On the Impossibility of Infinite Causal Regresses
A Defense of Aristotle's Arguments in his Metaphysics
1. Introduction
Philosophers who write on Aristotle and his works often focus either on reconciling seemingly contradictory passages within the Aristotelian corpus or on evaluating his arguments from a contemporary philosophical perspective. The focus of this post fits in the latter category. The question under consideration is, “Do Aristotle’s arguments against the possibility of infinite causal regresses stand up under scrutiny?” In other words, do we still, in the contemporary philosophical milieu, have reasons to accept Aristotle’s arguments regarding causal regresses? In what follows, I argue that we do have good reasons to uphold Aristotle’s position about the impossibility of infinite causal regresses. In the next section, I clarify some important terminology central to the discussion. Then I consider each of Aristotle’s four causes, first presenting summaries of Aristotle’s laconic arguments against the possibility of an infinite regress for any of the four types of causes (found in Chapter 2, Book II of Metaphysics), and second offering my own reasons in support of his conclusions. I end with a summary of my arguments.
2. Preliminaries
To understand Aristotle’s arguments properly, we must be clear on Aristotle’s project in Metaphysics, as well as on some key terms that he utilized throughout. First, at least part of Aristotle’s goal was to elucidate a special kind of knowledge (epistémé) that Vasilis Politis has called “explanatory knowledge.”[1] This kind of knowledge has to do with the most fundamental facts about reality such as the nature of being qua being and the necessity of discerning the four causes of any given thing[2] in order to obtain such knowledge. These four causes (aitiai) are the final, formal, material, and efficient causes. Some scholars understand each of these four causes more in terms of an “explanation” rather than a “cause,”[3] whereas others seldom mention the notion of an explanation when discussing the four causes.[4] However, it is perhaps best to hold a middle position on this issue where the meaning of “aitia” is understood to have a broad domain such that in some contexts “explanation” would be the best translation whereas in other contexts “cause” or some other word would be the best translation.
Each of the four causes can be understood to provide an answer to a question about a particular thing (e.g. Why? How? Who? What?).[5] So, a final cause could be given in response to a question about why a certain thing exists or why a particular action was performed. In other words, the final cause identifies the purpose for which something exists or that for the sake of which an action was performed. For example, to cite a final cause for my eating breakfast this morning would be to say that I did so in order to nourish my body or so that I would have energy later in the day. Similarly, to cite a final cause for a statue in the town square would be to say that it was built for the purpose of commemorating beloved citizens.
A formal cause could be cited in response to a question about the essence of a thing—what it means for a thing to be that thing. For example, the structure known as the Eiffel Tower is what it is because of the unique form that it has. It is, however, important not to confuse the form of a thing, or its formal cause, with its mere shape. For, although the shape of a thing is integral to its form, Aristotle does not think that the shape of a thing exhausts what is referenced when citing its form. So, for example, although imitation Eiffel Towers exist in various parts of the world, all of which have similar shapes to the Eiffel Tower in Paris, none of them are the Eiffel Tower, since only the structure in Paris has the form of the Eiffel Tower. Similarly, it is important to note that the form is not all that is needed to identify when picking out a particular thing, since Aristotle also held that a thing’s matter serves to individuate it from other things as well.
A material cause could be cited in response to a question about the stuff out of which a thing is made. For example, the material cause of a brick house is brick and the material cause of a wooden barn is wood. Finally, an efficient cause could be cited in response to a question about how a certain thing came to be or about how a certain event came to take place. For example, the efficient cause of a tree catching on fire would be the lightning that struck it, the efficient cause of an inflated balloon (as opposed to a deflated one) would be my forceful exhalation into it, and the efficient cause of a watch would be the artisan (or the artisan’s labor).
One last note: Aristotle did not hold that everything can be explained in terms of each of the four types of causes he identified, but this does not mean that such things lack any explanation. An example of something that does not have a final cause would be a “coincidence” or “accident” of the sort that Aristotle discussed in Book V of Metaphysics. However, such accidents could still involve one or more of the four types of causes and thus would still be subject to Aristotle’s arguments. With these key ideas in place, the stage is set for an examination of Aristotle’s arguments for the impossibility of an infinite causal regress for any of these four causes.
3. Final Cause
First, consider Aristotle’s argument against the possibility of an infinite regress of final causes. In general, the arguments Aristotle provided against the possibility of infinite regresses for any of the four causes could be formulated as a modus tollens syllogism, which would look something like “If it is the case that A, then it is the case that B. It is not the case that B. Therefore, it is not the case that A.” However, for some of the causes (the final cause being one of them) Aristotle provided additional arguments in support of his overarching conclusion that none of the causes could go on ad infinitum. One of his arguments against an infinite regress of final causes starts with the assertion that if there were such a regress, then it would be the case that one could go “walking for the sake of health, this for the sake of happiness, happiness for the sake of something else, and so one thing always for the sake of another.”[6] However, Aristotle denied that one could do one thing for the sake of another and that thing for the sake of something else ad infinitum.
Although he did not provide any elaboration on this argument, his reasoning seems to be that such a regress would be a vicious infinite regress. That is, as opposed to a mere infinite regress where the explanation that the immediately preceding cause provides is a sufficient explanation for its successor on its own (and is not directly involved in any of the other succeeding links in the causal chain), a vicious infinite regress is such that one never reaches a sufficient explanation at any point in the causal chain. Thus, if Aristotle understood an infinite regress of final causes to be a vicious regress, then his argument against this possibility would be that it would render sufficient explanation in terms of final causes impossible (which is a terrible consequence; indeed, Aristotle wrote that those who affirm the existence of an infinite regress of final causes, in doing so, “destroy the good without knowing it[7]).
If I claim that I am going for a walk to improve my health, this explanation of my stroll is sufficient only if my goal of improving my health is intelligible. However, my goal of improving my health is intelligible only if it has a sufficient explanation. I may cite my desire for happiness as the purpose for which I aim to improve my health. If this process is repeated ad infinitum, without ever reaching a stopping point in an ultimate final cause of something performed or something desired for its own sake, then there will be no point in this infinite regress at which one could find a sufficient explanation—it will be a vicious infinite regress.
Aristotle gave a similar argument towards the end of Chapter 2, Book II of Metaphysics. There, he began with the premise that rational action requires there to be a purpose for which one acts. However, if there were an infinite regress of final causes, then there would be no purpose for which one acts, making rational action impossible. As Aristotle put it, “no one would try to do anything if he were not going to come to a limit. Nor would there be reason in the world; the reasonable man, at least, always acts for a purpose; and this is a limit, for the end is a limit.”[8] It seems as though Aristotle’s reasoning is that there must be either a final cause or something done/desired for its own sake as a stopping point or else the regress is vicious.
One might wish to argue against Aristotle’s claim by suggesting that one could conceive of a being that has the ability to hold an infinite amount of desires for things, where each of these things is desired for its own sake. For example, this quasi-divine being could desire happiness for its own sake, love for its own sake, sociality for its own sake, and so on ad infinitum, and there is nothing logically problematic with such a case.
However, this objection misses the point of Aristotle’s argument. For, supposing that it is possible for such a being to exist, the infinite amount of purposes/desires this being would have would not constitute an infinite regress. For, if each of this being’s desires were intrinsic, then they would depend upon nothing else for a sufficient explanation, yet to have an infinite regress there would have to be something, A, desired because of B, and B desired because of C, and so on.
It seems as though there are good reasons to agree with Aristotle that there cannot be an infinite regress of final causes. The burden of proof would be on the objector to explain how one could have an infinite regress of final causes without collapsing into irrationality.
4. Formal and Material Causes
I treat the formal cause and the material cause together because the possibility of gunky material could pose a counterexample against both of Aristotle’s arguments concerning the impossibility of an infinite causal regress for either of these types of causes. Consider first the possibility of an infinite regress of formal causes. Recall that the form of something is the essence of that thing; or, as Jonathan Lear has described it, the form is the essence of a thing that “instantiates an order, or proportion, in the matter.”[9] The form identifies what it is, essentially, to be some thing.
Suppose that there is something, X, that has the form Y, and suppose further that Y has the form Z and Z has the form A, and so on ad infinitum. This is what would be the case if an infinite regress of formal causes were possible. For example, if a machine were composed of ten parts, and those ten parts were themselves each composed of ten parts, and so on, you might think that the whole, as well as each of the parts, could have different formal causes. However, said Aristotle, to have a sufficient explanation for the formal cause of X (i.e., Y) one would also need a sufficient explanation of the formal cause of Y, provided that Y has a formal cause (i.e., Z). This process of looking to the underlying formal cause of each stage of “explanation” would go on forever without reaching a sufficient explanation of anything.
The problem seems to be that the set of relations between each formal cause in an infinite regress is transitive. In other words, if X depends on Y for a sufficient explanation, and Y depends on Z for a sufficient explanation, then X depends on Z for a sufficient explanation. Though I say more about this below, note here that this problem for an infinite regress of formal causes is an example of what Aristotle termed a series of per se (literally “through itself”) causes. Although the well-known example Aristotle gave of a series of per se causes involves efficient causes (i.e., a hand moving a stick moving a ball), the category of “per se cause” can be generalized to any of the four types of causes. It is an infinite series of per se causes (for any of the causes) that Aristotle denies is possible.
Consider next Aristotle’s argument against the possibility of an infinite regress of material causes. Working with the popular conception of material composition of his time, Aristotle wrote that if there were an infinite regress of material causes, then it would be such that flesh proceeds from earth, and earth proceeds from air, and air from fire, and so on ad infinitum. (Set aside the fact that the popular conception of material composition at that time included roughly four types of matter.) However, for the same reason that he denied the possibility of infinite regresses for final and formal causes, Aristotle denied that such a regress of material causes is possible as well, namely, such a scenario would rule out the possibility of sufficient explanation. One might object, however, by offering the following argument:
I. If gunky material is possible, then there could be an infinite regress of material/formal causes.
II. Gunky material is possible.
III. Therefore, there could be an infinite regress of material/formal causes.
To evaluate this argument, we need to be clear on what gunky material is supposed to be. According to Robert Koons and Thomas Pickavance, “x is mereologically gunky if and only if x has no atomic parts,” where “atomic parts” is synonymous with “proper parts.”[10] In other words, if something, X, is gunky, then it is composed of Y and Z, and Y is composed of A and B, whereas Z is composed of C and D, and so on ad infinitum. So, if something is gunky, then it involves an infinite regress of material causes.
But why think that gunky material poses a counterexample to the impossibility of material and formal causes? The reason is that “gunk” can be applied conceptually to things other than material objects. That is, rather than conceiving of something that is composed of matter, which is composed of other matter, which is composed of other matter, and so on, one could conceive of something that takes a certain form, which takes a different form, and so on (perhaps an example of an infinite regress of formal causes would be some object that exhibits a fractal structure at a macro level as well as at all of its sub-levels, where there is an infinite number of sub-levels). Thus, if gunk (either material or formal) is possible, then it seems that Aristotle’s arguments regarding these specific causes are unsound.
How might Aristotle respond to this objection? One way in which he could respond would be to appeal to his distinction between a potential infinity and an actual infinity. Curiously, Aristotle maintained that a thing, e.g., a magnitude, could be potentially infinite but could not be actually infinite. A magnitude, Aristotle would say, is infinitely divisible but cannot be infinitely divided. Although scholars disagree over how to reconcile these seemingly contradictory positions (as well as over other positions related to his notion of infinity, such as his concept of time), in this paper I adopt Ursula Coope’s interpretation:
The sense in which the infinite is ‘in no other way than’ potentially is this: the potential that we ascribe to something when we say that it is infinitely divisible is a potential that cannot be completely fulfilled. This need not commit Aristotle to the strange view that something is at one and the same time potentially F and incapable of being F. The potential in question (since it has no complete fulfilment) cannot be described as a potential to be F. It is, rather, the potential that is fulfilled as completely as possible in the undergoing of a process of division ad infinitum.[11]
Aristotle’s response would be to say that gunk is possible in one sense but impossible in another. That is, gunky material (or gunk that takes infinitely many forms) is possible insofar as it could undergo a process of division (revealing each level of material or formal cause) indefinitely, but such a process could never actually be completed.
Taking this tactic would provide a response to the main argument in favor of the existence of gunk, namely, its conceivability.[12] The argument from the conceivability of gunk could be stated as follows:
A. If gunk is conceivable, then it is possible.
B. Gunk is conceivable.
C. Therefore, gunk is possible.
D. If gunk is possible, then an infinite regress of formal/material causes is possible.
E. Therefore, an infinite regress of formal/material causes is possible.
In response, Aristotle could say that it is obvious that we cannot conceptually divide a chunk of material infinitely many times (nor could we go through the process, in our minds, of identifying infinitely many forms the chunk and its parts take). Rather, we can conceive of being able to divide a chunk of material indefinitely and, prima facie, we find nothing blatantly contradictory about the concept of gunk. Aristotle’s response is capable of accommodating these conceptions. For, since we cannot conceive of the completion of the process of dividing a chunk of matter infinitely many times but can only conceive of the process of dividing this chunk, the conceivability argument in favor of the existence of gunk matches up with Aristotle’s idea of a potential infinite. So, if the conceivability argument for the existence of gunk establishes anything, it only establishes the possibility of potentially infinite material, not actually infinite material. But, if any given material thing is only potentially infinite, then it is actually finite, and if any given material thing is actually finite, then there is not an infinite chain of either material or formal causes. I conclude, then, that we also have good reason to agree with Aristotle that infinite regresses for both formal and material causes are impossible.
5. Efficient Cause
Finally, consider Aristotle’s argument against the possibility of an infinite regress of efficient causes. To give a modernized version of Aristotle’s example (which involved the sun being acted on by “Strife”[13]), suppose that there is a blue railroad car that is pushed by a yellow railroad car. Suppose, further, that the yellow car is pushed by a green car, which is pushed by a red car, and so on ad infinitum. This is an example of an infinite series of efficient causes. However, Aristotle denies that this is a possibility, since one would never reach a sufficient explanation for the movement of any one of the railroad cars. Such a series, if it were to have a sufficient explanation of the movement at some point along the causal chain, requires a first mover that does not itself need an efficient cause.
To understand Aristotle’s reasoning, note first that an infinite chain of efficient causes would involve transitive relations. So, if the yellow car requires the green car for its movement, and the green car requires the red car for its movement, then the yellow car requires the red car for its movement. If the red car were removed from the chain of causation, then not only would the green car lack its efficient cause of movement, but so also would every other railroad car ahead of the red one. Thus, to have a sufficient explanation of the efficient cause of the movement of the yellow car, one would need a sufficient explanation for the movement of every other railroad car behind it, which would be impossible if the causal chain were infinite.
Contrast this with what would be the case if the causal chain involved per accidens causes rather than per se causes. John Duns Scotus gave a clear distinction between these two types of causes:
Per se or essentially ordered causes differ from accidentally [per accidens] ordered causes.... In essentially ordered causes, the second depends upon the first precisely in its act of causation. In accidentally ordered causes this is not the case, although the second may depend upon the first for its existence, or in some other way. Thus a son depends upon his father for existence but is not dependent upon him in exercising his own causality [that is, in himself begetting a son], since he can act just as well whether his father be living or dead.[14]
In other words, in a series of per accidens causes, B does not depend upon its predecessor, A, to cause its successor, C. A series of per accidens causes is not transitive, as is a series of per se causes. For example, suppose that the state of the universe at the present moment was efficiently caused by the immediately preceding state, and suppose that the immediately preceding state was caused by the state immediately preceding that one, and so on ad infinitum. This could be explained in either of two ways. First, if this series of efficient causes were understood to be a series of per se causes, then the series would exemplify transitive relationships, which would imply that it could not extend infinitely into the past. Second, if this series were understood to be a series of per accidens causes, then each state of the universe would be causally independent of its predecessor.
An objection to Aristotle’s position would hold that the universe (or series of universes) involves a series of per accidens causes. If this were the case, then we would not need to appeal to a preceding state of the universe to have a sufficient explanation for the current state of the universe causing its successor. Rather, we could find a sufficient explanation for the efficient causal connection between any two states of the universe in that pair alone. And the same would hold true even if there were an infinite series of states of the universe (or an infinite series of universes). So, there could be an infinite series of efficient causes that is not a vicious infinite regress.
There are a few was to respond. First, if we are concerned with successive states of the same universe, and if we assume that the universe had a beginning, then the series would only be potentially infinite, rather than actually infinite. However, the most plausible version of the objection holds that the infinite series of efficient causes consists in successive universes rather than successive states of the same universe. It is no problem to this most plausible version that the current universe had a beginning. For the present universe could have had a beginning and it still be the case that the present universe is only one in an actually infinite chain of universes, each of which is the efficient cause of its successor.
A second way to respond is to say that there is a conceptual problem with an actually infinite series of universes, each of which is an efficient cause of its successor. To get to the present universe, there would have to be an infinite number of previous universes that already caused their successors. However, this would require an infinite amount of time, and it is impossible to traverse an infinite amount of time. A similar objection (regarding an infinite series of states of the same universe rather than an infinite series of universes) is that, to get to the present state of the universe, the universe would have had to go through an infinite amount of changes, which would take an infinite amount of time. Yet, once again, it is impossible to traverse an infinite amount of time.
However, this second way to respond runs into a problem because it assumes a view of time that the objector need not accept. For the objector could assert an eternalist view of time according to which all moments of time have equal ontological status. If the objector affirms an eternalist view of time, then he need not accept the claim that an infinite series of universes (or an infinite series of states of the universe) must involve traversing an infinite span of time. For, on an eternalist view of time, there is no ‘present’ that ‘moves through’ or ‘traverses’ time.
Yet, there is a dilemma that arises at this point. The first horn is this: if the objector affirms an eternalist view of time, then the infinite series of efficient causes cannot be a series of per accidens causes, but rather must be a series of per se causes. But if the series consists of per se causes, then it cannot be actually infinite because each cause would depend upon its predecessor for a sufficient explanation for its own causal powers—a vicious regress ensues. The reason why the series of universes (or states of the universe) must be a series of per se causes (given the assumption of eternalism) is that the whole series becomes dependent upon each part; and if the whole series is dependent upon each part, then each part stands in a transitive relation to is predecessors and successors, which is characteristic of a series of per se causes. The whole becomes dependent upon each part because the absence of any one part destroys the whole and gives rise to separate, smaller series of causes.
The second horn is that, if the objector does not affirm eternalism, then he faces the previous problem of traversing an infinite amount of time, or undergoing an infinite number of changes, both of which are impossible. For recall that eternalism is what enabled the objector to avoid the problem with affirming that the present universe (or the present state of the universe) was reached via an actually infinite series of events in the past. So, on either horn of the dilemma, there cannot be an infinite series of efficient causes.
6. Conclusion
In summary, my claim is that we still, in the contemporary philosophical milieu, have good reasons to accept Aristotle’s arguments that he offered against the possibility of an infinite regress for any of his four types of causes. The main issue with a supposed infinite causal regress is when it involves a series of per se causes; for, such causes require a “first term” for there to be a sufficient explanation for any members of the series. Any series of final causes must be characterized as a series of per se causes and so cannot be infinite. Likewise, gunky material (or gunk that takes infinitely many forms) cannot be actually infinite since it too would involve a series of per se causes. An infinite series of efficient causes could be understood to involve either per se or per accidens causes; if the former, then it is impossible for there to be such a series; if the latter, then there is a dilemma both horns of which lead to the conclusion that the chain of efficient causes must be finite.
Works Cited
Aristotle, “Metaphysics,” in The Complete Works of Aristotle: The Revised Oxford Translation, Edited by Jonathan Barnes. Princeton: Princeton University Press, 1984.
Brown, Patterson. “Infinite Causal Regression,” in The Philosophical Review 75, no. 4 (1966): 510-525.
Coope, Ursula. “Aristotle on the Infinite,” in The Oxford Handbook of Aristotle. Edited by Christopher Shields. Oxford: Oxford University Press.
Falcon, Andrea. “Aristotle on Causality,” in Stanford Encyclopedia of Philosophy, (2015) https://plato.stanford.edu/entries/aristotle-causality/#Rel.
Koons, Robert, and Thomas Pickavance. The Atlas of Reality: A Comprehensive Guide to Metaphysics. Malden, MA: Blackwell, 2017.
Lear, Jonathan. Aristotle: The Desire to Understand. Cambridge: Cambridge University Press, 1988.
Politis, Vasilis. Routledge Philosophy Guidebook to Aristotle and the Metaphysics. New York: Routledge, 2004.
[1]Vasilis Politis, Routledge Philosophy Guidebook to Aristotle and the Metaphysics (New York: Routledge, 2004) 23.
[2]That is, any given thing that can be explained in terms of the four causes. Aristotle was not committed to the claim that everything must have each of the four causes as explanations.
[3]Politis, chapter 2 sections 3-4.
[4]Jonathan Lear, Aristotle: The Desire to Understand (Cambridge: Cambridge University Press, 1988), chapter 2 section 3.
[5]Andrea Falcon, “Aristotle on Causality,” in Stanford Encyclopedia of Philosophy, section 2 (2015) https://plato.stanford.edu/entries/aristotle-causality/#Rel.
[6]Aristotle, “Metaphysics,” in The Complete Works of Aristotle: The Revised Oxford Translation, Jonathan Barnes, ed. (Princeton: Princeton University Press, 1984) 994a10.
[7]Ibid., 994b12.
[8]Ibid., 994b13.
[9]Lear, 29.
[10]Robert Koons and Thomas Pickavance, The Atlas of Reality: A Comprehensive Guide to Metaphysics (Malden, MA: Blackwell, 2017) 494. Emphasis theirs.
[11]Ursula Coope, “Aristotle on the Infinite,” in The Oxford Handbook of Aristotle, Christopher Shields, ed. (Oxford: Oxford University Press) 282. Emphasis original.
[12]Koons and Pickavance, 496.
[13]Metaphysics, 994a7.
[14]Quoted in Patterson Brown, “Infinite Causal Regression,” in The Philosophical Review 75, no. 4 (1966): 513. Emphasis original.