Wednesday, July 3, 2013

Essence and Ontological Dependence

This is my term paper from my independent study last quarter on ontological dependence. I will say beforehand that I did not have enough time to make it great, and there is a lot more I could have said. However, I believe it contains a relatively good summary of Kit Fine's position, and I think the stuff toward the end about causation is somewhat original (albeit sketchy). So hopefully someone will find it interesting and useful.

I.  Introduction – Examples and What We Want

In many areas of philosophy, as well as common discourse, it is normal to say that one thing depends on another. Moreoever, one of these uses of the word 'depends' is a distinctly ontological sense, as opposed to, say, a notion of epistemological dependence or logical dependence. I will use the term 'dependence' throughout this essay to stand for this particularly ontological notion, unless otherwise stated. So for instance, we might say that a composite depends on its constituents. Or we might say a smile depends on the mouth of which it is a smile. Or that a hole depends on the thing which it is a hole in. This is a philosophical datum and the only reason one would deny it or feign incomprehension seems to be hard-headedness.

Nevertheless, while most people are prepared to affirm some dependence claims, it is not entirely clear what this notion of dependence means, nor is it clear what sort of criterion we can give to identify when one thing depends on another. Certainly there are features of relations which we can use to rule out their being relations of dependence. For instance, plausibly, x depends on y only if y does not depend on x. So we know that the relation is asymmetric. But this still does not help us to say what dependence is, nor does it give us any necessary or sufficient conditions for a relation of dependence holding.

I will try to explain some approaches to this idea of dependence. Some of them will be more fruitful than others, and I'll try to point out some of the issues which accompany each of them. We will see how they handle cases like the ones listed above, and whether they satisfy the necessary conditions for being a good theory of ontological dependence. We will see that the best explanation of dependence is one which ties it to the idea of essence. Finally, we will examine whether this notion relates in any special way to other notions like causation.

II. The Essential Background

It is plausible to think that there is some connection between the idea of ontological dependence and that of essence. The essence of something can be thought of as the nature of a thing, or simply what it is to be that type of thing (this latter phrase is in fact the literal translation of Aristotle's term for 'essence'). Properties then can be said to be part of the essence of something, and these we will call the essential properties of a thing. Any good reductive definition of essence then is going to be one which tries to capture this notion. One can of course define the word 'essence' however one wants, but the hope is that the definition will capture most of the intuitive meaning.

One way of explaining essence is to say the essence of something is the set of all that thing's essential properties, and then reduce the idea of an essential property to a modal notion. Let us offer the following modal definition of essential properties:

Property P is an essential property of x just in case necessarily if x exists then x is P.

The term 'necessarily' is used here in the most broadly logical or metaphysical sense, rather than, say, a merely physical or epistemic sense. This definition seems to capture some of our intuitions about essence on the face of it. For instance, it seems somewhat plausible that to say I'm essentially human means it's not possible for me to exist and yet not be human.

What then follows about the idea of ontological dependence? Well, the relation of dependence is one between entities. And when we say that something depends on something else, we take this to mean the one couldn't exist without the other. So the most natural way to define ontological dependence in terms of our modal conception of essence is as the following modal definition of dependence:

X ontologically depends on Y just in case 'existing only if Y exists' is an essential property of X.

It may seem a bit unfair and a misnomer to simply call this the modal definition of dependence, since no modal terms are explicitly mentioned in the definition at all. Nevertheless, it is easy to remember it by this name and it helps us to remember that essence is going to be analyzed in modal terms.

Now, by our definition of an essential property, it will follow by the rules of logic that X depends on Y just in case necessarily X exists only if Y exists. As we see then, if this account works it will be a successful definition of ontological dependence entirely in terms of the notions of existence and metaphysical modality. Unfortunately, the problem is that this definition does not work. For, in short, it does not capture the asymmetry which holds between a dependent and the thing upon which it depends. Let's take a look at some examples. We will bring these examples back later when considering the plausibility of other accounts, so it is good to keep them in mind.

Consider the case of Socrates and his singleton set, i.e the set containing only him. Sets are abstract objects, and thus they exist necessarily. But if the consequent of an implication is necessarily true, then the implication is necessarily true. So necessarily, Socrates exists only if his singleton set exists. From the modal definition of dependence it follows that Socrates depends on his singleton. But this seems wrong; it is the set which depends on him, if anything. So we see one problem with the modal definition of dependence is that it often gets things backward and it does not preserve the asymmetry of dependence.

Suppose we also have two necessarily existing objects. They can both be abstract objects even, such as the property of being red and the number 2. Necessarily, if 2 exists, then the property of being red exists. So it would follow on the modal definition that the number 2 depends on the property of being red. It appears then the modal definition of dependence also creates dependence where it does not even exist.

Consider also the case of me; I exist only if I exist. In fact, this is a logical truth, so necessarily I exist only if I exist. It follows then that I depend on myself. This could be taken as an objection in itself if one thinks that to avoid circularity ontological dependence must be antisymmetric, i.e if X depends on Y then Y does not depend on X. But at the very least it seems it should not follow as a logical truth that I depend on myself.

Other counter-examples can be adduced, but these help to bring out some of the core problems with the modal account of dependence. This leaves us with two options: Either (i) we can reject the definition of dependence in terms of essence altogether, or else (ii) we can identify a problem with the modal definition of essence and modify it accordingly.

There are some reasons against the first proposal and some reasons in favor of the second proposal. Against the first proposal, it seems that in some important sense when, for instance, we say my smile depends on my mouth, we are saying that my smile just couldn't be the way it is were it not for my mouth i.e it could not have its essence were it not for my mouth. In favor of the second proposal Kit Fine, who originally brought up many of these counter-examples, considers the modal definition of essence itself to be problematic, and moreover thinks he has an alternative conception of essence which suffers from none of these problems and is also able to accurately account for dependence. If one can reduce dependence to essence, it is better to do that than to introduce a new primitive notion of dependence. So instead of abandoning the tie between dependence and essence we should examine whether this Finean picture of essence is helpful.

Before going into Fine's own theory of essence we should lay out his problem with the modal conception of essence. His counter-examples against the modal definition of an essential property are pretty much the same ones brought against the modal definition of ontological dependence. To take the example of singleton Socrates again, it seems that it doesn't have anything to do with what Socrates is that he be a member of singleton Socrates and thus it does not seem to be part of his essence, even though necessarily if he exists he is a member of this set. So the modal conception cannot be an accurate representation of what we normally mean by claims about essence. Fine proposes then an understanding of essence which is not in terms of modality. It is to Fine's own picture that we now turn.

III. A More Fine-Grained Account

Before I begin I feel I should make a few remarks about Fine exegesis. In different papers on this topic Fine says slightly different things, and so the reader should keep in mind that when presenting what I call the Finean account I will be presenting what seems to me to be the most coherent synthesis of all these different strands, generally favoring what he says in later papers as opposed to earlier ones.

Now, to get clear, like any theory of essence, Fine's is trying to capture what is meant when we say the essence of something is just what it is to be that thing. Fine starts with the notion of the operator "true in virtue of the identity of the F's." This is to be treated as a sentential operator, represented by □F which is always indexed relative to some predicate. We will call this 'the essentialist operator'. So, for instance, □FQ should literally be translated as saying it is true in virtue of the F's that Q. Now, whether or not this idea can be reduced, Fine for his purposes takes this operator as a primitive notion, which is not to be defined in simpler terms. Still, it can be explained a little bit more to give us an intuitive notion. Roughly, □FQ means that Q is true in virtue of the things which are F being what they are by their very nature. □FQ may also be able to be explained as Q being true in virtue of the state of affairs of the F's each being self-identical. We might also be able to say □FQ means there is no other fact than the F's being themselves which explains Q. These seem to be the best interpretations I can give to this operator.

Given that we have some notion of this "true in virtue of the identity of" operator, the rest follows. Similarly to the modal notion, we give the following Finean definition of an essential property:

Property F is an essential property of x just in case if x exists then it is true in virtue of the identity of x that x is F.

This requires a bit of explanation. I said earlier that the essentialist operator is always relative to a predicate, whereas here in natural language it is relative to a variable. This can easily be dealt with if we use as our predicate one which denotes the property of being identical to x, and thus only denotes x. Call this property I. Then to say it is true in virtue of the identity of x that P is the case, we can say □IP.

Given that this Finean definition makes sense, let us define the essence of x as the set of all propositions true in virtue of the identity of x (where □I is the operator 'true in virtue of the identity of x'):

The essence of x =df the set of all propositions P such that □IP

We will define dependence in terms of essence. Before moving onto dependence though, which is pretty straightforward given a correct characterization of essence, we must point out the distinction Fine makes between constitutive and consequential essence, and a certain restriction of essence necessary for a proper account of dependence. Fine understands constitutive essence as follows:

Proposition P belongs to the constitutive essence of x just in case P is not logically entailed by some more basic proposition in the essence of x.

So the propositions in the constitutive essence of something are the most basic propositions of that thing's essence. Consequential essence on the other hand is defined oppositely:

Proposition P belongs to the consequential essence of x just in case P is entailed by propositions in the constitutive essence of x.

Consequential essence then is the set of all the essential truths about a thing which can be derived logically from the thing's constitutive essence.

The problem then is that we have to restrict the consequential essence of an object appropriately if we are to not get the sorts of counter-examples the modal account suffered from. For the logical truths can be derived from any proposition, and for any object x it is a logical truth that x = x, thus entailing any object at all will be in the consequential essence. To the end of avoiding this we define the notion of a generalization of a proposition for proposition P(y) with y a constituent of that proposition (i.e a term in the formula expressing the proposition):

The generalization of a proposition P(y) =df the proposition that for all v, P(v)

This lays the ground for the definition of generalizing out:

Object y can be generalized out of a collection of propositions C just in case for all P(y), if C contains P(y) then C contains the generalization of P(y).

Now we can finally give our sought-after Finean definition of ontological dependence:

x ontologically depends on y just in case y is a constituent in a proposition in the essence of x and y cannot be generalized out of the consequential essence of x.

This definition which includes the clause about generalizing out prevents things being dependent on any object whatsoever. As far as the examples we brought against the modal account go, since this definition does not make any explicit reference to metaphysical necessity, there is no guarantee that because something exists necessarily that it will end up being a constituent in a proposition in the essence of an object. So the singleton Socrates example can be avoided for instance, along with any other counter-example which is derived strictly from the properties of implication and modality.

But how does this work with our every day examples? Take the case of the smile depending on the mouth of which it is a smile. It is plausible to believe that the smile can only be itself in virtue of the mouth's being there; so it is true in virtue of the smile's identity that the mouth exists if the smile does, and thus the mouth is part of a proposition in the smile's essence. So it follows straightforwardly that the smile depends on the mouth. Just as we wanted. Fine's picture then appears to be able to bear much fruit.

IV. Case One: Duns Scotus and Causation

It is nice evidence in its favor that Fine's account of dependence is able to handle the cases we want as we want it to. Still, dependence is not only supposed to  play a role in every day needs, but is also supposed to do a very large amount of work in abstract metaphysical thinking. Given its central role, we should examine whether it can provide any illumination or bears any relation to a more meaty notion, like causation.

One of the best people to turn to for this is the late-13th century thinker, Duns Scotus. Fine's account is best described as being a neo-Aristotelian account of essence. In this respect then Fine's essentialism is probably one of the most congenial for interaction with medieval thought and Scotus in particular of any contemporary account. After all, most medieval philosophers took a broadly Aristotelian metaphysics for granted, including an Aristotelian notion of essence.

Now if essence is going to be helpful in understanding the notion of causation, as the name suggests it will most likely be helpful when we come to Scotus's idea of an essentially ordered causal series. In Scotus's thought, all causal series can be divided into two broad categories, accidental and essential. Essentially ordered causal series can be separated by the following three criteria:

(1) In essentially ordered causes, the posterior depend on the prior to exert their causal influence.
(2) In essentially ordered causes, the prior are more perfect (important) than the posterior.
(3) In essentially ordered causes, all the causes are simultaneously required to produce the effect.

Accidentally ordered causal series are those series which do not satisfy these criteria. Scotus takes it that in any essentially ordered causal series, the relation of causation will be transitive, so that if x causes y and y causes z then x causes z.

These criteria require some expounding. As regards claim (1), it is pretty clear what is meant. It is saying the later causes in the series could not exert their causal influence were it not for the prior causes in the series, since they depend for their ability to exert their causal influence on the prior causes. As far as (2) goes, the best I can make of this is that the higher a thing is in a causal series, i.e the more things it is causally prior to, the more important is its causal influence for producing the lower causal effects. While probably more can be said of this idea of "importance", clearly we have some understanding of this. For instance, while I might have gotten a little bit of help from the TA, the instructor was much more important in causing me to pass my math exam. This makes sense. With respect to point (3), this is simply saying that if at a time t an effect in an essentially ordered causal series exists, then all the causes in the series also exist at t and exert their causal influence at t to produce the effect.

With that said, the distinction is mostly clear. So, now that we have some understanding we can give a couple examples to illustrate the distinction.  One famous (if imperfect) example of an essentially ordered causal series is a man moving a ball by means of a stick with his arm. The effect here is the movement of the ball. Arguably, in this causal series it is in virtue, and indeed primarily in virtue, of the arm's motion that the stick moves the ball at all; so criterion (1) and (2) are satisfied. And the arm must be exerting its causal influence at the same time that the ball pushes the stick in order for the ball to be moving; so criterion (3) is satisfied. Hence, this counts as an essentially ordered causal series.

An example of an accidentally ordered series is a series of fathers causing the existence of their sons. While it is sufficient for being an accidentally ordered series that the series fail to satisfy any of (1) through (3), this one appears to fail all of them. (2) seems to be clearly not satisfied in this case; if anything, it is the posterior rather than the prior in the series which are more important; I depend more on my dad's causal influence than my grandfather's in order to begin existing. And clearly my dad can beget me even if my grandfather has already ceased to exist, contra (1) and (3). So this is a perfect example of an accidentally ordered causal series.

Before getting to the point there is one more notion to get out of the way, that of an 'accidental unity' as it is called by the medievals. While some people may get scared by the 'spooky' scholastic terminology, the notion is relatively simple. An accidental unity is just the composite of an object and some feature (accident) which that object has. Now, as far as what it counts as a unity or composite in virtue of, it is in virtue of the relation of the feature's inhering in the object. An example would be the object white-Socrates. This is not just reducible to Socrates, for Socrates can fail to be white, but clearly white-Socrates cannot fail to be white. For it is a composite of Socrates and his whiteness.

Now, with all that said, how can a Finean definition of essence contribute to our understanding of causation here? While I'm not so sure about (2), I would suggest that it is definitely applicable in further analyzing criteria (1) and (3) of an essentially ordered causal series. I will examine the point about (1) first, since I think it actually helps us to understand why (3) is true as well.

It seems likely on the face of it that (1) can be further analyzed with our notion of ontological dependence, especially considering that the very word 'dependence' appears in it. But let us go back to the example of the arm, stick, and ball. In this series, all the causes in the series are acting so as to produce the motion of the ball. So the effect being produced is the motion of the ball. [It is interesting to note that this effect is an accidental unity: the composite of the ball plus the feature of its being in motion (though this need not always be the case; substances taken alone can often be effects as well).]

Now, let us ask what is actually causing the motion of the ball, in the most strict sense of being a sufficient rather than merely partial cause of the ball's motion: Is it properly speaking the stick and the arm, or is it the causing-stick and causing-arm, i.e the accidental unity of the stick plus its feature F of causing this ball's motion in this causal series (and similarly for the causing-arm)? It seems to be the latter, for if you do not have the stick plus this feature F, then you will not have any motion at all. [I should note: It is consistent with what I've said that F can possibly be reduced further to a conglomeration of even more basic features.]

But then, given the causes are properly speaking the causing-stick and the causing-arm it becomes quite easy to analyze (1) further: For we can say the causing-stick depends on the causing-arm in precisely the sense of our Finean definition earlier, viz the causing-arm appears as a constituent in an essential truth about the causing-stick. For let us take our feature F in full: It is the feature of the stick's causing this ball's motion in this causal series. Now the stick only has this feature because of the force imparted to it by the arm. So the accidental unity of the causing-stick has its very identity in virtue of the action of the causing-arm. But this statement is true in virtue of the identity of the causing-stick; so the causing-arm is a constituent in an essential proposition of the causing-stick, and so the causing-stick depends on the causing-arm (and thus, derivatively, on the arm).

If that is all clear, then (3) makes sense as well in a pretty straightforward way. For on the Finean account of essence, while not all necessary truths about a thing are essential truths, it is plausible to think that all essential truths are necessary truths about the thing. That is to say, if it is true in virtue of the identity of x that P, then necessarily if x exists then P is true. Now, going back to (3) obviously the effect depends on its most immediate cause in order to be produced; but then if what I've said about (1) is right, the most immediate cause depends ontologically—in the most strict Finean sense--on all the prior causes. But given that the immediate cause depends on the prior causes, it is true in virtue of the identity of the immediate cause that it exists only if the prior causes exist. So, given what I've said about essential truths entailing necessary truths, it will follow that necessarily if the immediate cause exists then so do the prior causes. But if x's existence necessarily entails y's existence in this sense, then at all times at which x exists, y exists. So if the immediate cause of the effect exists, then all the causes of the effect exist at the same time. So, given that we are dealing with an essentially ordered series and have (1), criterion (3) will follow.

As a side point, I think it is interesting to note that (1) appears to follow from (3); this may be part of the reason why in the cases of accidental series we can often refute (1) by just refuting (3). If (1) entails (3), which itself entails the existence of the prior causes, then having the prior causes not exist will show not only (3) fails but that (1) fails as well; thus, for instance, it is enough to point out that my grandfather doesn't exist to show that in the causal series of fathers the posterior do not depend on the prior for their causal efficacy.

All said and done then, Fine's notion appears helpful here. Of course, the claims I've made may need to be modified somewhat on further consideration, but I think they are on the right track. Very roughly, the point I'm trying to get across is that the causes in essentially ordered series are accidental unities, that these unities depend in the full Finean sense on the prior ones, and so (1) and (3) will follow. It seems very plausible to me that much more can be said about this than I have said here, and I have a strong inchoate idea about how far this could go in other directions and how much more precise it could be made. Yet even if one does not find this plausible as an explanation of what is actually going on in these cases of causation, it still might be a way to explain what (1) and (3) actually mean in the hands of medieval philosophers.

So, at the very least, it does seem that the Finean notion of dependence can potentially play a role in helping us to further analyze and understand important metaphysical notions like causation. In virtue of this, I would suggest that a Finean essentialist definition of dependence is very important and requires further investigation. Other important areas that seem fruitful for investigation, just to list a couple, might be the area of grounding, and whether these notions of ground are the same as ontological dependence or not, as well as the idea of reduction and whether reduction claims are a species of dependence claims.

Sources Consulted
-Aristotle, and W. D. Ross. Aristotle's Metaphysics. Oxford: Clarendon Press, 1924.
-Fine, Kit. "Essence and Modality." Philosophical Perspectives 8 (Logic and Language) (1994): 1-16.
-Fine, Kit. "Ontological Dependence." Proceedings of the Aristotelian Society 95 (1995):  269-290.
-Fine, Kit. "The Logic Of Essence." Journal of Philosophical Logic 24.3 (1995): 241-273.
-Fine, Kit. "Senses of Essence." In Sinnott-Armstrong, W., Raffman, D. and Asher, N. (eds.): Modality, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus. New York: Cambridge University Press (1995): 53-73.
-Gorman, Michael. "Ontological Priority and John Duns Scotus." The Philosophical Quarterly 43.173 (1993): 460-471.
-Koslicki, Kathrin. "Varieties of Ontological Dependence." In Correia, F. and Schnieder, B (eds.) (2012): 186-213.
-Weingart, R.G. "The Logic of Essentially Ordered Causes." Notre Dame Journal of Formal Logic 12.4 (1971): 406-422.
-Zalta, E. N. "Essence And Modality." Mind 115.459 (2006): 659-694.

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