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.