, ‘for all x, if x is A, then x is B’ brings our minds to the proposition that A implies B, where the meanings of ‘A’, ‘implies’, and ‘B’ are grasped directly (though the fact that those terms have those meanings may not itself be grasped directly); and ‘there is an x such that x is A’ brings our minds to the proposition that A is exemplified.

If I’m right (and I might not be), then not only is there no such thing as non-self-exemplification, but there is also no such thing as bearing R to oneself, for any R. Interestingly, this means there is no such thing as being self-identical.

The Principle of Instantiation

Some philosophers since the time of Aristotle have thought that properties only exist if they are exemplified. I deny this for several reasons. One is that my account of propositions—an account that I think makes the best sense of the nature of truth—entails that properties are parts of propositions. Given that there are false propositions that contain properties that are not exemplified (e.g., the proposition that there are unicorns), I’m committed to thinking that there are properties that are not exemplified. Another reason I deny the principle of instantiation is that it seems that I can directly grasp properties—such as in dreams or by concentration—regardless of whether they are exemplified. For example, it seems to me that I can grasp redness regardless of whether there are any red objects. This leads me to suspect that redness exists regardless of whether there are any red objects. A third reason is that my account of facts leads me to think that some true propositions correspond to complexes of properties that may or may not be exemplified: e.g. yellow is brighter than brown corresponds to a fact containing yellow and brown linked by a brighter than relation. It seems to me that this fact would continue to exist even if there were no yellow objects. So, I deny the principle of instantiation.

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