Fourth Way

What is greater or less in the genus of quantity is not more perfect since it arises from the matter. What is greater or lesser in virtual quantity arises from form and therefore always has a paradigm, i.e. maximal perfection. For virtual quantity in a genus (i.e. quality) this form is a paradigm within nature or imagination, and like all things in nature (or a genus) it need not exist. For virtual quantities transcending a genus the paradigm is outside of nature and therefore exists necessarily.


The Fourth Way

The first axiom in Leibniz’s DM is

[T]hose forms or natures which are not susceptible of [perfection] to the highest degree, say the nature of numbers or of figures, do not permit of perfection.

Said another way, what is greater or lesser so as not have a greatest is not greater by being more perfect.

Contrapositively, we get the first premise of the Fourth Way, that whenever something is more or less great by being more perfect, there is something most perfect.  Leibniz doesn’t bother to point out that some things are, in fact, more or less perfect than others though STA does, but given this there exists some maximally perfect being.

The Fourth Way, fire, and entropy

The Fourth Way makes the claim that because things are more or less hot there is something maximally hot. This was based on STA’s idea that fire was a chemical released by burning, meaning that a campfire took fire out of logs just like a still takes alcohol out of fermented things. His example was incorrect but the principle remains as a valuable though unarticulated postulate for chemists, which is assumed in their long list of separation processes. If we wanted to update the fire example we could do so with any property of pure substances: e.g. given that some drinks are more and less intoxicating, there is something maximally intoxicating.

Digging deeper in the Fourth Way one finds STA’s reliance on the idea that every act communicates itself so far as possible. “Communicates” is a transliteration, not a translation – what he means by the term is the complementary description to participation. Participation is the dependence of a part on something that it common, the way players participate on teams or interlocutors participate in discussions. This generalizes to the fact that matter participates in form, and then further generalizes to potency participating in act. The reverse activity from act to potency is what STA calls communicatio, though there is no corresponding technical term in English.*

So why STA was wrong about fire being a chemical existing in either a pure or mixed state, he was right that heat is an act of some potency, and that this act communicates itself or diffuses itself as far as possible. The communicatio of heat is familiar from the phenomena that we label entropy, though we give an accidental description of it as a tendency to disorder. Nothing about the phenomena changes if you view nature as diffusive self-giving or dissipating tendency to disorder, but these are completely different views of what nature is and what it is up to. Our description is equivalent to describing a car as an exhaust-making tool, or breathing as a process that seeks to make carbon dioxide.

On the communicatio account of entropy the closest analogue to the Fourth Way, ironically enough, is Sean Carroll’s argument that the cascade of entropy is necessarily infinite. Reformulated in STA’s terms, this is nothing but an application of the principle that all finite diffusions or communications of act are participants in an infinite and unlimited act. I’d agree with Carroll, of course, and he might even have a whole shelf full of models that point to the need for some time with infinite energy, but I’m pretty sure that if we took the idea seriously then, just like Aristotle did in Physics VIII, we’d find that there’s a limit to how much energy we could hope to find in any given physical system. So what if your theory demands more actuality than a physical system can provide? That’s a pretty good account of what a cosmological argument is.


*One synonym for communicatio is “diffusio” which is the term STA tends to apply to the communicatio of the good (cf. “the good is diffusive of itself”).

The source text of the Fourth Way

STA says twice in the Fourth Way that the argument is taken from Metaphysics II. The specific text is pretty clearly 993b 24. The Greek text is garbled, but STA smooths it out and gives a commentary that concludes to the existence of a separate form who is the cause of existence. For another translation, see here, paragraphs 292-5.

Whatever is called supreme among other things is so in virtue of something being caused in those others that is predicated of them univocally, in the way that fire is the cause of heat in the elements. And so since heat is said univocally of fire and the thing that is composed of elements, it follows that fire is the hottest thing.

[Aristotle] mentions univocation because sometimes an effect is not similar to its cause in a way that makes it of the same species, due to the excellence of the cause. The sun, for example, is a cause of heat in lower things, but the inferior things cannot receive the effects of the sun or of other celestial bodies so as to be one species with them, since they share in matter. Because of this we do not say that the sun is the hottest thing in the way fire is, but that the sun is something more than even what is hottest.

Truth, however, is not limited to a species but relates to all that is, and because the cause of truth is one with its effect in both name and logos, it follows that what is a cause to things derived from it, so far as they are true, is the supreme truth.

Aristotle later concludes that the principles of things that always exist, sc. the celestial bodies, are necessarily supremely true. He gives two reasons: (1) they are not “sometimes true and sometimes not” and because of this they transcend what is generable and corruptible in truth, that sometimes exist and sometimes do not. (2) Nothing is a cause of the celestial bodies else unless it is a cause of their being. And because if this something transcends even the celestial bodies both in being and truth, since even if these are incorruptible they nevertheless have a cause of being moved and even of their being, as the Philosopher explicitly says.

This has to be the case since it is necessary that all things that are composite or exist by taking part in something else reduce, as to their causes, to things which exist by definition (quae sunt per essentiam). All corporeal things are actual beings only so far as they exist by taking part in forms. So there must be some separate substance which exists by definition which is the source of corporeal substance.


Chain relatives and the Fourth Way

I’ve claimed that all the Five Ways begin with a type of chain relative, i.e. repeatable relations like “being to the left of” or “being fathered”. But what about the Fourth Way? STA seems to mention no chain relatives at all, but simply says right out of the gate that things that are more and less good, true, and dignified, etc. (GTDE) exist relative to something maximal. Nevertheless, we understand the claim better if we take it as a conclusion for a reductio ad absurdum that assumes the GTDE has no maximal but is only relatively greater and less.

Start here:

[The] bald assertion of a difference between fair and foul things, virtuous and vicious actions, offers no standard whereby to determine their difference no reason for the similarity of all fair things qua fair and for their difference from all that are foul. So long as these are only characteristics of material individuals no standard can be found, for to measure individuals against one another is to seccumb to relativism.

Harold Cherniss, The Philosophical Economy of the Theory of Ideas. 

Logically, things are either more or less GTDE only relative to each other or ultimately to something maximal. Said another way, iff we take the more and less GTDE as a chain relative where something less relates to something greater, with the greater in turn being something less relative to some greater, etc; then this either goes on without ever requiring some ultimate, or some ultimate is required. But if the first, then GTDE is arbitrary and consists in nothing more than the irrational prejudice. I stress that it is an irrational prejudice to set it apart from what we are doing when we declare something better by hypothesis, since the whole point in treating something as if it is greater in GTDE is to find out what is in fact greater, i.e. to discover some standard why things are more and less what they are. But to assume that all one ever has are chain relatives is to dogmatically rule out discovering anything that is truly better in fact, and so to deny any point of framing hypotheses about it. But it is reasonable to form hypotheses about what is more or less GTDE, and so these things must exist relative to something maximal.

This throws light on an important difference between what is more and less in mathematical and virtual quantity. Mathematical quantities are given in greater or less on some continuum or set of ordered points, say, the number line. This number line fixes what is greater or less in terms of position or direction: what is to the right is greater than what is to the left. But in order to develop the analogue to position or direction in virtual quantities we need some standard S1 different from the things which we order. If S1 is itself variable in GTDE to S2, then unless S2 is given we cannot be sure even of the “direction” we have set up for the things falling under S1. The difference between the more and less in quantity and the GTDE is that what sets the direction of the greater an less in quantity is not itself a quantity, but what sets the order of, say, goods is itself a good. This is why the order of integers need not have a greatest but the order of virtual quantities must, and why, even though things greater and less in virtual quantity are chain relatives that can have an indefinite order of things merely relatively greater and lesser, it is impossible that all virtual quantities be of this kind.

Leibniz, the Fourth Way

Leibniz’s Discourse on Metaphysics opens with a proof logically equivalent to the Fourth Way:

Whatever is more and less with no greatest possible is not more and less perfect

So (by contraposition) whatever is more and less perfect is such relative to the greatest possible perfection.

His first claim is supported by an insight into numbers, which admit of no maximum and are not better or worse by being more or less. We can hit the same conclusion by considering privations: if a threshold has to be the same width as a 30” door, there is no maximal way it can fall short of being that size, since falling 30″ short would leave one with no threshold at all. And so if anything is better and worse, there must be some greatest possible perfection.

The Augustinian tradition established that the greatest possible perfection is God. In giving a critique of idolatry, Augustine pointed out that if one could think of something better than the object they were considering, then the object they were considering was not God. So by the same contrapositive move  Leibniz made, God is the object than which nothing greater can be thought.

Fourth Way, and its real difficulty

Here’s the Fourth Way in a sentence: there are things that can only be said perfectly and precisely of a being that all recognize as God. St. Thomas lists three or four: good, true, dignity and existing, but he gestures in the direction of many more.

Mistaken or imperfect notions are used analogously to the correct or perfect. Malaria said of “A disease caused by bad swamp air” and “fever caused by a pathogenic protozoa that invades red blood cells” is used like this, as is heat when said of (the supposed element) fire, phlogiston, and mean molecular motion or “dropped the Hiroshima bomb” when said of Truman and the Enola Gay.

Imperfect or imprecise notions need not be separable from some subject and can even belong to it essentially or necessarily. While we can have malaria without swamp air or swamp air without malaria, it does not follow that we can have fire without heat or a dropping of the Hiroshima bomb without the Enola Gay (or some plane like it). But we can still have to distinguish these sorts of essential or necessary things into a primary and secondary.

Though I’m speaking of analogous uses of terms and how things are known, they are shorthand to make a metaphysical point. True, the drift of the argument is this:

Mistaken and imprecise notions are said analogously to the true one.

All notions that are separable from some subject or secondary to it are imprecise.

But the point is not to talk about how something is known but about the reality that is being said of the thing, and when considered this way it is hard not to notice that existence is said separably of any natural substance. On a substance-ontology, where everything traces back to substance and neither the universe nor matter nor forms/laws in mathematical abstraction are substance, it’s clear that natural substances exist only derivatively from a supernatural deus. But the contemporary mind has a great deal of metaphysical confusion about things like universes, physical laws and conserved quantities which makes us less able to conclude to divinity. We recognize easily that natural substance depends on something everlasting, uniform, and even abstract-intelligible but we hesitate to call it “God”.  We run the same argument on the idea of “dignity” and think it should conclude to us.


Fleshing out the Fourth Way

The Fourth Way is a general argument that God is X to a maximal degree where X is “things like” (huiusmodi) good, true, dignity, being, etc. This means that God is most of all what we mean by these things, and even though we call other things good this is only because the first things we name are not the highest instances of what deserve that name. We can show this by looking at the great number of things that the Fourth Way is talking about in particular:

1a.) Being. A being exists just as a pair is even, i.e. by definition. But while some group that is by definition even can cease to be even by ceasing to be, what by definition exists can’t cease to exist. The individual we could call a being could only be an individual whose non-existence would involve a contradiction. This is no individual in the universe (all of them have a genesis) nor the universe (which is not an individual but a collection)

2a.) True. A thing is true when it exists relative to an intellect, but a thing only exists relative to a creator.*

2b.) Power. Power is the ability to be responsible for the existence of another.


3a.) Good. A good satisfies an appetite and so the highest good satisfies the highest appetite. But everything desires to exist and all intellects desire truth, and both of these terms are divine from 1 and 2.

Corollary 1: what we seek for ourselves requires going outside ourselves. The desire to for existence  is not limited to our mere desire not to die.

Corollary 2: Here is another vantage point to see the shallowness of understanding divine goodness as “moral perfection”

3b.) Dignity. Dignity belongs to a thing so far as it is an end and not a means. But the highest good, as such, can never be a means but only an end.

3c.) Person. If the person is subordinate to a non-personal highest good then objectification, alienation and the degradation of persons are the highest good of a person. The consequent is a contradiction, therefore, etc.

1b.) Life. To live is to exist in what acts for itself. But a person acts for himself.

4.) One. One is the negation of division, but things are divisible so far as they await some further existence in space, in time, or of their intrinsic matter. But to await further being, as such, is not to be.

5.) Devotion. The limit of devotion is worship. 


Objection: Being heard does not require existence to a divine ear, so truth does not require existence to a non-divine mind.

Reponse: This illustrates the difference between the objectivity of sense and of intelligence. Sense objectivity is content to attain the thing as it is for the one sensing. Whether you’re a dung beetle or not will affect you awareness of sweet-smelling things, whether you are a polar bear or not will affect what temperature is too cold or oppressively hot. But intelligence seeks an objectivity that is just the thing itself and nothing more – the pure object unconditioned by subjectivity. But to attain this requires a pure “being seen” from no perspective, i.e. from no limited vantage point. What we mean by objectivity, and so truth, cannot involve a vantage point within the things we seek to understand.

This allows another development:

2c.) Beauty. The beauty appropriate to this sort of thing is sublimity, and the sublime is that which overwhelms the cognitive powers. But perfect objectivity totally overwhelms all created cognitive powers, therefore.


Perseity and the Fourth Way, Part III

… Aristotle develops Plato’s account of perseity as “communion” into an account of the various relationships of universality between the subject and the predicate. We can first note that some predicates are said of all instances of some subject. Such predication seems to always involve perseity, though it need not be made explicit. In looking for an explanation of malaria, for example, we might notice that all cases of malaria arise from being near swamps, but this does not mean that it getting malaria and being near swamps considered precisely as such have a per se relation to each other. We can observe, for example, that the two are connected always or as a rule without being convinced that there is any intrinsic feature of a swamp that is the direct cause of malaria.

A more fundamental relation between subject and predicate is one that exists between them in virtue of something intrinsic or per se to them. For example, we don’t just believe that fire and its heat are simply together as a rule, we are also convinced that there is something intrinsic to fire that makes this so. Again, we do not just observe cones being a third of the area of the cylinders that contain them, we also can see that it is an intrinsic feature of the cone that makes this the case. We are (perhaps) not entitled to hold that these particular convictions are indefeasible, and perhaps either one is open to being overturned by the discovery of a cold fire or a new and more complete theory of geometry, but to be mistaken about which features are intrinsic to things is not the same thing as to deny that we can come to know any intrinsic features of some subject. At the bare minimum an intrinsic feature is a heuristic that guides our explanations of things from what merely happens to be so towards what must be so.

Aristotle’s account of the per se is based on the more fundamental axiom that our explanations of what things are must start off confused and imprecise and gradually be made more complete. Malaria does not come to us with a label or tag that tells us exactly what place to look for it or how we are to consider any of the objects in that place. It might first be related to being in hot climates; and then not to a hot climate as such but to hot areas with swamps; and then not to the swampiness of the place as such but to an extrinsic feature of swamps (sc. that mosquitoes adapted to use them as ecosystems); and then not to mosquitoes as such but to the fact that mosquitoes both carry and transmit a certain parasite. Notice that, with each progressive development in our understanding, we might be relatively convinced that we have found malaria as such. We might be convinced that malaria is just a peculiar way of being weakened or broken down by heat, just as some people still believe that colds are a peculiar way of being weakened or broken down by the cold. Again, we might be convinced that malaria is just a swamp fever, or that it is caused by something either intrinsic to swamps (e.g. their brackish) or something else. Every stage in this process might be supported by evidence to the point of convincing a rational observer; but for all that, we can recognize from our comfortable perch as outside observers that we have not found malaria itself until we have found the parasite. This terminal point of the explanation is simply when we reach to what the thing is in itself, that is, when we come to get a distinct look at the thing which we first understood only nominally and in a confused way.

Notice that on this account of explanation it consists in moving from some X to an account of what X is intrinsically or in itself. Explanation does not terminate in some brute fact in the face of which we can say nothing more than “it just is that way”, but rather in moving from something that is merely named to what the thing named is in itself. The explanation does not end with a shrug that can do no more than accept that “all explanations have to stop somewhere” but with the conviction that we have actually found the thing which we had initially done no more than name. The simplest account we can give of this sense of explanation is that it consists simply in discovering what we mean. We meant something by malaria, but this initial meaning occurred in a jumble of confused facts that required a difficult process of discovery and many sophisticated theories and tools to discover that malaria itself is the name for a mosquito-borne parasite.

Because this account of explanation is based on the general fact that explanations move from the confused to the distinct, every sort of cause will admit will move from some X that is merely named to the X itself. For example, the if we witnessed the first atomic attack on Hiroshima, we would want to know who was responsible for it and so we would be looking for an explanation in the order of agent causes. Now notice that the first person we could actually see dropping the bomb would be the bombardier on the plane, though it would be pretty easy to establish that he only dropped it at the behest of the flight commander. But neither of these persons is who we are looking for when we ask who is responsible for the event, but  only the one who was responsible for all of them doing what they did, sc. Harry Truman. Likewise, if we caught the Watergate spies, they would be the first persons we knew were responsible for the break in, but they would not be the ones we are looking for when we ask who is responsible for the break in.

Just as there is a long series of diverse subordinate agents there is a corresponding series of distinct goals or final causes: the bombardier was only intending to pull a lever at the proper time while Truman had the much broader motive of terrifying his enemies into unconditional surrender. Here again, explaining a fact consists in discovering who we mean when we consider “the one responsible for this” or what motive we are looking for when we ask “why did this happen?” Truman is not a brute fact explaining why the bomb dropped, he is the one we meant to talk about from the beginning when we spoke of the one responsible for the action. Again, it is ridiculous to say that the explanation of motives “breaks down” after we discover the motive to terrify the Japanese into submission, since this would be like saying that our ability to look for something “breaks down” after we find it.

On this account of explanation, the explanans is simply “the thing itself”: e.g. malaria itself is the parasite as opposed to any other environmental feature, the one who dropped the bomb was Truman himself as opposed to any of his subordinates. Though speaking of a “thing itself” certainly suggests the familiar Platonic theory, Aristotle’s account of explanation is a complete redefinition and repudiation of it. The things themselves are not separated entities, or even forms inhabiting matter, but just the precise realities that we first target in our merely nominal and confused accounts. The trajectory of explanation is not from the facts to a form that is outside of them but from a name which we impose in the midst of a confused awareness of facts to a thing among those facts that actually deserves the name. The thing itself – or the thing per se – is not given separately from what we start with, but within what we start with, though indistinctly.

Aristotle distinguished two senses of perseity. In the first, any intrinsic connection between a subject and predicate will be a per se connection. In this sense, when we say an exothermic reaction is hot we say something per se, since it falls in the very definition of exothermic reaction that they give off heat. There is, however, a stricter sense in which it is not precisely the exothermic reaction that is hot, but only the mean molecular motion, since it is only this latter that is precisely what heat is, and it is in virtue of exothermic reactions giving rise to such motion that they are hot. Aristotle called the looser sense of the per se kath’ auto, which can be unproblematically translated as  “per se”, but he called the stricter sense katholou (or “universal” in the genitive case) which we will here call primo since this was the Medieval usage. It is this strict sense of the per se – the per se and primo – that we target when we seek to explain something, even if, for practical reasons, we are often content with explanations that fall short of this level of rigor.

The Per se and Primo in The Fourth Way


Any causal explanation targets the primo and per se, and all cosmological arguments are a causal explanations of various things manifest to sensation. We can see that the Fourth Way is appealing to this principle because it twice appeals to the Medieval theory of fire as the cause of what was hot, which the Medievals saw as the per se and primo cause of heat, in exactly the same way that we now see mean molecular motion and the per se and primo cause of heat. It is crucial that we describe the Fourth Way as reaching, for example, what is per se and primo good, true, etc. because there are all sorts of things that are per se good – virtue, charity, food, and even everything that exists – which are nevertheless not good such first. This is why it is not enough to appeal to a principle like “things that are participated reduce to things that are essential”. Just as a thing can be essentially hot without being what is hot first, so too a thing can be essentially good without being what is good first of all.[1]

St. Thomas places the principle that the causal explanations reduce to some first in at the logical beginning of his cosmological arguments, though he first applies it to the special case of a first cause of motion, saying that a series of causes cannot be infinite because: “then there would not be a first mover, and it would follow that there would be no other movers, since a second mover does not move except by the motion of the first mover, as a stick does not move unless it is moved by the hand.” [2] St. Thomas’s example is clearly from the order of efficient causes, and we saw above that the a first cause is necessary in this order since such a cause arises simply from giving a distinct account of what one means in speaking about “what is responsible for the motion”. One simply can’t mean to speak about an instrument or something with a derivative responsibility for an action when he asks about what is responsible for an action. Doing so would be like answering a child who asked “why are we driving to Church?” by saying “because I’m pointing the car towards it”. To ask the question about my what intention is responsible for the action means asking about what is responsible first of all. Any other explanation explains only in a qualified sense, and is in some way an indistinct grasp of the facts.[3] While it is true that there are all sorts of reasons why we do not press our questions to completely distinct answers – reasons ranging from practical concerns to the dimness of our intellect to the desire to restrict ourselves to a limited domain of explanation – nevertheless St. Thomas is claiming that the completely distinct answer to “what is responsible for the stick moving” is “God”.

The Fourth Way starts from no specific class of facts, but from any fact about the world which, when understood per se and primo, deserves to be called God. St. Thomas need not be seen as restricting himself only to “transcendental perfections”, as the manual Thomists have read him. The Fourth Way can, in fact, start with things given in all the other four proofs, and can reach all the conclusions they reach by its own proper way of proceeding and without appeal to any extra premises. For example, we see movers that are more and less immobile, and so there must be some mover that is immobile per se and first; we see causes that are more and less causal, so some cause must be per se and first; and we see necessary things that are more and less necessary, and thus there is something whose necessity is per se and first. If such a being is “what all call God” in the preceeding proofs, it is also in this case.

Reading the Fourth Way in this way leads to several good results, which I will here only sketch in outline:

It gives the proof scientific value, even in the contemporary sense of science. The Fourth Way, as we have continually stressed, appeals to a principle that is common in all causal explanations, not just those that are supposedly metaphysical, but also those that are scientific, or medical. We are looking for the per se and primo just as much when we are looking for the cause of malaria or diabetes[4] as we are when we are looking to establish the existence of God. This explains why this proof is uniquely concerned with proving its relation to the empirical and scientific, not only by twice appealing to the Medival account of the per se and primo cause of heat, but also by referencing De Caelo et mundo, an essentially Astronomical book.

It gives a simple and elegant account of the analogy of names from creatures to God. On our account of the per se and primo, it is the end point of an explanation that starts from something that is merely named and moves to something most deserving of the name. But this how St. Thomas divides analogous names from univocal and metaphorical names in the Summa theologiae. If, St. Thomas says, we consider the thing we impose the name on first then we will call the creature “good” or “existent”, but if we consider what the name signifies, then we see goodness and existence as belonging not to the creature but to God. Words like “good” or “existent” can be understood as naming either the things we first grasp in an indistinct and simply nominal manner, and in this sense we “mean” to indicate creatures when we speak of them. But we can never mean to indicate the indistinct and secondary as such in a causal explanation, and so in the proper sense of meaning or signification we do not signify the creature. It is precisely this double sense of meaning, arising with respect to a single word, that gives rise to the diverse proportional or analogous names that are said of God and creatures.

It can contribute to a larger dialogue about the explanatory necessity of form. Though Thomists frequently lament that the modern sciences have apparently cast out all formal and final causes, they have not yet come up with a principle actually useful to modern science that points to the explanatory power of form. But an understanding of perseity seems to be just such a principle, for it reduces causal explanations to something “in itself” or “of itself”, which have been, since Plato, unmistakable references to formal causality; and such causes become final causes as soon as we recognize the role that they play in a causal process that brings them about.


[1] This premise seems to be particularly important to preserve the real integrity and perseity of creatures, and to keep a proof for the existence of God from negating their proper existence. This problem becomes particularly acute when we consider the question of human freedom in the face of the causal power of God; though, as we have just seen, there is no problem with saying that the creature is essentially free and even autonomous, we only deny that this essential freedom is the first such essential freedom.

[2] ST Note that the principle that causal explanations reduce to some first, though it occurs temporally at the end of the argument, is logically the first premise of the argument. No other principle or truth in the argument is more general. This general conclusion about causes is presupposed in the subsequent proofs.

[3] It’s interesting to note that some explanations are explicitly targeting means, and so are targeting things that are in themselves secondary. But even when we ask these “how” questions in the order of means, we are still we are asking for something that is first. A catapult, for example, in an instrument that uses a rock as an instrument to destroy things, but if someone asks “how did we destroy the city wall” the answer is not “with rocks” but “with catapults”. If we said only the first, we would mean that the rock was our primary instrument, i.e. that we held it in hand and hammered the wall, or hurled it at the wall with our bare hands.

[4] The recent finding of the ATP/P2X7R pathway by researchers at Boston’s Children’s Hospital is simply a finding of the per se and primo cause of diabetes

Draft: Perseity and the Fourth Way, parts 1 and 2

(I noodled around with the first part and so will just post the whole thing. Apologies for the weird gaps and loss of blockquotes that come with just copying and dumping worddocs. Footnote 13 is fun.)

St. Thomas’s Fourth Way is given in a shorthand that omits all the formal accounts of the concepts being used:

In some things are more and less good, true, noble, and other such things. But more and less are said about diverse things so far as they approach in diverse ways something which is most, as what is more hot more approaches what is maximally hot. Therefore something is most true, best, and noblest, and as a consequence, maximally existing (ens).

The first difficulty is that the author gives no indication what formal characteristic he has in mind that ties together the good, true, or noble though he clearly speaks of “other such things”. Just what sort of things are we to include? Richard Dawkins has leapt on this ambiguity and parodies the argument as something that would be just as effective at proving the existence of something maximally stinky.  A second difficulty is in identifying in what sense things are more and less to the extent that they approach some maximum. Anyone reading the argument, for example, can easily see that the claim is nonsense when applied to the clearest sense of more and less, sc. in spatial magnitude, number, temporal duration, etc.. Even in the cases where physical science has been able to confirm certain maximum limits of more and less in physical quantities, these limits do not seem to followfrom an axiom about the nature of the more and less but simply from experimental confirmation that finds a maximum when it is there to find. The absolute velocity of light is not a deduction from the nature of velocity, nor is absolute zero from the mere phenomenological experience of things that were more and less warm, still less is either of them a deduction from a general axiom of the sort that St. Thomas appears to be appealing to.


The success of St. Thomas’s proof rests more on the clarification of the second difficulty than the first. Even if we cannot isolate what formal characteristic unifies goodness, truth, and dignity, we can readily admit that they admit of degrees. This leaves us only to articulate a coherent account of the supposed axiom that the more and less are always such with respect to some maximum. Our claim here is that the maximum is that which is per seand primo in the sense that Aristotle articulates in Posterior Analytics I c. 4-6. There are two grades underneath this which constitute the more and less that fall under the maximum. The first is that which is per se but not primo, and last what is neither per se nor primo.


Other Accounts of the More and Less


There are three notionally different accounts of the more and less (1.) that the more and less are combinations of act and potency and the maximum is non-composed act (2.) That the more and less are participated being and the maximum is the essential, and (3.) The more and less are things exemplified by an exterior formal cause, and the maximum is the first exemplar cause. Though we separate them for the sake of clarity most authors will appeal to more than one of these accounts, for example by identifying a non-composed act with something essential, or even weaving together all three accounts.[1]


(1) For the Thomists of the Leonine revival, there was a clear account of the more and less in terms of the relation between potency and act. Thus Grenier rests his account of the Fourth Way on the “principle of causality” that “the cause of any being composed of potency and act is a being which is not composed of potency and act.” O’Brien[2] argues that the more and less are the limited while the maximum is the unlimited, and “limitation” is understood to mean simply act’s composition with potency. Though hardly a Leonine Thomist, Owens appears to concede this an act-potency foundation to the more and less.[3] Edward Feser preserves this tradition by seeing the fundamental account of the principle of causality as being that composite acts are caused by pure or non-composite acts. All of these interpretations are in line with the first of the twenty four Thomistic theses sc. that being is entirely divided into pure act on the one hand and a composition of act and potency on the other, with the first being the cause of the second. Indeed, this interpretation of the Fourth Way can be understood as establishing the truth of the thesis.

While it is entirely possible to demonstratively prove pure actuality from the nature of composite actuality, to restrict ourselves to this interpretation of the fundamental axiom of the Fourth Way would lead to an incoherence in Thomas’s own text since, for him, whatever account we give of this principle must include the more and less hot as one of its concrete instances. All commentators agree that purely material substances are act-potency composites and there is no doubt that heat either is such a substance or is the effect of one. Attempts to wave off St. Thomas’s example are difficult to swallow and even when interpreters of the proof do not seek to minimize the relevance of the example of heat, their interpretations frequently read as though they would have been happier if St. Thomas had not tried to give this concrete example of the principle he was working from.[4]

(2) Interpreting the more an less as degrees of participated being relating to something essential can appeal to a number of very suggestive and powerful Thomistic texts, many of which are laid out by Gerrigou-Legrange[5] in his characteristically thorough devotion to the littera. Consider first De potentia 3.5:


If anything is to be found participated in various degrees by several objects, it must be that, starting with the one in which it is found in the highest degree, it is attributed to all the others in which it is found imperfectly. For those things that are predicated according to more and less, this they have by reason of their greater or less approximation to one of some kind; for if any one of these were to possess this perfection in its own right, then there is no reason why it should be found in a higher degree in the one rather than the other.


Here we have a doctrine of more and less clearly tied to a notion of participation. The very possibility of hierarchy is grounded on the idea that only the maximally such can possess the formal element of the hierarchy essentially. The basis for using the word “essentially” is from ST. q. 3. a. 4: “whatever is found in anything by participation must be caused in it by that to which it belong essentially, as iron is ignited by fire”.[6] Thus this  interpretation avoids the interpretive pitfall we saw in (1) by giving an account of how fire is a concrete example of the principle in question.

Use of “participation” language has often been taken as a proof of the Platonic character of the Fourth Way[7] and St. Thomas himself can be quoted in support of this: “all things that are diversified by participation in the more and less perfect are caused by one first being that possesses being most perfectly. Hence Plato said that unity must come before multitude.”[8] There are, however, two difficulties in this. First, using Plato as a supporting authority is not the same thing as making him the basis of one’s opinion, and St. Thomas, both here and elsewhere, seems only to be using Plato as a supporting authority. Secondly, the Fourth Way not only is the only proof that directly quotes Aristotle, but it also seems to go out of its way to establish its bona fides as empirical science. Thomas gives the empirical example of heat not once but twice during the proof, and he directly quotes from a passage in Aristotle that is attempting to prove that the sun is somehow the cause of all being. Such a robust interest in empirical science is hard to square with an account of the proof as “Platonic”, since anything deserving the name of Platonic natural science would not arise until the eighteenth century. Indeed, the impossibility of natural science seems to be the raison d’être of the doctrine of participation, which accounted for any intelligibility of the world not in terms of any immanent feature of the world but in terms of a separate world of forms. Thus, interpreting the proof as Platonic would run into the same problem we saw in (1), sc. it could not account for fire being an example of the principle St. Thomas was appealing to.

A more general problem in the participation account is that it leaves the proof itself as either false or uncertain. Applying the distinction to the proof gives us the following major premises: whatever has X by participation is being caused by what has X essentially. But whatever has X in a merely greater or less degree[9] has it by participation. The difficulty is that multiple beings can have one and the same thing essentially without being the cause of the participated reality. Thus, even if a participated being reduces to something essential, the essential itself is a multitude which turn is explained by a participation in the essential, and so on ad infinitum. St. Thomas’s example is a case in point: fire is essentially hot, but it is not the reason why all other hot things are so. The blood of a living animal (at least under normal circumstances) is essentially hot, along with exothermic reactions and the sun, but not because of any presence of fire within them. And so St. Thomas’s principle is either false, or we need to find some more subtle account of the essential which allows for an order of causality among things that have something essentially.

(3) Appeals to exemplar causality are some of the most ancient accounts of the Fourth Way. Banez gives the briefest explanation by first raising the objection that, if all things that were more an less were caused by some maximum then white would be the cause of all other colors and a man would be the cause of all other animals. Banez responds that white is the cause of other colors as a exemplar cause, because it surpasses others with respect to light, which is the formally the essence of color (formale quid respectu coloris) and because it has more light than the rest of the colors it is the measure of all of them.[10] He also claims that “the same must be said about man with respect to the rest of the animals”, but provides no further account of the matter.[11]

On of the most elegant and forceful accounts of the exemplar causality in the Fourth Way is given by Rebecca Loop in her thesis Exemplary Causality in the First Being.[12]  Her argument is as follows:


1.)    The more and less exist with respect to a standard from which they really fall short of.

2.)    It is only possible to really fall short of a standard if that standard is really possible.

3.)    In order for a standard to be really possible, and not just logically possible, it must either exist or be in the power of some agent to bring about.

4.)    Thus there is a real standard of goodness, which is not just more or less (i.e. relatively) good, which either exists or is in the power of an agent to make.

5.)    Thus, there either is a being that is absolutely good, or who can bring forth absolute goodness from its own power.

6.)    Such a being all call God.


On this account, God is a “maximal being” in the sense of being a standard by which all other things are judged, and so is the exemplar of all things that are, by definition, more or less good, true, and noble in relation to it. The proof works by translating “more and less” into “the deficient” and then appealing to the axiom that deficiency is a relation to a really possible standard. For all its simplicity, however, and in spite of the argument being to all appearances a sound one, it is clearly Leibnizian and not Thomistic, given its appeal to the principle that the possible is that which either exists or falls in the power of an agent. Without this crucial premise, we are left with a Thomistic account of exemplar causality as a form by which an agent brings forth an effect, and so the Fourth Way can only be seen as collapsing into the Second Way or as presupposing the argument of the Fifth Way. But the argument clearly cannot appeal to something proven afterwards, and it gives no indication that it presupposes an argument from efficient causality. This is all the more remarkable since, for St. Thomas, the causal principle is formally responsible for the truth of his theistic argument, and so to leave off mentioning the reality of a first agent cause would render a proof from exemplar causality unsound. If the proof is nothing but an appeal to exemplar causes, then it is simply a corollary to God’s agent causality of the world. Why would one bother to reestablish the proof ab initio from sensible data if it is a logical consequence of an earlier proof?

The appeal to exemplar causes shares in the same general problem of the previous two accounts. While all can serve as the basis of sound cosmological arguments, they fail to give an adequate account of the empirical application of the principles St. Thomas is working from in the Fourth Way. It is striking how often interpretations of the Fourth Way are belied by the text of the proof itself: it is called the most Platonic of the proofs in spite of being the only one to quote Aristotle directly, and the proof is frequently presented as purely metaphysical in spite of twice claiming it is working from principles that have physical application. Given that St. Thomas will say, later in the proof, that the more and less are things that relate to something maximal in a genus, one might even suspect that St. Thomas is starting with an explicitly empirical premise about things with a generic unity that he takes as able to be generalized to things with an analogical unity. As we will see, the ability to make this generalization is, for St. Thomas, a feature of the very logic of a scientific explanations, and so will apply first to empirical science and by extension to metaphysics.



Perseity is a logical feature of predicates in systematic accounts of a subject, one which is above all necessary in such accounts that seek to explain what some subject is, what properties it has, how it came about, or to give some other genus of cause for it. The need to articulate perseity first arose in response to sophistry, and in both Plato and Aristotle the per se is viewed as the proper opposite to sophistical predication and argumentation. In fact, the first discussion of perseity arises in Plato’s Sophist, and is used as his final and most damning account of sophistry. The argumentation of Sophist is prolix and obscure, but we can get the general sense of it as a response to an argument like this:


If two things are joined together into one class – i.e. given the same description – then they are the same.

But motion and rest, straight and curved, good and evil, etc. can each be joined in one class, sc. “being” or “lines” or “human acts”.

Therefore, motion and rest are the same, as are straight and curved, good and evil, etc.[13]


Plato’s response is that combining things in a class does not mean that any possible combination is allowed; rather, it makes them the same just so far as they are so combined and no further. Black and white can each have color predicated of them, and so far as this goes they are one and the same, but neither can be predicated of the other. In later, more formalized terminology, black is the same as white qua color but not qua black, with qua signaling the presence of what Plato called the ability for combination or communion. Plato sees the failure to discern these differing modes of communion as to live in “non-being”, and he makes this the definitive mark of the sophist.[14]

Aristotle’s develops Plato’s account of perseity as “communion” into an account of the various relationships of universality between the subject and the predicate.





[1] Del Prado, N. De veritate fundamentali philosophiae christianae Saint Paul’s, Freiburg, 1911. pp 227-232.  See also the forceful and thorough weaving together of these notions by Edward Feser in Aquinas One World, Oxford, 2009. pp 99-109

[2] O’Brien, Thomas C, Metaphysics and the Existence of God. The Thomist Press. Washington D.C. 1960.

[3] Owens, Joseph St. Thomas on the Existence of God.ed. John R. Catan. St. University of New York Press. Albany 1980 P. 136. originally published in Monist, v. 58, 1974. p. 203-215.

[4] Thus Gilson: “Thomas’s example of the more and less hot should cause no illusions. It is simply a comparison, a manuducio, to help us understand the principal thesis. Certainly the “supremely hot” is only a relative supreme degree”. Gilson Etienne, Thomism: The Philosophy of Thomas Aquinas. A translation of Le thomisme sixth edition. by Shook, L.K. and Maurer, A. Pontifical Institute of Medieval Studies, Toronto, 2002. p 136. cf. also Elders who claims that the example “is only a comparison and not an instance” or “only an example”  Philosophical Theology of Thomas Aquinas, p. 123 and 113. The claims are obscure and even baffling: certainly the point in making a comparison is to identify commonality between things compared. A thing might be only an example, but it still must exemplify the principle. Pace Gilson, to say that the supremely hot is only ‘relative’ is to undercut precisely what would allow it to be similar to the summum bonum. This is supposing that “relative supreme degree” has any coherent sense, to say nothing of having a sense that could be included in an axiom at the basis of Thomas’s proof. How, for example, would something “relatively supreme” be any different from something that was simply “more and less”?  In fairness to Elders, he does attempt to integrate the nature of fire into his account of the fourth way by pointing out its active character, which “stresses the active character of efficient causality” (p. 116 ibid). This might, however, create more problems than it solves: for what seems to be a simple proof based on the more and less in a formal characteristic is now seeing as being exemplified by an aspect of efficient causality.

[5] See The One God. Trans. Dom Bede Rose. B Herder Book Company, St. Louis. 1946. pp. 145-148 .

[6] The text is from De spiritualibus creaturis. A. 10. It should be noted that St. Thomas here appears to give an alternate proof to the Fourth Way based on the deficient character of the human intellect. Owens appeals not only to this text but also to the proof for a subsistent existence in De ente et essentia. See Owens, Joseph, An elementary Christian metaphysics. Bruce, USA, 1963. One purely ontological presentation of the argument in the Fourth Way is given in II Sententiae D. 1 q. 1 a. 1 which concludes to something whose “natura sit ipsum sum esse.” on the basis of things whose nature can be understood without knowing whether they exist. Thomists in search of a purely metaphysical statement of the Fourth Way would do well to appeal to this text, assuming that St. Thomas did not intentionally set out to make this sort of proof more empirically based by working from principles that had application in physical science – though we claim this is exactly what he does in the Fourth Way.

[7] Cf. Copleston “[T]his argument puts one in mind at once of Plato’s Symposium and Republic…Aquinas was not immediately acquainted with either work, but the Platonic line of thought was familiar to him from other writers Thomas Aquinas Harper and Rowe, USA, 1976. pp125-6 also Gilson, ibid p 72 “No doubt this inquiry [into the Fourth Way] would be fruitless if we do not introduce the Platonic and Augustinian idea of participation” and Smith, Gerard Natural Theology  Macmillan, New York, 1951. p 133

[8] Ibid.

[9] We use “more and less” as divided from “the maximum”, and so modify the former by “merely”. Certainly, there is another sense in which the maximum is “more”.

[10] While Cajetan adds some precisions and to some extent disagrees with Banez, he nevertheless concludes his commentary on the Fourth Way saying “All colors, in the measure that they approach white, have something more of light, and consequently have the nature (ratio) of color more perfectly.” Opera Omnia Iussu Impensaque Leonis XIII P. M. Edita. Volume IV, p. 51.

[11] Banez, Scholastica Commentaria in primam partem summa theologicae. P. I Q. 2 a. 3 reprinted by Brown, Debuque. 1934. Translation is my own.

[12] In The Aquinas Review, Volume V, no. 1 1998.

[13] One of the Port-Royal syllogisms plays with the same ambiguity, though it presents it as a Barbara syllogism:


He who calls you an animal speaks the truth

He who calls you a jackass calls you an animal

Therefore, he who calls you a jackass speaks the truth.


The argument generalizes to a sophistical template that can make anything into its opposite. First, find a general class for the two opposites. Now make the major term “speaks the truth”, the middle term the predication of the class of one opposite, and the minor premise the predication of the opposites of each other, e.g.:


He who says black is a color speaks the truth

He who says black is white says black is a color.

Therefore, he who says black is white speaks the truth.


[14] See Plato Sophist XXXXX. Arisotle concurs with Plato’s judgment in Sophistical Refutations, XXXXsaying that the Sophist deals with non-being so far as he shuns perseity.

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