Aristotle begins his Metaphysics by saying something about human nature, “All men by nature desire to know” (Met. A, 980b22). If it is by our nature, we might be so bold as to count it among our essential properties. But, what does it mean to “desire”? And in particular, what does it mean to desire knowledge? Socrates provides the following account of “desire” in Plato’s Symposium:
Then this is what it is to love something which is not at hand, which the lover does not have: it is to desire the preservation of what he now has in time to come, so that he will have it then… So such a man or anyone else who has a desire desires what is not at hand and not present, what he does not have, and what he is not, and that of which he is in need; for such are the objects of desire and love… (Symposium 200d-e).
If this is so, to desire knowledge is to love something that is not at hand. It is to want and to keep knowledge. This also means that to have and to hold knowledge satisfies the desire for it. Such a situation is reflected in a quote that I saw posted on the blog of a friend and colleague. The quote is from an article by Lorraine Daston. The quote is as follows:
Therein lies the paradox of wonder: it is the beginning of inquiry (Descartes remarks that people deficient in wonder “are ordinarily quite ignorant”), but the end of inquiry also puts an end to wonder. The marvel that stopped us in our tracks—an aurora borealis, cognate words in languages separated by continents and centuries, the peacock’s tail—becomes only an apparent marvel once explained. Aesthetic appreciation may linger (it is no accident that the vernacular descendants of the Latin word for wonder, admiratio, convey esteem), but composure has returned. We are delighted but no longer discombobulated; what was once an earthquake of the soul is subdued into an agreeable frisson. At least within the classical philosophical tradition, from Aristotle to Descartes (and arguably beyond, to Adam Smith and even to Kant), this negative correlation between wonder and explanation is strong and tenacious. Explanation lies at the heart of the distinction between marvels and miracles in the Latin Christian tradition. What is the difference? Thomas Aquinas answers: marvels (mirabilia) are inexplicable to most but not all people (e.g. the eclipse that transfixes the ignorant peasant but not the learned astronomer); miracles (miracula) are inexplicable to everyone. Wonder is a barometer of ignorance: the learned experience it rarely; God, never. Wonder is not only a peculiarly human passion; it is also one that, at least on this account, underscores the limits of human knowledge. The more we know, the less we wonder.
Daston’s thesis is actually moves in quite the opposite. She holds that our understanding of “wonder” has evolved and adapted such that wonder is not snuffed out by knowledge, but is generated by knowledge. Not to disregard her thesis, but I do want to consider this more ancient notion of wonder for a moment. As Aristotle tells us that:
…it is owing to their wonder that men both now being and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g. about the phenomena of the moon and those of the sun and the stars, and about the genesis of the universe. And a man who is puzzled and wonders thinks himself ignorant (whence even the lover of myth is in a sense a lover of wisdom, for myth is composed of wonders); therefore since they philosophized in order to escape from ignorance, evidently they were pursuing science in order to know, and not for any utilitarian end (Met. A, 982b11-22).
Now if naturalism is true, then the world may be filled with marvels, perhaps very inexplicable marvels like consciousness, but it is not filled with that which is, in principle, inexplicable for us. This does not mean that, on naturalism, reality could ever be fully disenchanted. There seems to be practical limitations that would prevent us from explaining everything. At the same time, it does mean that the relationship between reality and our minds is such that it is merely accidental that we have the desire to know. We could, in principle, uncover all of the marvels that exist and satisfy this desire. In snuffing it out, the desire would cease to exist in us. So actually having the desire for knowledge would be accidental if everything in existence were knowable for us. But, if the actuality of desiring knowledge is an essential feature of the human intellect, then there must be some sense in which, in principle, reality is not fully knowable or explicable. This would be true if there were true supernatural miracles and mysteries. The argument would be as follows:
1. All humans actually desire knowledge essentially. [Premise]
2. If naturalism is true, then the actuality of human desire for knowledge is accidental. [Premise]
3. If the actuality of human desire for knowledge is accidental, then it is not the case that all humans actually desire knowledge essentially. [Premise]
4. Therefore, it is not the case that naturalism is true.
Now there are a few ways the naturalist could object:
Objection 1: Though naturalism is true, there are some natural mysteries that are unknowable, intractable, or inexplicable in principle. For instance, we may not be able to know or understand why there is something rather than nothing. We might not be able to know if there is a multiverse, or what occurred before the big bang. We might not be able to explain consciousness. We might not be able to fully explain those soft sciences that involve human behavior (owing to human freedom, or chaos, or indeterminism).
Reply to 1: It seems to me that if there are per se mysterious features of reality, there is no reason to be a naturalist. I take naturalism to be the claim that all of reality can be accounted for by the natural sciences. If certain aspects of reality are not merely really difficult to account for by natural scientific methodology, but intrinsically and essentially beyond the scope of the natural sciences, then I would say that metaphysical naturalism is a failure (or just a vacuous metaphysical position).
Objection 2: One could bite the bullet and say that humans don’t actually desire knowledge in an essential way. It is merely an accidental property of our mental constitution. Perhaps the capacity to desire knowledge is essential to humans, but not the actuality.
Reply to 2: This seems like a more powerful objection than the first. Humans satisfy desires all the time. In fact, there is a famous argument from desire put forth by C.S. Lewis, which argues that all natural desires have an object in reality that can satisfy their desires. So it might seem that the existence of the humanly unknowable or inexplicable contradicts this premise. However, the argument from desire does not hold that all desires are satisfied. The hungry child who is a victim of famine may never get the food that satisfies her, though such food exists. There may be knowledge that exists, say in the mind of an omniscient God, that we desire, but can never possess (due to our natural limitations). So the fact that we cannot completely satisfy our desire for knowledge, and that all natural desires have corresponding objects, does not mean that there is nothing to know when it comes to the truly miraculous or mysterious.
Now one might say that nothing really is truly miraculous or mysterious. We can, in principle, explain everything naturally, we are just limited by time and other pressing needs. And one might even be willing to grant that humans possess the capacity to desire wisdom in an essential way (the potential/power to desire knowledge), but that capacity can be fulfilled in the following way: we actually desire knowledge when we are actually ignorant and potentially in a state of knowledge. When we change to a state of potentially desiring knowledge, we are actually in a state of knowledge and are potentially ignorant. We could, in principle, be in a state of potentially desiring all knowledge, if we can be in a state of actually knowing all things (potentially ignorant). So this objection amounts to the claim that we humans have the capacity for omniscience essentially (perhaps as a collective and through various mediums of storing knowledge).
I find this response too strong. I don’t think any naturalist would want to hold it either. Ultimately, I think the idea that humans will always be in some actual state of desire for knowledge rests on a certain intuition about the relationship between the human capacity for knowledge and the way reality is. My intuition is that not everything can be known by us. And this, to me, stands in the way of metaphysical naturalism. For what else is the naturalist claiming than that reality falls completely under the genus “natural”. And so reality can be completely defined and comprehended by our intellects. If this is not the naturalist’s claim, then I am not sure what naturalism is supposed to be (at times I suspect it really is just the denial of souls and God, but that is not a positive metaphysical position).
One might point out that we don’t always actually desire knowledge (small babies, the sleeping, etc.). Furthermore, some desire knowledge more than others. Doesn’t this indicate that, while the capacity to desire knowledge may be essential, the actuality of that desire can change and is accidental to our circumstances and personal dispositions. A response might be to consider Aristotle’s musical man. In a sense, one can argue that all humans, sleeping, and even the very young, have a natural desire to know is a first actuality insofar as one has an intellect that is always deprived of knowledge that it desires to have. The second actuality might be something like the active awareness of that desire, which motivates one’s investigations. Even the very young explore their world with their eyes, hands, and mouth. So, I don’t think it is the case that even the very young escape this state.
Ex-apologist presents an interesting argument against a form of classical theism that includes a classical view of creation: classical theismcvc (click here to read the original article). The argument is based on what he calls the principle of material causality, or PMC, which features in the first premise of his argument. The second premise states an implication of classical theismcvc and shows that one cannot hold to the PMC and to classical theismcvc at the same time, i.e. the two are inconsistent. Since one has good reason to hold to the PMC, classical theismcvc must be abandoned, so the argument goes. Ex-apologists formulates it this way:
1. All concrete objects that have an originating or sustaining cause have a material cause of their existence.
2. If classical theismcvc is true, then the universe is a concrete object that has an originating or sustaining cause without a material cause of its existence.
3. Therefore, classical theismcvc is false. 
The argument is essentially valid, so the question of soundness comes down to the truth of the premises. In this critique, I will explore the notion of the principle of material causality, PMC, and show why, with a more precise notion of PMC in place, the argument cannot be successful. But first we must understand what ex-apologist means by a few of his terms.
Classical Theism: “…the view that there is a personal god who is omnipotent, omniscient, and morally perfect.”
The Classical View of Creation: “the view that consists in the following three theses: (i) God is wholly distinct from the natural world; (ii) God is the originating or sustaining cause of the natural world; and (iii) God created the natural world ex nihilo.”
Originating cause: “…an efficient cause of the temporal beginning of a thing’s existence…”
Sustaining cause: “…an efficient cause of a thing’s continued existence.”
Matter cause: “…the things or stuff from which another thing is made…” [Note: Ex-apologist’s (1), his PMC, is restricted to concrete objects that have either a sustaining or originating cause. So no question is begged against God, since God is typically held to be uncaused. Also, though it is not explicitly stated, I take creation ex nihilo to be defined as the causation of something without pre-existing matter]
First, something more should be said about what “universe” means, so as to avoid equivocation. With contemporary talk of multiverses, the word “universe” has been relegated to mean this particular spatio-temporal expanse. There may be parent universes that have generated our own universe along with countless sister universes. Of course, classical theismcvc claims that God has created and sustains the whole natural world, which would include the multiverse and any other natural thing beyond or outside of that. So the argument should avoid talk of the universe and instead just speak of the “natural world” as that which includes the totality of nature, whatever that was, is, or may be.
Ex-apologist uses a disjunction to say that God is the originating OR sustaining cause of the natural world. Now, some theists might object and say that God is both the originating AND the sustaining cause of the natural world. However, I think he is quite right to insist upon the disjunction. The idea of a “first cause” is not necessarily the same as an “originating cause”, which implies that the effect has a temporal beginning or begins to exist. When, for instance, Aquinas calls God the “first cause,” he does not mean to imply that God preceded the existence of the universe in time. In fact, as an Aristotelian, he thought that the best science of his day indicated that the universe could very well be past eternal (see SCG II.33 and SCG II.38). Instead of thinking that God is temporally first in efficient causal priority, Aquinas thought God, who transcends time altogether, had priority or primacy as a causal explanation of everything, i.e. there is nothing beyond or beside God in the causal series out of which the universe is created. This is not to say that God can use secondary causes, but they are not “beside” God in the sense that they are uncaused and per se necessary. God is pure actuality, and He explains the actuality of all other things. I suspect that this is why ex-apologist is making use of the disjunction “originating or sustaining cause.” For, the universe need not be finite in the past for classical theismcvc to be true, and historically speaking, many proponents of classical theismcvc explicitly embraced the possibility that the natural world or cosmos lacked an originating cause.
Let us consider the principle of material causation more closely and whether it is genuinely inconsistent with creation ex nihilo. Now, as I have said, the doctrine of creation ex nihilo is the claim that God caused the natural world without using pre-existing matter. But this does not mean that the natural world lacks material causality at any moment when it exists. Suppose there were a possible world where God creates, ex nihilo, a singular bronze sphere. Would the principle of material causation hold for this sphere? Yes. The sphere is materially caused by the bronze from which it is composed. The Aristotelian would not say that the sphere lacks a material cause merely because it wasn’t created from pre-existing bronze, or pre-existing copper and tin. Rather, the Aristotelian would say that a material cause did not precede the effect in time. That is, God did not use bronze or the components of bronze that existed prior to His willing the brazen sphere’s existence. In fact, even if the sphere were eternal, we could say that God creates the brazen sphere from no pre-existing matter even though bronze is the matter that “sustains” the sphere in existence as a secondary cause. Thus the brazen sphere is created ex nihilo and has a material cause. Likewise, the natural world could have a material cause at any moment it exists while not coming to be from pre-existing matter.
So what is going on here? How can some object be created ex nihilo and have a material cause? We need to make a parallel distinction to the one we find in efficient causality between originating and sustaining such that there can be an originating material cause for a thing and a sustaining material cause. We can define an originating material cause as the pre-existing matter out of which a concrete object begins to exist (e.g. the unformed bronze, or copper and tin). We can define a sustaining material cause as the matter that composes concrete object at all times that the concrete object continues to exist (e.g. the bronze currently in the sphere while it is existing). As the sphere and the bronze from which it is composed simultaneously exist as an effect of God’s will, the brazen sphere exists ex nihilo, from no pre-existing matter. Now, one might object by saying that this is not “creation” since creation must involve motion or change out of which something comes to be. This would be contrary, however, to what Aquinas argues in, for instance, the Summa Contra Gentiles II.17 where he specifically denies that creation involves motion or change. For Aquinas, genuine creation is not merely changing one thing into another, but the very actualization of substance itself. Creation is just what one calls the relationship between the first cause, God, and his effects, i.e. the creation of non-divine substance. Anything actualized by God, i.e. the being of pure actuality, is a created thing. So, for Aquinas, creation ex nihilo merely follows from the notion that God is the uncaused cause of all other things. It should also be noted that matter, the underlying stuff, is always a composite of act and potency. Consequently, on the Aristotelian-Thomistic metaphysical view, there simply cannot be uncaused or uncreated matter that co-exists with God from which other things are made. For such matter would have to receive its actuality from another, and so it must have a caused if it exists—a cause that will somehow trace back to the Being of Pure Actuality. Admittedly this is the Aristotelian-Thomistic notion of matter, and perhaps ex-apologist would like to distance himself from such an understanding of matter towards a more modern notion of matter as pure extended stuff. Perhaps pure extension can exist uncaused along with God. It is less clear whether standard particle theory, which seems to comport better with hylomorphism than early modern notions of matter, can be uncaused or self-actualizing. Either way, I think more needs to be said about what matter actually is.
Now consider ex-apologist’s argument and the disjunctions involved therein. Those disjunctions will prove important to this discussion. We may grant that a concrete object that has an originating OR sustaining [efficient] cause has a material cause, but for ex-apologist’s argument to work, there must always be an originating material cause. Otherwise, one might escape his argument through the following formulation, PCM’:
(4) All concrete objects that have an originating or sustaining efficient cause have an originating or sustaining material cause of their existence.
This reformulation will not force the falsity of classical theismcvc because it need not be the case that the universe has an originating material case. So:
(5) If classical theismcvc is true, then the natural world is a concrete object that has an originating or sustaining efficient cause and not an originating material cause of its existence.
(6) Therefore, if classical theismcvc is true, the natural world has a sustaining material cause of its existence.
Many classical theists will want to reject the notion that all of creation is material, but the thesis isn’t explicitly contrary to classical theismcvc, as ex-apologist defines it. So, the conclusion is consistent with classical theismcvc. To avoid this escape, ex-apologist will have to say that all concrete objects that have an originating or sustaining efficient cause, must have an originating material cause of their existence. This means that he must have an even stronger PMC’’ which states:
(7) All concrete objects that have an originating or sustaining efficient cause have an originating material cause of their existence.
From this, he can argue:
(8) If classical theismcvc is true, then the natural world is a concrete object that has an originating or sustaining efficient cause and not an originating material cause of its existence.
(9) Therefore, classical theismcvc is false.
Now PMC’’, as found in (7), seems a bit odd in that it maintains the disjunction with respect to efficient causality as though something could have an originating material cause (be composed from pre-existing unformed matter) simply because it has a sustaining efficient cause. Return to our possible world of the brazen sphere for a moment. Suppose God, or some other efficient cause, sustained the matter in the appropriate configuration for all eternity. Such a sphere would have a sustaining efficient cause but no originating material out of which the composite concrete object comes to be. This scenario has, at least, prima facie plausibility. So I see no good reason to suppose that a sufficient condition of having originating matter is for a concrete object to have a sustaining efficient cause. If something is eternal and sustained in existence (i.e. it has a sustaining efficient cause and no originating efficient cause), there is no good reason to think it came to be from pre-existing matter, and there is good reason to think that it would be incoherent to suppose it could have an originating material cause. Given that, (7) appears to be a false principle, and we should clarify our principle of material causality once again to PMC’’’:
10) All concrete objects that have an originating efficient cause have an originating material cause of their existence.
From here, one could argue:
11) If classical theismcvc is true, then the natural world is a concrete object that has an originating efficient cause and not an originating material cause of its existence.
(12) Therefore, classical theismcvc is false.
The problem, of course, is that (11) is too strong. Classical theism does not depend upon there being an originating efficient cause of the universe, just that there must be a first cause in order of explanation that could be either originating or sustaining. The universe need not have a temporal beginning at all. So it seems to me that ex-apologist needs argue, independently of whatever classical theismcvc may imply about the natural world, to say that it indeed has originating causes:
(13) All concrete objects that have an originating efficient cause have an originating material cause of their existence.
(14) The natural world has an originating efficient cause.
(15) If classical theismcvc is true, then the natural world does not have an originating material cause of its existence.
(16) Therefore, classical theismcvc is false.
Now what could be said of this argument? One might object to (13). Ex-apologist anticipates a rejection of his PMC via quantum mechanics or libertarian free will. I am not certain that his discussion is successful with respect to libertarian freewill, since he suggests that since an agent’s free will is caused by energy from outside of the natural causal order, freely willed choice is not genuinely caused ex nihilo. According to ex-apologist, the story would be that energy from outside the natural causal order was part of the causal explanation of the will, and so the choice would not be genuinely ex nihilo. It’s not clear to me that such an event would not be ex nihilo because of some supernatural energy. I am not sure what this energy would be, but it is not clear that it is equivalent to or convertible with matter in any sense of the term, or that a free will choice is somehow composed from this pre-existing supernatural energy. And it seems to me that if this point is pushed too hard, determinism threatens. For if this supernatural energy is the something like the “pre-existing matter” out of which an agent’s choices emerges, then even if our choices are inexplicable within the natural causal order (since it is not closed), it may be explicable and determined within the supernatural causal order and determined there within. The libertarian must maintain that alternative choice is possible, and so whatever this supernatural energy is, it cannot be determining things in the way pre-existing matter/energy determines things within the natural causal order. So it is a disanalogous energy.
I would think that a more straightforward defeater for (13) would be the creation of immaterial souls or intellects. There are plausible arguments for the immateriality of the soul or part of the soul, and those arguments would have to be addressed by ex-apologist if his argument is to have any merit. My personal favorite is James Ross’s argument for the immateriality of thought (which I have blogged about here), though there are many other such arguments. Ross says that physical and material process are indeterminate, and so do not perfectly align with truth-preserving determinate processes such as we find in the intellect’s formal and deductive rational processes. He concludes that these intellectual processes cannot be material processes. If so, these processes are concrete and also have originating efficient causes in the agent. Insofar as they are immaterial, they lack a material cause in their origination, and they are not sustained by matter. Rather, hylomorphicists, like me, argue that the originating causes are formal and efficient rather than material.
With respect to (14), ex-apologist will have to sustain an enormous burden of proof. For this is not merely the claim that the universe began to exist at some finite point in the past, but that the whole of nature, itself, is a concrete object that began to exist at some point, and so came from pre-existing matter. What’s more, if the totality of nature was composed from pre-existing matter, then that matter would have to be, by definition, beyond that which is within the scope of the natural world, and so would be supernatural. This is, of course, problematic for any sensible definition of “natural” since matter has always been taken to be a prime example of that which is natural. Of course we need to pin down what “natural” and “material” mean to consider whether it is even coherent to talk about supernatural matter. Moreover, natural material things would have to be ultimately composed out of whatever this supernatural matter is. And since other things begin to exist out of this matter, all concreta that begins to exist would have to be ultimately composed out of this supernatural stuff. Also, there would have to be a supernatural efficient cause of the universe, to maintain this argument—some sort of demiurge. This is a very untoward consequence of attempting to sustain (13) and (14), as it would be a defeater for naturalism as much as it would be a defeater for classical theismcvc. In other words, in using (13)-(15) to defeat classical theismcvc, one is, in effect, arguing in favor of the sort of cosmogony one finds in Plato’s Timaeus. I doubt that ex-apologist wants to defend the notion that there is a demiurge who fashions the natural world out of supernatural matter.
Summary: many classical theists would reject (13) on the grounds that the soul or part of the soul begins to exist, but lacks a material cause. Those arguments should not be ignored. Furthermore, classical theismcvc is neutral with respect to (14), so it is a premise that ex-apologist would need to justify independently. The ultimate problem is that (13) and (14), taken together, would undercut naturalism as much as classical theismcvc and lead to the absurd conclusion that the natural world is made out of some spooky supernatural “stuff”. I doubt any naturalist would want to defend (14) on its own merits, and it would be unfair to saddle the classical theist with defending (14), though there are some theists who seem keen on the idea of a finite past (I’m looking at you, Dr. Craig). It is for these reasons that I do not think a successful argument against classical theism from material causality can be had.
Ultimately the PMC is not incompatible with creation ex nihilo. At best, creation ex nihilo is incompatible with the notion that all concreta which has an originating efficient cause has an originating material cause, but only if it is assumed that the natural world has an originating efficient cause. Does the natural world have an originating cause? I’m not sure we can know. If it does have one, I am not sure that it is so much better to posit that it came to be from a demiurge and supernatural matter than from God ex nihilo.
 All quotes taken from Ex-apologist (2014, December, 04) “Theism and Material Causality”. Retrieved from http://exapologist.blogspot.com.es/2014/12/theism-and-material-causality.html
Whenever I discuss the ontological argument with my atheistic friends, I find that they always get hung up on the same word, “greater”. They want to infuse it with moral or aesthetic meaning, and so suspect that it is subjectively defined. They don’t think there is any objective way to determine that one thing is ontologically greater than another (a flea is no greater than a child and the fact that you would swat one and not the other is just based on speciesist opinions). Indeed, to fully explain what Anselm meant by the definition, we would have to develop the neo-platonic notion of the Great Chain of Being, which is far more central to the argument than most contemporary philosophers of religion realize. Nonetheless, that requires some metaphysical assumptions from which many atheists will shy away. I want to sidestep that whole discussion by using something other than “greater.” My proposal is to run the ontological argument on a “more actual” relation. I think you can still derive the traditional divine attributes from this term, but it doesn’t suffer from seeming subjective (what is more actual is an objective question). Nonetheless, understanding what is meant by “actual” will require some metaphysics. When discussing proofs for God, metaphysics is inescapable.
What do I mean by “more actual”? I am appealing to the distinction between act and potency in the Aristotelian-Thomistic sense of the word. For Thomas, God is the only being that is purely actual. This is because God’s essence is His existence. God is “I am”. The distinction between act and potency is an important one in the history of philosophy. It is that distinction, which allowed Aristotle to provide a response to the Eleatics, who denied change. The Eleatics argued that change was impossible because it would have to involve being arising from non-being. Since nothing comes from nothing, change cannot arise from non-being. Instead, Aristotle said that change occurs when a potential is actualized. So, a seed can become a plant because it is potentially a plant. And it undergoes that change when it is acted upon by actual things like water, soil, heat, etc. We see change happen all around us, and it is rooted in the nature of things. For instance, I am potentially bald, a potential that I am slowly actualizing with every lost hair follicle. So, while act and potency are metaphysical concepts, they are fairly close to our commonsense. The log is potentially fire, smoke, and ash. The log is actually hard and damp.
An ontological argument that exploits the notion of actuality is a bit odd and perhaps shocking for my Thomistic friends. It is commonly thought that Thomas Aquinas did not accept the soundness of such arguments, a point that I am not going to discuss here. Nonetheless, I think the premises of such an argument could be defended. The argument would run like this:
1. God is that than which none more actual can be conceived (definition).
2. If God exists only in the mind, something more actual than God can be conceived (premise).
3. If something more actual than God can be conceived, something more actual than God can be conceived (tautology).
4. If something more actual than God can be conceived, something more actual than ‘that which none more actual can be conceived’ can be conceived (from 1 and 3).
5. Nothing more actual than ‘that which none more actual can be conceived’ can be conceived (premise).
6. Therefore, it is not the case that God exists only in the mind (from 2,4,5).
7. If it isn’t the case that something exists only in the mind, then it exists in reality (premise).
8. Therefore, God exists in reality (from 6 and 7).
Now, there are a few premises and a definition. The definition, I think, is fair. Aquinas takes great pains to show that whatever is pure actuality has the divine attributes. So a being than which none more actual can be conceived would be purely actual, and so simple, a se, necessary, immutable, eternal, omnipotent, omniscient, and good.
Furthermore, I think (2) is defensible. Generally that which exists merely as a conception is less actual, in some way, than its counterpart in reality. You can’t be cut by the thought of a knife. Also, (5) seems plausible. For if something more actual than ‘that than which none more actual can be conceived’, a contradiction arises. Lastly, all that is meant in (7) is that if something doesn’t just exist in the mind, that means it exists independently of our minds, which is to say that it exists in reality. I suspect someone might say that it is a false dichotomy to insist that if something doesn’t just exist in the mind, then it must exist in reality, but I can’t think of any alternative. And if an alternative could be found, I am sure the argument could be adjusted in the relevant ways.
One last note is to consider whether this argument is susceptible to parody. I think it is less susceptible. Consider Gaunilo’s island. Could we define an island than which none more actual can be conceived? Well, every island is a composite of act and potency by nature. So no island can be maximally or purely actual. One can admit that islands that exist in reality are more actual than islands that exist in the mind, but this does not mean that ‘an island than which none more actual can be conceived’ would necessarily exist, since there is no such thing. There are, at best, islands that are more actual than other islands, but that doesn’t lead to parody.
After developing three figures of the categorical syllogism, Aristotle bombastically claims, in Prior Analytics A23:
It is clear from what has been said that the deductions in these figures are made perfect by means of the universal deductions in the first figure and are reduced to them. That every deduction without qualification can be so treated, will be clear presently, when it has been proved that every deduction is formed through one or other of these figures (40b17-22, emphasis mine).
Contrary to this, Augustus De Morgan argues that there are deductions that cannot be reduced to a syllogism.
There is another process which is often necessary, in the formation of the premises of a syllogism, involving transformation which is neither done by syllogism, nor immediately reducible to it. It is the substitution, in a compound phrase, of the name of the genus for that of the species, which the use of the name is particular (FL, p. 114).
The most notorious example is, the horse head argument (HHA): ‘horse is animal, therefore the head of a horse is the head of an animal’. I should clarify that De Morgan uses ‘man’ rather than ‘horse’ in his example, but otherwise, the argument is the same. Now, our predicate logic is quite powerful and can handle compound substitutions ably. Here is an indirect proof that seems to comport to the demands of HHA:
Hx – x is a horse
Ax – x is an animal
Cxy – x is the head of y
1. (∀x)(Hx ⊃ Ax) (premise)
2. ~(∀y)(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)] (IP)
3. (∃y)~(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)](2 QN)
4. (∃y)(∃x)~[(Hx & Cyx) ⊃ (Ax & Cyx)] (3 QN)
5. (∃x)~[(Hx & Cux) ⊃ (Ax & Cux)] (4 EI)
6. ~[(Hv & Cuv) ⊃ (Av & Cuv)] (5 EI)
7. ~[~(Hv & Cuv) ∨ (Av & Cuv)] (6 Impl)
8. ~~(Hv & Cuv) & ~(Av & Cuv) (7 DeM)
9. (Hv & Cuv) & ~(Av & Cuv) (8 DN)
10. Hv & Cuv (9 Simp)
11. Hv (10 Simp)
12. Hv ⊃ Av (1 UI)
13. Av (11, 12 MP)
14. ~(Av & Cuv) (9 Simp)
15. ~Av ∨ ~Cuv
16. ~~Av (13 DN)
17. ~Cuv (15, 16 DS)
18. Cuv (10 Simp)
19. Cuv & ~Cuv 17, 18 Conj)
20. (∀y)(∀x)[(Hx & Cyx) ⊃ (Ax & Cyx)] (2-19 IP)
So, the inference seems to be valid, given the rules of first order predicate calculus. Is it really the case, though, that a parallel proof cannot be rendered in a Categorical syllogism? A categorical syllogism has three terms, and two premises, yet the above argument has one premise, which leads directly to the conclusion. So we need to identify the terms that would operate in a syllogistic version of HHA. And we need to allow that the reduction will contain two premises.
We must be cautious in how we articulate this syllogism, as Aristotle warns:
It is not the same, either in fact or in speech, for A to belong to all of that to which B belongs, and for A to belong to all of that to all of which B belongs; for nothing prevents B from belonging to C, though not to every C: e.g. let B stand for beautiful, and C for white. If beauty belongs to something white, it is true to say that beauty belongs to that which is white; but not perhaps to everything that is white. If then A belongs to B, but not to everything of which B is predicated, then whether B belongs to every C or merely belongs to C, it is not necessary that A should belong, I do not say to every C, but even to C at all. But if A belongs to everything of which B is truly said, it will follow that A can be said of all of that of all of which B is said. If however A is said of that of all of which B may be said, nothing prevents B belonging to C, and yet A not belonging to every C or to any C at all. If then we take three terms it is clear that the expression ‘A is said of all of which B is said’ means this, ‘A is said of all the things of which B is said’. And if B is said of all of a third term, so also is A; but if B is not said of all of the third term, there is no necessity that A should be said of all of it (APr 49b14-31).
So we don’t want to say that because all horses are animals, everything that a horse has, like a head, is something that every animal has. Some animals, after all, could be headless! And what we really mean to say is that, since ‘animal’ is the genus of ‘horse’, and since a horse has a head, an animal has a head. Perhaps, then, we should formulate the argument as follows:
21. All horses are animals.
22. All horses are those that have heads.
∴23. Some of those that have heads are animals.
By making the conclusion particular, we do not run the risk of affirming that all animals have heads to the consternation of amoebas and sponges. The preceding argument is Darapti, and it is a valid syllogism, barring any objections on the grounds of existential import.1 However, it is not quite what HHA demands. Recall that we need to conclude that ‘the head of a horse is the head of an animal’, since ‘horse is animal’. To approximate the conclusion more closely, we might use repetition. Aristotle mentions the use of repetition in the syllogism, but stipulates how it is to be used. We find in Prior Analytics A38:
A term which is repeated in the propositions ought to be joined to the first extreme, not to the middle. I mean for example that if a deduction should be made proving that there is knowledge of justice, that it is good, the expression ‘that it is good’ (or ‘qua good’) should be joined to the first term. Let A stand for knowledge that it is good, B for good, C for justice. It is true to predicate A of B. For of the good there is knowledge that it is good. Also it is true to predicate B of C. For justice is identical with a good. In this way an analysis of the argument can be made (APr 49a11-18).
So, Aristotle sets down that A is ‘knowledge that it is good’, B is ‘good’, and C is ‘justice’. Formally, the proof would be:
24. AaB (Knowledge, that it is good, belongs to all good.)
25. BaC (Good belongs to all justice.)
∴ 26. AaC (Knowledge, that it is good, belongs to all justice.)
Let us set down that D is ‘animal, qua horse’, E is ‘horse’, and F is ‘head’. Still making use of Darapti, the argument would then be:
27. DaE (Animal, qua horse, belongs to all horse.)
28. FaE (Head belongs to all horse.)
∴29. DiF (Animal, qua horse, belongs to some head.)
Or, in a more readable English prose:
30. Every horse is an animal in virtue of being a horse.
31. Every horse is that which has a head.
∴32. Some of those which have heads are animals, in virtue of being horses.
Now one might protest that the conclusion reached here is particular, whereas in predicate calculus one reaches a universal conclusion. But what does that universal conclusion really say? It says that, for all things x and y, if x is a horse and y is the head of x, then x is an animal and y is the head of x. In effect, it is not saying that the head of a horse is an animal head, but that if something is a horse and it happens, also, to have a head, then it is an animal that happens to have a head. Is this the same as HHA? There is no real sense in which the deduction formed by predicate logic has anything to do with the relationship between genus and species, as De Morgan indicates. But the categorical syllogism that we have formed does have this information, in that a horse belongs to its genus in virtue of belonging to its species.
I grant that the conclusion of the categorical syllogism is syntactically divergent from HHA. Nonetheless, I think it captures a similar, if not the same, sense. Perhaps this is the best we can do.
1For those who are particularly bothered by the “existential fallacy”, we could run a similar argument on Datisi.
Aristotle. 1995. “Prior Analytics.” In The Complete Works of Aristotle: The Revised Oxford Translation. Trans. A.J. Jenkinson. Ed. J. Barnes. Vol. I. Princeton, New Jersey: Princeton University Press.
De Morgan, A. 1847. Formal Logic. London: Taylor and Walton Booksellers and Publishers.
If knowledge is something like justified true belief, then omniscience would appear to require a multitude, if not an infinity, of justifications. So one might think that omniscience is a costly hypothesis. But, here is one way to get omniscience on the cheap:
Suppose there is a subject such that this subject believed the truth, the whole truth, and nothing but the truth. Suppose, also, that this subject knew its own nature.
If the subject knew of its nature, then it would know that all beliefs it held were true. So it would have belief, p, and beliefs about why p is true, etc. If this subject knew that it only held true beliefs, then that one bit of knowledge would justify every other belief, and every belief believed to justify other beliefs. Such a being would be omniscient.
How might such a mind apprehend the fact that it believes all and only truths? If such a mind were to intellectually grasp its own nature, then it would know that it believes all truths and no falsehoods. It would be a true believer that knows it is a true believer. This is something like what Aristotle describes when he says that the Divine Mind is thought thinking itself (Metaphysics XII.9; 1074b33-34).
There have been some important updates to the SEP entry “Medieval Theories of Modality” by Simo Knuuttila. Here is an excerpt pertaining to my interests in the contemporary analysis of Aristotle:
There are several recent works on Aristotle’s modal syllogistics, but no generally accepted historical reconstruction which would make it a coherent theory. It was apparently based on various assumptions which were not fully compatible (Hintikka 1973, Striker 2009). Some commentators have been interested in finding coherent layers of the theory by explicating them in terms of Aristotle’s other views (van Rijen 1989; Patterson 1995). There are also several formal reconstructions such as Rini 2010 (modern predicate logic), Ebert and Nortmann 2007 (possible worlds semantics), various set-theoretical approaches discussed in Johnson 2004, and Malink 2006 (mereological semantics).
I’m going to take a closer look at Striker’s position, as I am not convinced that Aristotle’s modal syllogistic is based on assumptions that are “not fully compatible”. I think the issue is one of getting clear on Aristotle’s metaphysics at the time that the Prior Analytics were composed, and to realize that some of those metaphysical presuppositions did not remain constant as Aristotle went on to work on De Caelo and Metaphysics. I like Malink’s approach of using the Topics in order to understand what is going on. Perhaps a post or two dedicated to the “Two Barbaras” problem is in order!
According to David Charles, one difference between Aristotle and modern essentialists is what he calls the Existence Assumption (EA), which states:
If one understands the term ‘water’, one must therein know that the kind has instances (Charles 2000, 16).
It is the modern essentialist who believes that the determining factor of any necessary part of the sense of a term is the referent, and so knowledge of the terms instances is required even in the earliest stages of scientific investigation.
For, one cannot understand ‘water’ without knowing that water is in fact instantiated by certain specific examples (Charles 2000, 17).
Charles contrasts this with Aristotle, whom he claims rejects EA. That is, one need not have knowledge either of the instances of a kind or whether there are instances of a kind to know the sense of a term. In fact, Charles goes so far as to say that Aristotle faces a challenge, “…of showing that one can determinately grasp natural-kind terms without knowing (even derivatively) of some cases that they are instances of that kind” (Charles 2000, 18). But why think Aristotle should be burdened with such a challenge at all? Consider, for instance, the goat-stag, of which he says “…you may know what the account or the name signifies when I say goat-stag, but it is impossible to know what a goat-stag is” (Aristotle 1985, 152; Post. An. 92b4). I’ve always taken this to mean that one cannot give an essential definition to a goat-stag since it lacks a referent. One can provide a sense to the term “goat-stag”, but the resulting definition will not be anything more than a nominal definition. And Aristotle is quite clear that definition alone does a demonstration make. In other words, a definition does not necessarily provide the what-it-is of a thing, nor proves whether there is such a thing. Thus:
For definitions do not in addition make clear either that what is said is possible, or that it is that of which they say they are definitions, but it is always possible to say ‘Why?’ If, therefore, the definer proves either what a thing is or what its name signifies, then if a definition has nothing at all to do with what a thing is, it will be an account signifying the same as a name. But that is absurd. For, first, there would be definitions even of non-substances, and of things that are not–or one can signify even things that are not (Aristotle 1985, 153; Post. An. 92b23-29).
Charles picks up on this and notes that this seems to suggest that, for Aristotle, definitions are not restricted objects and kinds, but can extend to non-existents as well (Charles 2000, 28). Key to understanding Charles will be his three stages of enquiry (Charles 2000, 24):
Stage I: This stage is achieved when one knows an account of what a name or another name-like expression signifies (section [A]: 93b30-2).
Stage II: This stage is achieved when one knows that what is signified by a name or name-like expression exists (section [B]:93b32).
Stage III: This stage is achieved when one knows the essence of the object/kind signified by a name or name-like expression (section [B]: 93b32-3).
Charles offers three interpretations of Aristotle based on four questions (Charles 2000, 30):
(A) Does Aristotle accept the three-stage view? Does he think that every case of scientific enquiry involves a first stage where one need not know of the existence of the kind, but must know an account of what the name signifies?
(B) Are any Stage I accounts identical in content (in Aristotle’s view) with any definition of a kind?
(C) Does Aristotle think that if one grasps an account which is in fact definitional one knows that it is so? Is the definitional nature of that account transparent to the person who grasps it?
(D) Are all accounts of what names signify regarded by Aristotle as definitional in some way?
Defending what he calls the “Liberal” view, Charles answers in the affirmative to (A), (C), and (D), but denies (B). He also develops to “Restrictive Views”: Restrictive View 1 answers affirmatively to (A) and (B) , but in the negative to (C) and (D), and Restrictive View 2 answers in the affirmative to (B) and (C), but negatively to (A) and (D) (Charles 200, 30).
I am inclined to accept (A) and (D) as true. I find a progressive development of signification to be plausibly found in Aristotle, and certainly the above quotes suggest that even the goat-stag account is definitional in some way, i.e. what some may call a nominal definition.
Charles argues in favor of (C) by saying:
…[D]efinitions are accounts which reveal what something is (B.3, 91aI) and, thus, make its nature known to us (B.3, 90B16). Thus, if we grasp an account which makes known to us the nature of something, we grasp its definition. There is no more to grasping a definition than grasping a knowledge-giving/revealing account of this type. If so, there can be no case in which we grasp an account which makes a kind’s nature known to us but do not grasp its definition (Charles 2000, 30; fn14).
He entertains two ways to avoid this argument. The first is to say that we might not label a particular account a definition, but Charles thinks this is a mere semantic objection and discounts it. I think this is unduly rejected, since the issue at stake is epistemic transparency for all who grasp accounts. If semantics are sufficient to render the matter opaque, we must deny (C). The second objection is even more troubling, that we might know the nature of a thing, but not know that we know. Charles points out that Aristotle defines definitions as making things known to us (Post. An. 90b16). Definitions need not make us know that we know! However, there does seem to be a third objection that Charles appears to side-step, namely that his own argument only appears to apply to Stage II-III accounts, i.e. to accounts of extents that have natures to be revealed. But if Stage I is an account, there is no reason to think (C) would hold.
I also have some concerns about (B), and Charles notes that his entire book is fundamentally a defense of affirming (A) and denying (B)–(C) and (D) being related but not central issues. The denial of (B) seems too strong. For it suggests that no Stage I account could even happen to be identical in content with any definition of a kind. But suppose I were to come upon a magic lamp, and relate to a magical genie my Stage I account of a goat-stag saying, “Genie, I wish the content of my definition to be identical to a definition of a kind that has instances.” Surely my nearly omnipotent genie could satisfy this simple request with a quick nod and blink… that is, unless Charles is somehow equivocating on “content”, i.e. that in a Stage I account the content is somehow merely verbal, whereas the content of, say, an essential definition, has another mysterious ontological status. If that is so, then I am not really sure I am clear on what he means by “definition” and whether he is using it univocally throughout his stages.
He never labeled the position of taking (A), (B), and (D) as true, and (C) as false. And this seems to be my position, as I am struggling to accept (C). Now it seems possible that (D) is true, but that not everyone accepts (D) (as is evidenced by the two restrictive views above) and that such a person might see the definitional nature of a particular account as opaque. But it seems to me that such a person would only be so insistent if she were only to admit Stage III accounts as definitions. And one might imagine that such a person might hear a Stage III account, say from a relevant, reputable, and authoritative scientist without recognizing it as an actual Stage III account. Thus, such a person might not accept that it is definitional, even when it fits her restricted notion of what may count as definitional in fact. Take, for instance, the Young Earth Creationist (YEC) who also holds to a restricted view of Aristotle’s Prior Analytics B.8-10–a coincidence of views one might imagine is not uncommon among the home-schooled. She grasps the definition of some missing link between humans and the great apes, but may deny that there were any such instances. The YEC might be able to recite the “definition” with the same precision as the Darwinian scientist, though it is the scientist’s “definition”, not hers. The YEC thinks homo heidelbergensis is none more real than the goat-stag. And so Charles’ argument in defense of (C) would fail on the YEC, since the YEC is unaware of any revealing nature of the homo heidelbergensis by which she might be made aware that she grasps a definition and knows it to be definitional. And while I may affirm (D), that both the YEC and the scientist use the name “homo heidelbergensis” definitionally, our YEC denies (D) on the grounds, say, that an account requires instances in order to be definition. This, of course, isn’t a defeater for (D) as much as it helps explain why she might not know that she has a definitional account even when she clearly is aware that the name has a sense.
Given all of this, I am still not clear on why Aristotle is said to reject EA. For it seems that EA applies to any definitional account that rises above Stage I. It is, after all, the essentialists assumption. And it’s evident from the above quotes from Aristotle that goat-stags and other non-substances are not defined essentially–as they lack essences. EA is an assumption that only underlies Stage II-III, to put it in Charles’ terms. Others would say that, on Aristotle, chimeras can only hope for nominal definitions and those definitions carry no existential import and cannot be used in demonstration. It seems, then, that Charles may be pushing a distinction without a difference. His point seems to be that Aristotle does not require instances in definitions, so long as the definitions are non-essential. Is there a modern essentialist who would disagree with that? Would Kripke really hold that “goat-stag” rigidly designates across possible worlds?
Aristotle. 1985. “Posterior Analytics“. In The Complete Works of Aristotle, vol. I. Ed. J. Barnes. New York: Oxford University Press
Charles, D. 2000. Aristotle On Meaning and Essence. New York: Oxford University Press