The most profound questions, to me, are the simplest ones. Why are we here? Is there an afterlife? How is it that God has always existed? To a finite mind, it is impossible to entirely wrap you head around such questions. Be that as it may, it is good to consider it. The following is a exploration of eternality. It centers on the following: proof for the existence of God and the infinite regress argument that so often accompanies it. Enjoy.
“Final and perfect happiness can consist in nothing else than the vision of the Divine Essence… For perfect happiness the intellect needs to reach the very Essence of the First Cause. And thus it will have its perfection through union with God… in which alone man’s happiness consists.”
-St. Thomas Aquinas
The pursuit of truth is as much about the journey as the destination. Proving the existence of god – insofar as such a thing is possible – is much the same way. The cosmological argument of the existence of god can be traced to Plato, Aristotle, and St. Thomas Aquinas (demonstrated in the first three of his Five Proofs). While there are various challenges to the argument, it is the premise of the impossibility of infinite causal regress on which the entire argument depends, without which it loses all force. The focus of this paper will be an analysis of infinite regress as conceived of by Aristotle and Aquinas. It could be argued that Aristotle’s argument finds its greatest acceptance in Christianity – rather than philosophy per se – specifically in the Summa Theologica and Summa Contra Gentiles, the pre-eminent works of Aquinas. Despite having different motivations for writing, Aristotle and Aquinas each make use of the argument of infinite regress. The point of each philosopher is to arrive at the place where reason can account for almost everything. I propose that many of the refutations of infinite regress do not focus on the argument itself; rather, they are misinterpretations of the argument. A brief summary of Plato’s cosmological argument is required and then the infinite regress arguments of Aristotle and Aquinas, taken separately and then together. It is important to understand the contextual argument surrounding infinite regress.
Context of Infinite Regress
Plato’s Timaeus provides one of the earliest versions of the cosmological argument. Plato looked at the universe as the handiwork of the demiurge or “craftsman.” This demiurge imposed order on a pre-existing chaotic universe. For Plato, motion exists and requires a divine source, the demiurge. In forming the universe, the demiurge made it according to a teleological model; it would exist in a state of becoming and be representative of a design or purpose. A further discussion of Plato’s argument is not necessary to this paper. However brief, this summarization provides one of the first contexts for the cosmological argument and its use of infinite regress. For Plato, infinite regress is an impossibility. The demiurge simply fashioned the universe out of the disorderly material already existing. However, it is Plato’s introduction of an “entity” (demiurge) that actually does the fashioning which is similar to the [first cause] arguments of Aristotle and Aquinas.
Undoubtedly, Aristotle borrowed heavily from his mentor with regards to the motion argument and this is reflected in his Metaphysics. A brief preview of Aristotle’s argument would be helpful: 1) motion exists; 2) things cannot be the cause of their own motion; 3) infinite regress is an impossibility; 4) something must have caused first motion; 5) that “something” is not caused to move by anything else; 6) motion is eternal and necessary; 7) the Unmoved Mover is eternal, necessary and must exist.
Although I will elaborate the steps of the argument in the subsequent paragraphs, it is important to understand the context of Aristotle’s argument. His Unmoved Mover argument provides the first efficient cause, the agent which brings something about (in this case motion). For Aristotle, things (i.e., an apple, a desk, a human) are in a state of becoming or moving toward an end. Hence, a seed – as raw material and a reasonable starting point – moves towards being a tree. This idea constitutes teleological thinking. Aristotle’s motion argument may be summed up best as actuality of potential, essentially a teleological assertion (teleology being that things/beings have an end or purpose). Aristotle’s definition of motion comes in his Physics:
We can define motion as the fulfillment of the movable as movable, the cause of the attribute being in contact with what can move so that the mover is also acted on. The mover or agent will always be the vehicle of a form, either a ‘this’ or ‘such’, which, when it acts, will be the source and cause of the change, e.g. the full-formed man begets man from what is potentially man (Aristotle Physics 3.2; 202a).
Bronze may be said to have the potential of being a statue; as such, it exists in this potential state. The motion argument states that something moves from potentiality to actuality; while moving from potential to actual, the bronze and the statue are in the previously mentioned state of becoming. Once the motion is completed, the bronze – which formerly had been only metal – is now at rest in the form of a statue and has reached its teleological end: a statue. It is the transition between lump of metal and fully formed statue that constitutes motion. This demonstrates that motion exists (as defined by Aristotle’s first criterion).
The next extension of the argument postulates that for something to be moved, something must move it (the bronze must be fashioned into the statue). The agent – in this case an artist – brings the thing into existence and is the efficient cause (as well as the actual fashioning by the blades or chisels). The pre-Socratics, most notably Parmenides, argued that a thing cannot come into existence out of non-being; hence, this idea is a hurdle Aristotle must overcome. By defining motion as the transition from potentiality to actuality, Aristotle reconciles his theory with Parmenides: A thing does not spring from non-being but instead it comes into being from prior material through motion (potential->motion->actuality); hence, Aristotle’s second criterion is met.
The next logical step comes in the form of the Unmoved Mover itself. Things cannot move without having been moved through another efficient cause. A thing that is not moving cannot cause motion in another thing; this would be akin to the idea that the artist fashioned the statue without moving in any sense. For Aristotle, motion is impossible unless there is an efficient cause. Since there can be no infinite regress, there must exist a first efficient cause. He concludes, therefore, that a first efficient cause which exists eternally is a necessary condition for first motion. Aristotle concludes that the something else – an Unmoved Mover – must have been the first efficient cause; a moved mover (or mover that is in motion) is not capable of being the originator of its own motion (analogous to a baby being the cause of its own existence). The third, fourth and fifth planks of the Aristotle’s criterion is therefore established. At least one more component to the equation must be added: the essence of motion. Essentially, Aristotle believes that motion is eternal and necessary (plank 6). If there were no motion, things would not be in a state of becoming, they would not move from bronze to statue. Movement makes “actuality” possible. Taken together, the theory is this: since there can be no infinite regress and since a moved mover cannot explain eternal motion, something else – something not in motion – must, therefore, exist to explain motion. For Aristotle, the Unmoved Mover provides that explanation: it is eternal and absolutely necessary due largely to the impossibility of infinite regress (plank 7). Exactly what is meant by infinite regress will be discussed in the subsequent section.
Despite the striking similarity between the arguments of Aristotle and Aquinas, a brief overview of Aquinas’ argument is necessary. A brief preview of Aquinas’ Motion argument: 1) There is motion; 2) Anything in motion must have been made to move by something else; 3) The chain of motion cannot extend backwards into infinity (infinite regress); 4) Something exists that caused first motion; 5) That “something” is God. Taken in simplistic terms, Aquinas’ argument is purely syllogistic (as is Aristotle’s). The clearest enunciation of his position states:
Therefore, whatever is not moved must be moved by another. If that by which it is moved be itself moved, then this also must needs be moved by another, and that by another again. But this cannot go on to infinity, because there would be no first mover, and, consequently, no other mover, seeing that subsequent movers move only inasmuch as they are moved by the first mover; as the staff moves only because it is moved by the hand. Therefore, it is necessary to arrive at a first mover, moved by no other; and this, everyone understands to be God (Aquinas, Summa Theologica I, Q.2, Art.3, ).
Aquinas’ God is not Aristotle’s Unmoved Mover. The first of the disparities is the idea of motion on the part of the first mover. For Aquinas, the first mover is “caused to move” by no other. Although “unmoved” applies to both arguments, there are differences in the conclusions of each philosopher. Plato concedes the possibility of many Unmoved Movers whereas Aquinas only allows for one. Aristotle does not allow the Unmoved Mover to move itself, Plato and Aquinas do. Aquinas sums up this idea as such:
In this sense Plato said that the prime mover moves himself insofar as he understands himself and wills and loves himself. In some respects, this is not in conflict with the arguments of Aristotle, for there is no difference between arriving at some first thing that moves itself, with Plato, and to come to a first that is in every way immobile, with Aristotle (Aquinas, Selected Writings 250-251).
Intra-Theory Challenges to the Possibility of Infinite Regress
A crucial point for both Aristotle and Aquinas – and to greater extent the purpose of this paper – is the impossibility of infinite regress. There are serious challenges to the claim that an infinite regress is impossible. Aquinas addresses the question at some length as we shall see later. Aristotle and Aquinas begin with empirical observations, and then both seek to claim that the only logical conclusion to their argument is God. For the argument to be valid, its conclusion must be the only adequate explanation. The hinge question becomes: Is an infinite regress of efficient causes possible? The first challenge to the denial of infinite causal regression is a mathematical one.
The mathematical challenge to the denial of infinite causal regression states that one type of infinite causal regression can be demonstrated (mathematical). If this is possible, why not allow the possibility of infinite regress of other types (causal)? The assertion: infinite regress is demonstrated in numbers. For example, to subtract 1 from 1 equals zero. To subtract 1 from 0 equals -1 and so on. Therefore, if an “infinity” can be demonstrated where god is not the logical conclusion, the infinite regress argument fails. The possibility of infinite regress is no less than the destruction of the cosmological argument. Kaiser observes:
The assumption or pretended demonstration that every series which has a last term must have a first is the logical fallacy which underlies all these four proofs. Modern mathematicians need only refer to the series of negative integers arranged in the following order: …-3, -2, -1, to provide a consistent and self-consistent instance to the contrary (Kaiser 157-158).
Obviously, the fundamental question vis-à-vis this refutation is: Were the philosophers denying the possibility of any type of infinite regress “in a series”? Almost certainly they were not. Both are trying to lay the foundation for an exploration of metaphysical reality. The existence of varied types of infinite series does not seriously challenge the impossibility an infinite regress of efficient causes. Adding something of the same kind to a series does not account for the existence of the series. It may explain how the series operates/continues but not whence or from what the series originates. Aquinas concurs with this idea by making a distinction between infinite causal regress per se and per accidens. His example of per se causality is the hand that holds the stick that moves the stone. With per se causality, the impossibility of an infinite regress, arises because each of the movents is connected to the movent immediately prior to it. Its causal efficacy is dependent on all prior movents and all move simultaneously. If the hand is not moving the stick at the same time as the stick is in contact with the stone, the stick will not move the stone. For Aquinas, there is no explanation other than an Unmoved Mover for the first efficient cause. The idea is analogous to links in a chain. The chain only works if each of the successive links works together. With per accidens causality, on the other hand, there is a possibility for infinite causal regress. The nature of per accidens infinite causal regress is generic; that is to say, it is possible to conceive an infinite causal regress, for example, of all of mankind. However, it is not possible to conceive of an infinite causal regress of one specific person. According to Aquinas:
In efficient causes it is impossible to proceed to infinity per se. Thus, there cannot be an infinite number of causes that are per se required for a certain effect: for instance, that a stone be moved by a stick, the stick moved by the hand, and so on to infinity. But it is not impossible to proceed to infinity accidentally as regards efficient causes…[It is for example,] accidental to this particular man as generator to be generated by another man: for he generates as a man and not as the son of another man. For all men generating hold one grade in the order of efficient causes – viz., the grade of a particular generator. Hence, it is not impossible for a man to be generated by man to infinity (Aquinas, Selected Writings (Aquinas I, Q. 46, Art. 2, Reply Obj. 7).
As Patterson Brown points out, not only did Aquinas allow for infinite regress, he allowed for certain types of infinite causal regress (Brown, “St. Thomas’ Doctrine of Necessary Being”, 512). Patterson notes that this is not the case with Aristotle; Aristotle did make a distinction between essential (material, formal, efficient, final) and accidental causes (those occurring through luck or chance) but this is not the distinction that Aquinas makes between essential and accidental “ordering of causes.” Duns Scotus presents a similar view:
It is one thing to speak of incidental causes (causae per accidens) as contrasted with those which are intended by their nature to produce a certain effect (causae per se). It is quite another to speak of causes which are ordered to one another essentially or of themselves (per se) and those which are ordered only accidentally (Scotus 40).
Patterson concludes that infinite causal regression is possible per accidens whereas infinite causal regression per se is not. Scotus clarifies this in a way that makes sense: a son depends on the father for his own existence but does not depend on his father for creating the existence of another (even if the father were dead, the son could still procreate). The son’s ability, within the series, to procreate can be termed infinite causal regression per accidens, and this ability to procreate is independent of the father. Note the difference between this type of causal regression and that of the hand and stick analogy. Without the hand, the stick cannot have any means of causation. The hand must move at the same time the stick moves in order for the stick to move the stone. But a son’s ability to “cause” is unaffected by the death of the father. Therefore, infinite causal regression per accidens is possible while the per se variety is not. Joseph Owens clarifies this point. When citing Aquinas, Owens labels the ability of the stone to move “essentially dependent”; the stone’s movement is dependent upon the movement of the stick. But this is not possible to infinity. Why? As Owens points out, movement for Aquinas was itself something that is essentially dependent and can therefore have no “‘first’ or primary instance in its own order” (Owens, “Aquinas on Infinite Regress,” 244). All moventia secunda – any and all movents after the first movent – move simultaneously with one another. Aquinas explains why:
In ordered movers and moved things…it must be the case that if you take away the first mover or if it ceases to move, none of the other things will be moved, because the first is the cause of moving in all the others. But if there were ordered movers and moved things to infinity, there would not be a first mover, but all would be as intermediate movers. Therefore none of them could be moved. And then nothing in the world would be moved (Aquinas, Selected Writings 251).
Owens also states that Aquinas and Aristotle differ in that Aquinas had only one Unmoved Mover whereas Aristotle allowed for many; this is an interesting difference but is beyond the scope of this paper. An easier way to conceptualize the difference between per se and per accidens is through assignment of “hand-stick” and “father-son” analogies to the components of the argument. For infinite causal regression per accidens, the father does not move the son the same way the hand moves the stick (this makes per accidens causal regression possible). The ability of the stick to move the stone is dependent upon the hand, not so with the son; his causal efficacy is independent of the father. The per se application refers to essentially ordered series. The more important issue here is that each of the points in an essentially ordered series is an intermediary. By this I mean that the relationship of the first mover to any of the intermediaries is, essentially, the same. Consider the stick example: The hand is as responsible for moving the stone as the stick. The stick is an intermediary and it in no way changes the relationship between the hand and the stone, which is essentially a dependent relationship since the stone is still reliant upon the hand for its movement (Brown, “Infinite Causal Regression,” 514). There is an implied transitivity to per se essentially causal ordering. If a causes b and b causes c, then a causes c and so on; this is the crux of the impossibility of the per se infinite regress assertion. With regards to per accidens causal regression, the relationship is intransitive (Brown, “Infinite Causal Regression,” 519). Hence, in our previous example of father-son-son’s son, a would not cause c. The difference seems to be one of specificity; per se is very specific whereas per accidens is not specific at all.
Therefore, the mathematical challenge to infinite causal regress is irrelevant because it addresses something not proposed by either Aristotle or Aquinas. All subsequent motion for Aristotle and Aquinas falls under “moventia secunda” or second movement. It does not matter whether there is a finite number of movents or an infinite number; they are all secondary to the first movent. Aquinas never states there cannot be infinite number of moved movers; rather, he states that no order of moved movers can account for itself. Hence, Owens points out that interpreting per se infinite causal regression as purely mathematical is misconstrued.
The next question one might raise when faced with the impossibility of infinite regress is: Why is it considered axiomatic by both Aristotle and Aquinas? The answer for both is that reason can provide an explanation of virtually all causes. Consider: if c moves b and b moves a, then what actually moves a? Patterson states that this can denoted by the variable x; x moves a. If we are looking for an explanation of what moves a in per se essentially ordered series, we are left with an infinite number of answers that could be true and no explanation is possible (reason fails to explain x). The classic exchange between a child and his father (viz. why is the sky blue? It is blue because the atmosphere filters blue spectra. Why does the atmosphere filter blue spectra? ad infinitum) demonstrates the frustration that accompanies infinite regress arguments as well as the aversion to infinite regress in both Aristotelian and Thomistic terms. For reason to be successful, x must be explained. It is more likely that the philosophers did not consider the limitations of reason vis-à-vis questions of this sort; that type of question, and the accompanying problems it brings, is addressed by Immanuel Kant.
The doctrine of the impossibility of infinite regress is such that it makes for strange bedfellows. Plato laid the seeds and Aristotle developed the idea further; finally, Aquinas gave the theory an application to the Christian worldview that continues to this day. The inclusion of David Hume and Immanuel Kant is, therefore, in no way unanticipated. Hume’s challenge to the rational exploits of philosophers like Aristotle and Aquinas at first seems crushing. But upon closer inspection it only shows the inability of empiricism to answer these types of questions while revealing only the minimal ability of rationalism. As such, these critiques are more global in perspective. Hume postulated that unless we can an experience infinity, we can have no knowledge of it (it is not the purpose of this paper to fully outline Hume’s philosophical contribution but to point out those of its features which are germane to my thesis). Hume notes that we form ideas through our impressions. Additionally, those impressions are absolutely essential to the formation of the ideas in our mind:
When we entertain, therefore, any suspicion, that a philosophical term is employed without any meaning or idea (as is but too frequent), we need but enquire, from what impression is that supposed idea derived (Hume 13).
This idea is a serious challenge to the assumptive validity of the infinite regress argument as infinite regress would neatly fall into the camp of “philosophical term.” If there is no experience with “infinity”, how, then, are we to have any sort of impression of it or any corresponding idea? Hume concedes that we can form new ideas from “unions” of ideas previously held but access to infinity is beyond our experience. Hume’s reply to these types of “philosophical terms” is certainly more of a global response to rationalism:
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion (Hume 114).
Hume’s answer to the denial of the possibility of infinite regress is that it neither true nor untrue; since we can have no experience with infinity, any argument on the subject should be burned. However, Kant recognizes the limitations of reason in grappling with things like infinity. It leaves the philosopher unsatisfied. For example, Kant postulated that “time” was a concept which cannot be considered either infinite or finite as both of these designations are constructed in our minds. Therefore, for Kant, it is impossible to gain knowledge solely through conceptual means. Concepts like infinity and finitude only exist in our minds. The only logical approach is a “union” of intuition and sense:
Our nature is so constituted that our intuition can never be other than sensible; that is, it contains the only mode in which we are affected by objects. The faculty, on the other hand, which enables us to think the object of sensible intuition is the understanding…Without sensibility no object would be given to us, without understanding no object would be thought…Only through their union can knowledge arise (Kant 93).
Kant was not necessarily arguing the unreliability of sense data. As in the famous instance of the “bent” stick submerged in the water, Kant knew that our perceptions can be fooled. His argument is that we have no reason to believe that our perception of reality resembles reality itself; we cannot know the object in itself. In the case of the bent stick, we correct our perception through prior experiences. However, as our only connection to reality and the phenomenal world is experience, it cannot be totally discounted (it is all we have). Of course, Kant speculated the existence of transcendental ideas, through which experience is possible (again, a full examination of Kant’s argument is beyond the scope of my analysis). These three were self, cosmos (totality) and God (Soccio , 206), though Kant concludes that the idea itself cannot be proven through experience:
The third idea of pure reason, which contains a merely relative supposition of a being that is the sole and sufficient cause of all cosmological series, is the idea of God. We have not the slightest ground to assume in an absolute manner (to suppose in itself) the object of this idea (Kant 559).
Though it cannot be empirically proven, the point of Kant’s reasoning is to show that the “idea of God” cannot be dismissed. The full impact of Kant’s argument on Hume is thus shown:
Crudely put, if there were no difference between the world and me, I could not even have an idea of ‘having and experience.’ But I do have experience. Indeed the skeptical arguments of Hume only make sense if Hume (or any skeptic) understands that he has experience. But experience itself presupposes precisely what the skeptic doubts: his own independent existence as a unified, continuing self that is part of an objective order, subject to causal laws (Kant , 208).
The empirical critique is, therefore, invalid. Although Kant’s rejection of ontological and cosmological proofs is convincing, he nevertheless carves out a niche in which they can operate. Strictly speaking, in this sense, he has not answered the cosmological argument and to a more relevant extent, the argument of infinite regress. However, in his third antimony, he wrestles with the idea of a first “causality” which does not operate within natural law but through “another cause antecedent to it” (Kant , 411). The resulting conclusion seems to be moderation where reason and empiricism are concerned. His critique of the cosmological and ontological proofs is more global and he challenges the assumptions from which Aristotle and Aquinas proceed. However, his own conclusion seems to admit the impossibility of infinite regress. Indeed, Kant has been accused of being a de facto metaphysician in his own right. Craig states that Kant infers a beginning to the universe:
A close examination of the antimony makes it evident that Kant is not arguing for a beginning of time itself, but for a beginning of the universe in time…This is even more evident in the antithesis when he speaks of time’s still existing prior to the beginning of the world…The states of time are differentiated by the events occurring in time, and thus prior to the first event would exist an undifferentiated temporal state. Kant’s thesis attempts to prove that the present event/state could never arise if it were preceded by an infinite number of events/states” (Craig , 167).
Kant’s dialectical approach assumes the impossibility of infinite regress in both the thesis and antithesis but argued from different perspectives. Clearly he did not think that such questions could be answered in an empirical sense but nevertheless implied the impossibility of infinite regress.
The possibility of infinite regress challenges metaphysical assumptions of both classical and modern philosophers. Many of the charges leveled against it are guilty of misinterpreting the text of the respective philosophers. That its proponents deny the possibility of any type of infinite regress is the most common by far. The cosmological proof of the existence of God/gods hinges on the impossibility of infinite causal regression. Inasmuch as subsequent philosophers have neglected to directly challenge it, it remains an open question. There is much more correction and reproof in research literature than there is open exploration. In this sense, philosophy has been guilty of interpreting what has been said more than saying something new. It does not matter that the subject is millennia old. Indeed, modern science has promulgated theories which seem to support claims made the age-old rationalists. One of the more notable is the Big Bang theory. Prior to the Big Bang theory, the steady state theory universe was the preeminent theory upon which science operated. Stephen Hawking explains why:
There were therefore a number of attempts to avoid the conclusion that there had been a Big Bang…Many people did not like the idea that time has a beginning, probably because it smacks of divine intervention (Hawking 49).
Science only attempts to explain the contents of the known universe whereas Aristotle and Aquinas attempted to explain the system, inside and out. Philosophers like Augustine assumed, on faith, the radical – and scientifically accurate as it turns out – position that the universe did not extend backwards into infinity. Time is a property of the known universe; more than that, modern physics has demonstrated that they share the same birthday. Taken in this way, time itself is a series, not unlike Aquinas’ per accidens causal regression. Yet, the position of Augustine, Aquinas and Aristotle (to a degree) is that God/gods exist outside the series. Proponents of an infinite past do not adequately answer the per se assertion of Aquinas: the existence of every series is dependent upon something outside of the series itself. Aquinas called this “something” God. While science is not ready to set a wedding date, it nevertheless stands to be counted with ancient philosophy once again.
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