Mental Causation I: The Exclusion Problem and Supervenience

Our commonsense intuitions and folk psychology point to the efficacy of mental properties. It seems that nothing could be more obvious than that things like beliefs and desires cause things to happen in the world. Analysis of the causal role of beliefs, desires, and other mental properties leads quickly to questions about this commonsense picture. Are beliefs and desires physical entities? Are they identical to neurological states? If they are not identical to neurological states, which should be considered the true cause of the effects claimed for mental causes, mental properties or brain properties? These sorts of considerations are at the heart of the exclusion argument put forward by Jaegwon Kim in a variety of versions over the last 30 years.

The basic issue that the exclusion argument attempts to elucidate is the following: if we are realists about mental causation and physicalism, then any mental event m that causes physical event p does so in virtue of m and p falling under mental kind M and physical kind P respectively. Does p have a physical cause as well as a mental cause? If p does not have a physical cause, in other words if m is a strictly nonphysical property, then m’s having causal efficacy is a violation of causal closure of the physical, which is at the heart of physicalism. Allowing nonphysical causes moves the discourse into Cartesian dualism with all the unsolved mysteries surrounding the relation of physical to nonphysical properties that accompany it. If we add another restriction to our interpretation of the causal sequence, that if p is a physical event it must have a physical cause, then the question becomes, if p has a physical cause, then what role would the purported mental cause play? The physical cause seems to exclude the mental cause (Kim 1998: 37-8).

So, what sort of options are there to deal with this exclusion?

I see four options for dealing with the problem, which I plan to deal with in later posts: reductionism, eliminitivism, nonreductive physicalism, and epistemic compatibilism. Here, though, I'll briefly follow Kim's argument showing why an appeal to supervenience is a nonstarter as a solution to the problem.

The claim that mental states supervene on physical states means that for any mental event m that instantiates mental property M at time t, there is some physical property P such that m has P at t and anything that has P has M. If supervenience fails, then the intelligibility of mental causation fails as well. The conjunction of supervenience with the causal closure of the physical provides the possibility of explaining mental causation within the general account of physical causation, but only if mental causation can be reconciled with causal closure and supervenience. Supervenience brings mental causation under the purview of physical causation. So mental causation without supervenience is unintelligible from the perspective of physicalism (Kim 1998: 37-41).

Unfortunately, mental causation is unintelligible if supervenience holds as well. Consider some mental property M that is purported to cause another mental property M*. In this case if supervenience holds, then M and M* each supervene on physical properties, say P and P* respectively. If this is the case then there are two potential explanations for why M* obtains, M and P*. This can be alleviated by claiming that M causes P*, but that solution only provides a new difficulty, namely, how to explain the downward causal powers of M. Or alternatively, we could claim instead that P causes P* granting causal power to M in a derivative or dependent sense. This however, brings us right back to the exclusion argument. Kim contends that the most natural way of viewing the relation of M to M* in this case is to say instead that P causes P*, M supervenes on P and M* supervenes on P*. On this view the mental properties depend for their existence on the physical subvenient properties, and all of the causal activity takes place on the physical level. The regularity between the mental properties is not an accidental one, though; there is a real causal regularity that explains the connection between these properties, and is able to do so without violating the causal closure of the physical or leading to overdetermination. But on the supervenience model the real causal action takes place at the physical level, not the mental level, and thus supervenience doesn't really offer an alternative that avoids the exclusion problem (Kim 1998: 41-7).

Kim, J. 1998. Mind in a Physical World. Cambridge: MIT Press.

I Put the "Super" in Supervenience

So, I'm taking a course in contemporary metaphysics this term, and I feel a bit like I've wandered into a foreign land of nonsense and speculation. For the most part, I am interested in the history of philosophy or philosophy of science and so my study of philosophy has to this point been fairly bereft of bizarre arguments about possible worlds, multiple realization, and some of the other arcane theoretical entities and relations that stalk the pages of philosophy journals.

I think I prefer it that way. We're into week 3 on "supervenience" and I still have no idea what that term is supposed to mean. The slogan version is simple enough: if property A "supervenes" on property B, then any two entities that are exactly the same in respect to their B-properties will be identical in respect of their A-properties. If mental properties supervene on neurophysiological properties, then any two identical brains will have identical thoughts.

Ok. So far, so good. The problem comes when you try to say anything further. Saying that mental properties supervene on neurophysiological properties doesn't tell us much at all about either set of properties, and it tells us absolutely nothing about the relation between the two sets of properties.

The way I read it, a supervenience claim is either an uninformative claim that the two sets of properties show covariance or an incomplete claim that one set of properties depends on the other. Either way, just saying that A supervenes on B is not saying much.

Maybe I don't really understand the philosophical import of this notion. Let's hope so, because otherwise it's going to be a long quarter.

Natural Grace

I was hipped to Bill Callahan's album Sometimes I wish we were an eagle by Matt at why birds don't talk, and it's one of the most beautiful albums I've heard in a long time. The instrumentation on all the songs is terrific, and even though the vocals are, let's say, not exactly ordinary, everything works together really well. You can sample the songs at the link above, and I would absolutely recommend it. A terrific conceptual theme runs through the album too, which is that there is beauty and meaning in ordinary life and in the natural world.


The first song on the album, "Jim Cain," is written from the perspective of noir fiction author James M. Cain, who wrote, among other things, The Postman Always Rings Twice and Double Indemnity. The first line of the song, "I started out in search of ordinary things," reminds me of the opening passage of Mildred Pierce in which Cain describes with terrific detail Mildred's husband Bert hanging nets to support the weight of the fruit on their avocado trees; an everyday event, which becomes charged with meaning as you read on and find out that their marriage is ending. This act winds up being his last real act as Mildred's husband.


"Eid Ma Clack Shaw" follows, with notions of love, memory, and dreams entangled throughout. This sparks interest in the philosophy student in me; all three of these phenomena share a similar ontological profile. Essentially, all three are events which occur only within the minds of people-- there are no dreams, memories, or love "out there" in the world independent of the experiencers, and yet all three are nonetheless entirely natural and meaningful. In the song the narrator "dreams the perfect song" and writes it down in a half-sleep state, only to find that when he awakes what he has written is nonsense. Are we supposed to infer that love and memory also share a disconnect with the waking world?


"The Wind and the Dove" is (as far as can make out) about the interconnectedness of the natural world as a metaphor for the interconnectedness of people: "Somewhere between the wind and the dove/Lies all I sought in you/And when the wind just dies, when the wind just dies/And the dove won't rise/From your window sill."


"Rococo Zephyr" pursues the theme of natural grace most explicitly, and does so beautifully. It's my favorite song on the album; the music is fantastic, and the lyrics are light and thoughtful at the same time. Natural metaphors for human relationships abound: "She lay beside me/Like a branch from, a tender willow tree/I was as still/As still as a river could be/When a rococo zephyr/Swept over her and me." The end of the song ("I used to be sort of blind/Now I can sort of see") apes the words of "Amazing Grace" but without the certainty that religious sentiment provides. The natural is beautiful, but beautifully imperfect as well.

"Too Many Birds": reminds me of a Wallace Stevens or William Carlos Williams poem. The lyrics are spare and descriptive of an object of perception (in this case a bird) but there is an implicit parallel being drawn between the object and the perceiver.

"My Friend" departs from the theme discussed here, but has a terrific line: "Now I'm not saying we're cut from the same tree/But like two pieces of the gallows/The pillar and the beam."

"All Thoughts are Prey to Some Beast" is another use of natural metaphors for the human experience: "The leafless tree looked like a brain/The birds within were all the thoughts and desires within me."

"Invocation of Ratiocination" is a (sort of strange) instrumental, but anyone familiar with church services will think "prayer" when they see "invocation," only what's being invoked here is not a deity or spirit, but human reason.

This emphasis on reason over faith is borne out further in "Faith/Void," the last track on the album. The sparse lyrical structure, musical simplicity and the repetition of the phrase "It's time to put God away," reminds me of the repetitive choruses used in Evangelical Church services, but the content is the opposite: here is not summoning the presence of a god, but recognizing the absence of one. The song doesn't argue against the concept of god (although it does make an oblique reference to the problem of evil), but instead is the expression of a conclusion already reached: "This is the end of faith, no more must I strive/To find my peace, to find my peace in a lie."

Amen, Bill.

My kind of expedition

Not too long ago I bought myself a single bottle of Bell's Expedition Stout. At $20/6-pack it was out of my self-stipulated price range for a beer I've never tried, but I was willing to cough up $3.50 for a single. I wish I had purchased a case. It is a phenomenal beer.

It was probably the darkest beer I've seen; it was almost black in the glass. It had a really distinct coffee aroma on the pour, and there was next to no foam. The first thing I tasted was a hint of coffee, then a little bit of chocolate flavor, and then the aftertaste was almost like caramel. All of this was the undertone for the very good, strong roasted flavor you expect from a stout. It was also unbelievably smooth for a beer with a 10.5% alcohol content.

I don't normally drink stouts or porters in the summertime; I usually opt for more hoppy beers when the weather is hot, but this is one stout I would drink in the middle of the desert.

Thankful for Colonialism

Okay, so not everything about Colonialism was good, but at least it gave us India Pale Ale. I have recently tried a really good one: Dogfish Head 90 Minute Imperial IPA. It has a really nice deep reddish color, and has a pleasant citrusy smell. Since it's an IPA it's extremely hoppy, but there is enough of a malty taste to balance it out. It has a pretty high alcohol content (9%) and as it got warmer in the glass, I thought the alcohol taste came through more and almost dominated the malt flavor in the aftertaste, but the initial hoppy bite is terrific.

It's a really good beer. It's a little on the pricey side for me ($11/4-pack), but it was worth it.

I give it 4 staggers out of 5.

What's So Great About Christianity (Part 2)

Part 2 of “What’s So Great About Christianity” is an argument that the political and moral virtues cherished in modern Western society are the direct inheritance of the West’s Christian roots. The implication we are supposed to draw from this is that if these virtues find their roots in Christian ideas, then they are unsupportable or unsupported outside the Christian conceptual framework. It is, I think, uncontroversial that Christianity was influential in the development of western values, so the validity of D’Souza’s argument will turn on whether these values are defensible without accepting the full Christian message.

In chapter five D’Souza argues that the modern concept of limited government is a product of Christ’s injunction to “render unto Caesar what is Caesar’s and to God what is God’s” in Matthew 22. It is important to note that even if the concept of limited government can be traced to Christ’s teachings, the first appearance of governments that were limited in the sense we mean when we say “limited government” came about as a product of the Enlightenment in Europe and America. It may be that the monarchies of the Middle Ages and early modern period were limited in their power by natural restrictions in resources or technology, so that people had a modicum of freedom of action unencumbered by governmental interference, but it likely wasn’t from lack of trying on the government’s part. These governments weren’t limited out of philosophical considerations about universal individual rights and liberties. Also, the notion of the separation of church and state may have conceptual roots in St. Augustine’s “City of God” as D’Souza claims, but it would be difficult to convince historians that anything like the modern separation existed in the Middle Ages. So, even if the idea is traced to Christian thought, it was not practiced by Christian society until well after the founding of Christianity.

It is unclear to me why D’Souza thinks Christianity specifically should be credited with the growth of religious tolerance (pp. 53-4); while it’s true that Christians (like the philosopher John Locke) were at the forefront of arguing for religious tolerance, it is equally true that their opponents, the people who wanted to limit religious freedom, were Christians as well.

D’Souza concludes chapter 5 by saying “Today courts wrongly interpret separation of church and state to mean that religion has no place in the public arena or that morality derived from religion should not be permitted to shape our laws” (56). But if there is not a non-religious justification for a law, then it seems to me at least arguable that the law is a violation of the prohibition of the establishment of religion. If the law is on the books only because of the religious rules of one particular sect, then it amounts to the government advocating that religion. Take as an example laws that prohibit the sale of alcohol on Sundays in certain areas. These laws clearly have no other purpose than to impose a particular religious moral prohibition on the community at large.

Chapter 6 compares the morality of Christianity to that of the ancient Greeks and Romans, in order to argue that Christian morality is more in concert with what we all believe today. He starts by arguing that Paul “repudiates an entire tradition of classical philosophy” (57) when he claims that people don’t do evil strictly out of ignorance of the good. The view that the philosophical problem of “weakness of will” is solved by claiming that ignorance is the cause of bad actions is Plato’s, but it certainly is not Aristotle’s view. Aristotle devotes a substantial portion of his “Nicomachean Ethics” to discussion about the problem of weakness of will, none of which is acknowledged by D'Souza. D’Souza also mischaracterizes the real content of Aristotle’s moral philosophy by claiming that he “cherished” the “great-souled” man. Aristotle does mention (as one type of virtuous man) the man who is better than others (more noble, wealthy, etc) and knows it, and certainly this is not something that we would consider to be a virtue today. But this idea of the great-souled man plays very little role in Aristotle’s ethics. The bulk of his discussion is centered on the concept of human well-being and virtues like courage, temperance, friendship, justice, and other traits that we still value today. These concepts get their first philosophical justification and discussion in the Greeks, not in Christian thought. Christianity certainly contributed to the development of moral philosophy, but the idea that it displaced Greek moral concepts in doing so is simply historically inaccurate.

His claims that Christianity invented the family are also historically debatable. He insinuates that in Greece homosexuality was the norm for sexual life, and little value was placed on marriage. Nothing I’ve read about ancient Greece confirms this. People married, lived together, had children, etc. in Greece (much as they did in most of the ancient world). Certainly the modern family structure has been influenced by Christianity, but D’Souza seems to imply that if it weren’t for Christianity, that nothing approximating the modern family would exist, and I can see very little evidence that this is true.

Chapter 7 attempts to argue that from the very beginning Christianity transformed notions of human dignity and laid the groundwork for our modern notions of human equality and freedom, a proposition that I think is false. D’Souza really does not take seriously the fact that there are not injunctions against slavery in the bible. There may be instructions to treat slaves well, but there is certainly nothing in the bible that directly admonishes people for owning slaves. This has to be accounted for if you are going to argue that the notions of human dignity and equality are the unique product of Christian thought. His response that Christians were discouraged from holding other Christians as slaves is no response at all if he is attempting to show that Christianity contains within it fully formed ideas of equal rights for all.

D’Souza criticizes the ancient Greeks for being a slaveholding society, but lauds the Christian founders of the U.S. as championing freedom 1800 years after the foundation of Christianity supposedly paved the way for equal rights for all. Never mind the fact that western nations had been ruled by Christian leaders since the end of the Roman Empire, and would have had the power to abolish slavery long ago. Never mind the fact that even in the U.S. it ultimately took a Civil War to finally deal with the problem of slavery in half the country.

I’m fully aware that slavery was a complicated political problem and a deeply entrenched institution that was not exclusively practiced within Christianity; slavery is a problem of human history, not only of Christian history. But then neither is the abolition of slavery an exclusively Christian achievement; D’Souza can’t credit only Christianity for the eventual abolition of slavery when Christian society took very few steps toward that abolition in the 12 or 13 centuries prior to the Enlightenment.

Ultimately, though, the second part of D’Souza’s book is built on one long non-sequitor. His argument is intended to imply that because the values we share as a western culture have their origins in Christian thought that if we give up Christianity we will be required to surrender of all of those values. But this simply does not follow. It mistakes the context of the discovery of an idea for the context of its justification. What ultimately or properly grounds a moral idea does not have to be identical to what was used to justify it in the first place. As children we may learn to be kind to others in order to avoid punishment from our parents, but once we reach adulthood, and we no longer are threatened by punishment, we may realize that there are perfectly good reasons to be kind to others that are entirely divorced from our parents’ prescriptions. Likewise, if Christianity has hit upon good moral ideas, then those will be rationally defensible outside the context of Christianity. The political and moral ideals valued in western society are now, whatever their roots, valued for their own sake, not because of their place in a religious metaphysic.

In addition to the fact that the values we have are now entrenched to the point that no loss of religious belief would necessitate a “re-valuation” of values, those values are not simply the common currency of conventional moral and political thought and without further philosophical justification. There is a lot of work that has been done in philosophy in the foundations of ethics and politics, with fully developed theories that provide objective foundations for democratic values and moral principles. D’Souza’s argument presumes that any attempt to ground morality without religion is bound to fail, but we have no reason to believe that it is impossible to provide the rational foundations of moral and political ideals without (explicitly or implicitly) invoking religious propositions to do so.

D'Souza, What's So Great About Christianity (Part One)

Dinesh D’Souza’s “What’s So Great about Christianity” is, according to his preface, a book whose goal is to answer the arguments of Dawkins, Hitchens, and Harris; D’Souza takes them to be representative examples of modern atheism. He intends his book to be for believers and unbelievers alike, but as we’ll see, much of the book is an exercise in preaching to the choir. It could be argued that some of the writers he’s targeting are guilty of some rhetorical excesses, but D’Souza returns excess for excess, and his argument erodes into ad hominem at several points.

In addition to attempting to tackle the criticisms of these writers, he wants to show that historically Christianity has been a force almost exclusively for good, that the discoveries of science don’t force Christians to give up any of their core beliefs (on the contrary, he finds confirmation of the Christian account of the way the world is in modern science), that faith is eminently reasonable, that the mass murders of the 20th century are the logical extension of acquiescence to atheism, and that the real motivation for atheism is “cowardly moral escapism” (xvii). Clearly there is no way that any author could thoroughly cover all the topics he proposes, considering counterarguments and evidence that is in tension with the arguments presented. I actually think that this is part of his rhetorical strategy, which I think can justifiably be called “scattershot argumentation”. Fire a collection of half truths, distortions, carefully mined quotations, and cobbled together arguments at your target, all the while ignoring the logical consequences of your conclusions or whether things you’ve said before are in conflict with what you’re claiming now. While the reader is trying to come to terms the barrage of fallacies and lacunae, reload and fire again.

Before I start to discuss the specifics of D’Souza’s book, I think it is important to note that it is at least possible that every one of D’Souza’s conclusions could be true (at least the ones that don’t contradict each other, and there are a few of those). The issue, though, is whether he has given us any reason to believe those conclusions. I’m going to argue that in fact he hasn’t, and that each of his arguments either fails or is irrelevant to the truth of the propositions he is defending.

That said, on to “Part One: The Future of Christianity.” There are two kinds of arguments in D’Souza’s book: those which are invalid and those which are irrelevant to the truth of Christianity (some fit in both categories). The first part of the book is full of arguments of the latter kind. In chapter one he trumpets the growth of traditional Christianity in the US and worldwide. Liberal Christianity is shrinking, and conservative Christianity is growing. He cites statistics showing the Southern Baptist Convention has grown from 8.7 million members in 1960 to 16.4 million now. What he fails to mention is that the population of the US has grown from 179 million in 1960 to 306 million today, making that near doubling of members a little less impressive: it represents an increase from 4.86% to 5.35% of the total US population. Growth to be sure, but the raw numbers don’t tell the whole story. He also ignores data that show that as people receive more education (which one would think is a good thing), they are less likely to believe religious accounts of the world. See this Gallup poll for instance. At any rate, the popularity of Christianity doesn’t bear on whether or not it’s true.

Chapter two offers a quasi-evolutionary account of why religion is becoming more popular, but it is important to note that if this argument is correct, it doesn’t entail anything at all about the truth of the teachings of religion.

Chapter three gives what I think is a fairly accurate (if simplified) summary of some the arguments of the “New Atheists” but a consequence of trying to argue against multiple authors simultaneously is that you have to lump together people who may not all hold the same beliefs. The implication of addressing them as the New Atheists is that one can lump them together without distortion on a broad range of issues, which may or may not be true.

One example of the type of rhetoric that I think demonstrates that this book is not really a serious attempt to engage those who disagree with D’Souza can be found on page 31, where he says that “the Christian villain, Satan, has now become the atheist hero.” I get his point, that Milton’s portrayal of Satan’s refusal to accept God’s authority is like the atheist’s refusal to do so, but this is a problem on two levels. I haven’t read Milton (well, I’ve tried, but… so boring…), but presumably Satan believed in the existence of the God he was flouting, whereas the atheist does not. But more to the point here, does D’Souza really think that it is conducive to the productive exchange of ideas to tell your opponent that if he disagrees with you he loves the Devil? It’s a silly rhetorical device designed to rally the troops and give them a quotable little turn of phrase.

Chapter four is an attempt to scare Christians about the motives of atheists. Apparently atheists want to steal your children. It’s true that some writers seem to advocate educational or governmental agencies interfering with the rights of parents to control what their children are taught, but the same is true of Christians who want to mandate that creationism is taught alongside evolution in science class.

He complains that the ACLU is advocating in court on behalf of proponents of evolutionary theory but not for proponents of Boyle’s Law (34). Fair enough, but I suppose if there were an organized effort on the part of Boyle’s Law deniers to teach a religious alternative to Boyle’s Law, they might be.

He criticizes Daniel Dennett’s proposal to teach religion as a “natural phenomenon,” saying that by this Dennett means that it should be taught as if it is untrue. Dennett neither says this nor implies it. In his book “Breaking the Spell” he offers the suggestion (page 25) that courses in comparative religion should be taught in public schools in which students are introduced to the ideas of the major religions without one religion being advocated. That doesn’t have anything to do with any of those religions being true or untrue.

D’Souza also seems to think there is a sneaky cabal of literature professors trying to destroy western civilization on college campuses. There are certainly some people who think that religions are all false, and want other people to believe that way, and some of those people are university professors, but he doesn’t offer any evidence that there is a widespread abuse of authority or belief coercion being practiced in universities. He offers up a few quotes from a couple of professors indicating that they think that they should try to dissuade students from holding their parents beliefs, and an uncited quotation from a “champion of agnosticism” to the effect that atheists try to get college students to have sex in order to break them of their religious beliefs (38). I’m inclined to view this quotation as a fabrication, if for no other reason than the fact that nobody has to encourage college students to have sex with each other.

Universal, not Universal

In an effort to start my blog by jumping right into a hot topic everybody is talking about, I’ve decided to write about two conflicting twenty year old solutions to a logical difficulty in a 2400 year old book.

The problem is this: in Aristotle’s Metaphysics vii, Aristotle says things that lead one to the logical conclusion that substance is a universal, then turns around and claims in vii.13 that substance is not a universal.

Daniel Graham (1987) and Frank Lewis (1991) offer different solutions to this problem, which I think are interesting in a couple of regards.

Graham’s identification of the problem is part of his thesis that the ontological framework of the early work of Aristotle in the Organon is “incommensurable” with the ontology of the later works (he calls the two “systems” S1 and S2 respectively).

Here’s how Graham sees the problem. After arguing that species is essence which is form which is substance, and despite the fact that his conception of form and essence require that those be universals, Aristotle argues in vii.13 that universals cannot be substance (Graham 1987: 252). He applies the substance criteria to the concept of the universal, and determines that the universal is ruled out as potential candidate for substance (Graham 1987: 253). Aristotle recognizes this difficulty at 1039a14-23 (Graham 1987: 254).

Graham argues that at this juncture in Aristotle’s argument it would make sense for the philosopher to jettison the requirement that substance cannot be a universal, but instead Aristotle argues the opposite (Graham 1987: 255). Graham’s diagnosis of the source of the contradiction of substance as universal and not universal is that the requirement that substance not be universal is an out of place holdover from S1­, which has no grounding in the S2 ontology (Graham 1987: 261). Graham takes this as support for his Two Systems Hypothesis.

Lewis seems to express broad agreement with Graham on the nature of the consistency problems of Metaphysics vii, but views the problem as resolvable internally, using the conceptual resources of the Metaphysics itself.

The problem as Lewis sees it is the following (310-11):

For primary substance, Aristotle is committed to the thesis that for any x, if x is a substance then x is not a universal, or, formally:

(x)(Substance (x) → ~Universal (x))

But Aristotle is also committed to:

(x)(Form (x) →Species (x))
(x)(Species(x) → Universal (x))

And therefore he must hold that (x)(Form (x) →Universal (x)) by transitivity and modus ponens.

But given that Aristotle also holds that (x)(Substance (x) → Form (x)), he must hold that (x)(Substance (x) → Universal (x)).

So we have a contradiction. A logical consequence of his views on form, species and universals requires that substance be a universal, but his explicit view is that substance cannot be universal.

Graham contends that this contradiction is irresolvable, and that Aristotle’s problem is generated by carrying over the “non-universal” criterion for primary substance from the S1 ontology to the S2 ontology, and that the solution would be to discard this assumption. Lewis’s solution to this contradiction, by contrast, is one that offers Aristotle a way out by modification of the way substance is predicated. Instead of being a one-place predicate, whereby some x is a substance simpliciter, in Lewis’s view the terms “substance” and “universal” come to stand for two-place, relations in the Metaphysics ontology. Substance is “substance-of” and universal is “universal-to”. Something can be universally predicated of another only if it is not the substance-of that very same thing.

Formally this is expressible as

(x)(Universal-to(x, y) → ~Substance-of (x, y))

Thus a form can be universal-to a particular bit of matter, so that, Universal-to(F, m); in this case the form would not be the substance of the matter, but would instead be the substance of a compound particular, c so that Substance-of (F, c). In this way, Aristotle can avoid the contradiction by saying the non-universal requirement is simply modified as relations of forms to different entities. Since the compound is not identical to the matter, the form Man could be the substance of Socrates, and predicated of (universal to) Socrates’ matter.

The solution is appealing, since it would allow us to avoid attributing what would appear to be an egregious and obvious contradiction to Aristotle, but it does have the consequence of eliminating the prospect of being able to fully reconcile the ontological framework of the early metaphysics of the Categories with the later ontology of the Metaphysics. In the earlier work, Aristotle allowed as primary substances only those entities that become hylomorphic compounds in the later work; it is particular men or horses that have primary claim to substance-hood, but in the later work, those entities have something which is more primary predicated of them as the “substance-of” them. So it seems that even Lewis’ solution is at least potentially supportive of Graham’s hypothesis.

One curious aspect of this solution, however, is that if the substance-of relation is to be considered as a distinct metaphysical relation, then if F is the substance-of something, then it is the substance-of something of which F is itself already a component. I have difficulty making sense of this. Normally we think of relations as between two distinct things (with the exception of the identity relation) so I’m unclear how this relation should be conceived.