Sober on Essentialist Explanations in Science

"My suggestion is that the gas's kinetic energy explains what it is for the gas to have the temperature it does. It does not explain why the gas has the temperature at the time in question. The relationship here is much like the one between a dispositional property and its physical basis. If zebras differ in fitness because of their leg structure, then there is a sense in which leg architecture explains fitness relationships. The relationship is not causal; it does not explain why those fitness values came into existence. Science not only explains why certain states of affairs and events come into existence; it also seeks to explain the nature of those events."

--Elliott Sober, The Nature of Selection, p. 75.

Note that explanation is hyperintensional, and that not just any necessarily coextensive term would work equally well in place of 'the gas's kinetic energy' here.

Essence and Counterpossibles

In my last post I made the point that the predicate position in real definitions is hyperintensional. So, even if two predicates have the same intension, i.e. necessarily apply to all the same things, they might not be able to be substituted for each other in the real definition while preserving truth value. This means that, among the necessary properties of a thing, we have to distinguish those which are essential to the thing from those which are not.

Maybe one way to do this is by using counterfactuals with impossible antecedents, also known as counterpossibles. 

The general idea is this. Counterpossibles, according to a certain semantics, are also hyperintensional. You can insert intensionally equivalent antecedents into the same counterfactual, but only some of these counterfactuals will be true while others will be false. So maybe we can use a particular counterpossible schema (as we will see, that in (1*)) to discriminate between properties that are essential and those that are non-essential. 

More specifically, we can take two intensionally equivalent properties F and G, insert F into the antecedent, insert G into the antecedent, and the counterfactual may have a different truth value depending on which of F or G is substituted. Thus, the essential vs. non-essential distinction will be able to be defined in terms of the truth or falsity of instances of a certain counterfactual schema. To make the point more vivid, the counterfactual schema will be like a box we can insert intensionally equivalent properties such as F or G into. If we put in G for instance and the box outputs TRUE then G is essential; if it outputs FALSE then G is not essential. Since counterpossibles are hyperintensional, the 'box' won't always give the same output for properties with the same intension.

So: Consider two intensionally equivalent properties F and G. This means that, necessarily, if anything has F in a world then it also has G in the same world, and vice versa. If F and G are intensionally equivalent then the properties λz[□Fz] and λz[□Gz] are also intensionally equivalent, and thus the formulas λz[□Fz](x) and λz[□Gz](x) are intensionally equivalent. Now, consider a counterfactual of the form:

• (C) If φ had been the case then A.

Since we are going with an interpretation allowing for non-trivially true counterpossibles, we can substitute in for φ either of two necessarily false propositions, P or Q, but it won't automatically follow that (C) will come out true under both substitutions.

So suppose it is true that a is necessarily F and necessarily G.

Let P be '¬λz[□Fz](a)', let Q be '¬λz[□Gz](a)' and let A be '¬λz[∃yy=z](a)'.

Again, it doesn't follow automatically from the semantics of counterpossibles that substituting P in for φ will give you the same truth value as substituting Q for φ, despite the fact that these two formulas are intensionally equivalent. What we can do then to distinguish whether F is essential or G is essential (or neither) is substitute in P for φ and Q for φ in (C). If (C) comes out true, then the property is essential; if it comes out false, then it is not.

With this hypothesis in mind, here is a very rough first stab. For any x:

• (1) For any P, if P is a de re necessary property of x, then P is an essential property of x if and only if had x lacked P then x would not exist.

More formally, let |x| be λz[z=x]: 

• (1*) For any P: If λz[□Pz](x) then: □|x|Px iff (¬λz[Pz](x) □→¬λz[∃yy=z](x)])

Again, keep in mind that the counterfactuals here are to have a semantics where they can be read as non-trivially true counterpossibles, and thus not according to the standard Lewis-Stalnaker semantics. Also, the 'essentialist box', □F, comes from Kit Fine's 'Logic of Essence'. Roughly, □FA means that in virtue of the essence of the F's, A holds. So if |x| is the property of being identical to x, then □|x|Px turns out to mean that in virtue of the essence of x P holds of x. Fine parses out the logic this way for its semantical and logical elegance.

Consider one example given by Kit Fine: Suppose we have the property λz[z∈{z}]. Intuitively, this is the property satisfied by something whenever it is in its singleton. Assuming that, necessarily, I am a member of my singleton, then this is a de re necessary property of me, i.e. λz[□z∈{z}](a) However, it seems to not be an essential property of me.

So, is it true that the following holds?

• (A) Had Alfredo lacked λz[z∈{z}], Alfredo would not exist.
• (A*) ¬λz[z∈{z}](a) □→ ¬λz[∃yy=z](a)

It seems that (A) does not hold. For it's irrelevant to my nature whether there are any abstract objects, such as sets, at all. After all, it seems that if nominalism were true, I would still exist. This lends some weight toward thinking that, if I had lacked λz[z∈{z}], I would still exist. But then by the criterion in (1), since the counterpossible does not hold for the property λz[z∈{z}], it must follow that λz[z∈{z}] is not essential to me. 

Given a de re necessary property of x, P, it might also be that the truth of the appropriate counterpossible is just a necessary condition for a property's being essential. In other words:

• (NEC) If P is essential to x, then were x to lack P x would not exist. 
• (NEC*) If □|x|Px, then (¬λz[Pz](x) □→¬λz[∃yy=z](x)]).

Or it might be a sufficient condition as well, i.e.:

• (SUFF) Given that if x were to lack P x would not exist, then P is essential to x.
• (SUFF*) If (¬λz[Pz](x) □→¬λz[∃yy=z](x)]), then □|x|Px.

Keeping in mind of course the sense of the term 'essence' in mind, and the relevant semantics for counterpossibles, (NEC) seems definitely true, and probably uncontentious. I suppose the interesting question is whether (SUFF) is true. I think the examples lend some support to the idea, such as the case of the singleton set given above.

In the case of (SUFF) it is particularly important that we use the right semantics for counterpossibles. If (SUFF) is true then this is very useful when talking to those who don't recognize the sense of essence at stake here: If they already know how to evaluate the counterpossible in the antecedent according to a 'non-trivial' semantics, then we simply say, "Plug in the property for the antecedent; if the counterfactual holds non-trivially, the property is essential. Now you know what I mean." This might also be a nice way to interpret people who give multiple definitions of 'essential' and 'accidental' properties, such as Aristotle. Aristotle gives a modal definition of essential properties which can sound like it might contradict other definitions of his; but (1) is 'modal' too, and it might be a way to interpret Aristotle that makes him consistent.

Probably potential counter-examples to the hypothesis come to mind. I know that I already see some issues. But it might be useful to see how far this hypothesis can go. And maybe if the hypothesis doesn't hold in general (I bet it doesn't) it might at least help us pick out an important class of the essential properties. After all, it seems in part that the reason we recognize λz[z∈{z}] as non-essential to me is because in some (non-trivial) sense had I lacked it λz[z∈{z}] I would still exist. Had nominalism been true, I'd have still been real (save if you're a Platonist/Pythagorean of a certain sort, in which case maybe you'd have good, non-trivial reason to deny that the counterfactual holds).

It might seem overly complicated to do this quasi-formally as I have, but one thing I'd like to do is look more at the formal semantics of essence such as Fine's for instance (hence the essentialist 'box' operator from Fine's papers), and see how this relates to the formal semantics of counterpossibles (whatever that happens to be). Given the inter-dependence of the two notions, maybe the correct semantics for counterpossibles will help us find the correct semantics for essence, and vice versa. Maybe the notion of essence will help us give a more principled similarity metric for counterpossibles in certain contexts. Also, maybe the notions of essence and counterpossible will relate closely to other notions, such as grounding, dependence and explanation. It might be an interesting project to see how far formal methods can help us here in finding relations between these concepts.

Essence and Hyperintensionality

The essence of something is the truthmaker of the real definition of the thing. So, to know what the essence of something is is to know its real definition. For instance, to know the essence of man is to know the proposition that man is a rational animal. This is traditionally thought to be the real definition of 'man'.

Here is the general schema for a real definition:

• S ise an F.

'S' is replaced by some kind-term (or maybe even individual-term?), the thing to be defined, and 'F' with some predicate, the definiens. The 'is' here is a special kind of 'is': the 'is' of real definition or essence. The conditions that have to be met for something to bee F are much more strict than for something to be F in other senses of 'be' (such as the more general sense of 'is', the 'is' of predication).

(Side-note: In some contexts is this a schema for reduction too? Interesting...)

Real definitions are 'fine-grained'. You cannot always substitute extensional equivalents into the predicate position to get the same truth value. For instance, suppose all and only the actually existing rational animals are animals which evolved by a certain evolutionary process P on earth. Even if this so, the following is not true:

• Man ise an animal which evolved by process P on earth.

After all, man could have evolved in some other way, or even not at all. Man could have randomly popped into existence. So it's certainly not part of the very definition of man that he evolved by a certain evolutionary process.

So real definitions are fine-grained. In fact, real definitions are very fine-grained; you cannot even substitute intensional equivalents into the predicate position and always retain the same truth value. Suppose for instance that, necessarily, any animal which is rational is the type of thing which can speak a language. This actually seems pretty plausible. (If not, think of some other necessary consequence of being rational. You could even use some fancy disjunctive, conjunctive, or conditional properties, though I try to avoid these.) Even if this is so, the following is not true:

• Man ise an language-capable animal.

At least, it's not true when we're talking about the 'is' of real definition. For this doesn't get to the heart of what man is; it's not what he is at the most fundamental level, but rather something he happens to be.

So, the predicate position in real definitions is a hyperintensional position, in the sense that substitution of intensional equivalents will not always preserve the same truth value. I take it these points cohere well with what has been said about real definition and essence up to now by others, such as Fine.

In the next post, I'll try to say something about how the hyperintensionality in real definitions means that counterpossibles will be very closely related to real definitions. Maybe this will help, at least a little, with the epistemology of essence.

Lately I have been suspecting that hyperintensionality, counterpossibles, essence, explanation, grounding, reduction, fundamentality, naturalness, intrinsicality, and lots of other things are very closely related. In the future I'd like to try to bring out some of these relationships. I'm not sure how successful this will be, but my metaphysical nose is leading me in this direction.

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.

Aristotelian Relativism

On the Aristotelian account of ethics, what is "good" for an agent depends on that agent's essence/nature/form as well as that form's characteristic natural ends. For example, it is good for a dog to reproduce, eat and drink, and have fully working senses, the reason being that reproduction, internal equilibrium, and various types of perception are some of the natural ends (in Greek, 'teloi') of a dog. When it comes to us humans the general outline remains the same, though we will have some differences insofar as humans are essentially different from dogs, and hence characterized by different natural ends.

Now, it seems plausible to think that there are necessary ethical truths. For instance, it is always wrong for people to torture little children just for the sake of it. But could the above Aristotelian account contradict this? It seems that, given human evolution, the conditions whereby natural selection brought about the existence of humans might have brought about evil counterparts, call them "anti-humans." All of their natural ends would be inverse to ours. For instance, while it is good and fulfilling of our ends to protect others, for the anti-humans it might be good and fulfilling of their ends to commit murder. Similarly, it might be good for them to rape, torture children, commit genocide, etc. Hence, what is good or bad is simply relative to whether you are a human or anti-human. Call this idea "Aristotelian Relativism."

There are a couple of ways an Aristotelian could get out of this relativism. First off, there is the theistic route. Given God's existence and the idea that goodness is grounded in his nature, this would provide an objective basis for the good which holds across all possible worlds. This prevents the instantiation of any species whose ends include raping and murdering their young, or something of that sort, thus making the anti-human scenario strictly speaking impossible.

There are also a couple of ways for a non-theist Aristotelian to respond. The first is to bite the bullet and say that such things which appear horrendous to us (and indeed are horrendous for us) would not be horrendous for some other kind of thing. It's not a reply we might like, but that's exactly what we should expect given that it is contrary to our nature to do these sorts of actions. When we see rape, cannibalism, and slaughter in the lower animals, though we are likely to be disturbed, we nevertheless admit that it is natural to those animals to bring about and flourish from these types of suffering.

A second and maybe more satisfying way to respond is to say that such a scenario is not metaphysically possible for a species of rational animals. Remember, though they may disturb us, we already acknowledge that cannibalism, slaughter, and forced sex can be fulfilling for some lower animals, as there are examples of this found in the natural world. But with rational animals it is different. Aristotle understood the essence of man not to consist in our purely biological properties, but rather in our rationality; hence, "rational animals". It is from this that he derived the virtues and goods that we already acknowledge. But that means that for anything which can be classified as a rational animal, it will be wrong for it to do the things such as murder, rape, and torture. Hence, the idea of an "anti-human" turns out to be contradictory. If anti-humans are rational animals, and Aristotle's derivation of the natural ends of rational animals is correct, then it's metaphysically impossible for murder, rape, and torture to be good for such creatures. Anti-humans, then, are metaphysically impossible, and the things we understand to be good for persons are necessarily good after all.

Does Conceivability Entail Possibility?

The following should probably be pretty clear to some people. Just another way of showing that conceivability does not imply possibility. The proof will go somewhat informally with a few hidden premises, and I'm not even sure if it's any good.

Suppose
(1) If I can conceive of a possible world, then such a world exists. (This doesn't mean it's actual of course.)
Further,
(2) I can conceive of a possible world which is empty.
(3) Therefore, there is an empty possible world.
(4) I can conceive of a necessary being.
One can easily deduce from (4) that
(5) Therefore, there is no empty possible world.
(6) Therefore, there is an empty possible world and there is no empty possible world.
(7) Therefore, ~(1). (because 1 implies a contradiction, viz. 6)

By "empty possible world" I mean a world in which no entities exist. Some may object that this is harder to understand than at first sight, and may in fact be inconceivable. For those who agree that it is conceivable we've shown that (1) is false. For the skeptic's sake let's take a less controversial example. Let's say that in every possible world there exists at least one entity. This isn't to say that in each world it is the same entity, i.e. we're not saying there exists something x such that x exists in all possible worlds. To illustrate the point let's use a little bit of basic sets. Take two sets A = {1,2} and  B = {3,4). These two sets are disjoint. If you tried to find a set which has as its elements/members all x such that x is in A and x is in B you'd come up with an empty set. In other words, they have no members in common. In an analogous way we can conceive of two possible worlds being "disjoint", that is, not having any entities in common. So we can say

(8) I can conceive of two "disjoint" possible worlds.
(9) Therefore, there are two disjoint possible worlds.

Remember, this is consistent with our rejection of (2).

(10) If there are two disjoint possible worlds, then there are no entities common to all possible worlds.
(11) Therefore, there are no entities common to all possible worlds
(12) If a necessary being is possible, then there are some entities which are common to all possible worlds.
(13) Therefore, there are some entities common to all possible worlds. (One could easily show that this follows.)

We've of course come to our flat contradiction with (11) and (13) and shown (1) to be false.

Without (1) how can we learn about metaphysical possibility? It seems to me that we'll have to go back to those good ol' essences, thus raising the further question of how we can know both essences and their implications. I wonder though how we can figure out why anything exists at all. We can't turn to essences to learn about the modal properties of being. Being has no "essence", since it's a transcendental. The falsity of (1) also has implications for those who want to create modal arguments for God. We can't just go based on God's conceivability. It's interesting to note that Robert Maydole's proof of the Maximally Great Being's (MBG) metaphysical possibility seems to rely on the very essence of the MGB.

P.S. Now we've got Ss. Augustine, Anselm, and Bonaventure praying for us on the side. :-)

Essences and Truthmakers

After reading David Oderberg's book Real Essentialism I've been concerned with getting a clear understanding of what "essences" are. Essences are not substances in themselves, over and above the entities which have them. On the other hand, they are supposed to provide explanatory power for the objects that have them, and they are supposed to have a specific sort of causal importance, in Aristotle's terms what is called "formal causation". In trying to make sense of these notions I have found truthmaking to be somewhat helpful (provided of course we have a good account of truthmaking). Here's an analysis:

Essence: For any entity X the essence of X is the truthmaker of the proposition that the real definition of X is [such and such].

To begin with, let's be clear about what exactly a truthmaker is. A truthmaker is some fact or aspect of reality in virtue of which a truthbearer, such as a proposition, statement, belief, etc., is true. How exactly is truthmaking helpful here? Well, it describes a real aspect of a thing.

Kit Fine provides a popular neo-Aristotelian definitional account of essences, saying that we can give real definitions of not only words, but entities, in order to explain what they are. These real definitions of objects are their essences. More work needs to be done on getting to the heart of what real definitions are and how we come to know them. (A possible account of what they are, which I am now somewhat doubtful of, is here.) But provided we have a clear understanding of this, Fine's account certainly seems to be on the right track, especially in the face of the failure of some modalist accounts. But according to the classical account, essences not only make things to be what they are; they provide explanations for causal powers. Definitions, which are linguistic entities, obviously do not.

As Kathrin Koslicki puts it in her paper "Essence, Necessity, and Explanation", "A definition, according to Aristotle, is a formula or statement of the essence, i.e. of what it is to be a certain kind of thing." She continues, "On Aristotle’s way of thinking, then, the explanatory power inherent in definitions, in their role as the linguistic correlates of essences, is a direct reflection of the causal power of essences." Since real definitions are the linguistic correlates of essences, truthmaking provides a way to get back to the essence itself.

Aristotelianism and the Christian Worldview

Originally posted here.

Introduction:
Throughout the centuries the Christian tradition has had a love-hate relationship with Aristotle. His logic and metaphysical categories provided strong tools for developing and formalizing such classic doctrines as the Incarnation and the Holy Trinity. On the other hand, he famously held that the universe was eternal and that there was no first man such as Adam, putting him at odds with Christian belief. Yet in the midst of this conflict, there is much to be gathered and adopted by the Christian. Here I’d like to examine a few of Aristotle’s ideas about the essences of things and see how they relate to the Christian view of man.

Essences:
The first thing to note is that humans, along with every other kind of thing, have “essences” or “natures”. An essence is simply that in virtue of which a thing is what it is. It’s what makes the definition of a thing true. It’s also the grounding of a thing’s essential properties, i.e. those properties which are intrinsic to that type of thing. Without essences we could not form inductive laws, we could not differentiate between kinds of things, and we couldn’t even properly define our concepts.

Essences entail that things have natural ends or functions (what Aristotle calls the “telos”). It would be incorrect to understand “function” in terms of the functions of human artifacts such as wheels or fishing rods. Rather, things have functions in the sense that they function in a certain natural way. So we can see clearly that by their very essences things like dogs or snakes have natural functions, including sensory perception, reproduction, self-change, and sustenance. This is what makes it good for them to pursue certain goals, like eating food or reproducing. To generalize, it is good for them to fulfill their functions.

This may seem irrelevant, but it has truly significant consequences for us as well. It gives medicine a normative structure, making sense of the strong and reasonable intuition that things such as broken bones or tumors are defects, while other things such as firmness of muscle or thorough digestion are indicators of health. It means that we all have certain functions which it is objectively good for us to fulfill. This can provide a foundation for objective morality and a guide to living our lives. Thus understood, essences are both indispensable and significant.

The Christian Picture:
So what is essential to humanity? Well, recall that essences are what differentiate things from entities of other kinds. In attempting to discover our essence then, it would be useful to see how we differ from other things. We share some characteristics with non-living things because we too are made of matter and have mass. But we are different from them precisely in virtue of the fact that we are alive. We are different from some living things like plants due to our sensory capabilities which we have in common with other animals. Yet we humans can be distinguished even from these creatures by our rationality. Unlike other animals, we can abstract from concrete particulars to general universal truths. Thus, humans are by their very essence rational animals.

How well does this fit into the Christian view of things? Consider the idea that God is a being with infinite knowledge, and thus an intellect. In Romans 11:33 for instance, Paul the Apostle praises God’s omniscience: ” O the depth of the riches of the wisdom and of the knowledge of God!” Aristotle’s view confirms precisely what the believer says, that is, that humans are by their very essence endowed with an intellect and will like God’s. As Genesis 1:27 says: “God created man to his own image: to the image of God he created him: male and female he created them.” Every human, male and female, is essentially made in God’s image.

We can also conclude from Aristotle’s view that, because humans have an essence with natural ends, there are some things that are objectively good for all of us, and that these objective moral truths are available to anyone who uses his or her reason and conscience. This confirms what we find in Romans 2:14-15: “For when the Gentiles, who have not the law, do by nature those things that are of the law; these, having not the law, are a law to themselves. Who show the work of the law written in their hearts, their conscience bearing witness to them.”

Much more could be said about all of these ideas. Yet it becomes clear how strongly these Aristotelian theses can be used to support what the Christian affirms. Hence, there is much fruit to be found by the Christian in the Aristotelian tradition, making the ancients very worthy of our attention.

Real Definition

In attempting to define things we can end up with a large amount of vagueness. For example, take the case of a kitty. When someone asks "what is a 'kitty'?" it is clearly insufficient to simply list properties which hold truly of it. For instance, in reply one might say that it is something small, furry, and cute. This would all be true. But that doesn't really help us to get at what a kitty is, does it? What we need here is not a mere nominal definition. We need a real definition.

The most precise and clear way of getting to a real definition is by what is called "genus-species classification". One must not confuse this with something like "biological species" which are these days based off of evolutionary lineage. In terms of giving real definitions of things, it usually has very little to do with that. The easiest way to understand this is with set theory and venn diagrams. In terms of set theory, a genus is just a type of superset and a species is a type of subset. A superset counts as a genus when all of the members of its subsets share certain particular attributes in common. A subset counts as a species when its members all have some special attribute which demarcates them from the members of the other subsets. This difference is called the "specific difference". So with the case of the kitty, the genus is "cat", since kitties have all of the attributes necessary to be included in the genus (superset) of cats. However, a kitty is different from other cats insofar as it is young. So the specific difference is the attribute of its youth. This creates a separate species from other cats, such as adult ones who have the specific difference of mature age. Maybe the venn diagram above is illuminating.

So to get a real definition of kitty we take the species and genus, giving us "young cat". Hypothetically, one could do this with any given natural kind of thing.