Is infinite regress of causation possible? Is infinite regress of causation necessary?

Question

For a number of reasons — including perhaps a desire to feel that we have a complete understanding of where we came from, or at least an understanding which is completely sufficient for all of our purposes — there is a strong tendency to suppose that an infinite regress of causes and effects is impossible. We see this for instance in the writings of Aristotle on a first mover. Traditionally in Greco-Roman influenced philosophy, this prime mover has been identified with the notion of a creator god. A more modern formulation comes from the Big Bang theory, which (although we study the question) happened for no reason that we know of; and perhaps occurred for no reason at all. Indeed, if time is a property of the universe, a good argument can be made that there is no such thing as "before" the Big Bang.

At the same time, we have gotten a lot of leverage in science from the ideas that everything happens for a reason, i.e. because it is caused by something else. This is sometimes described as the Principle of Sufficient Reason. Aristotle also applies this idea, except that the first mover is made an exception, something which exists literally for no reason. Indeed, the emotionally negative way that "no reason" is used in common speech, as something groundless and irrational, indicates how widespread the feeling is that the idea of uncaused events is deeply dissatisfying.

Almost all of our modes of critical thinking are infused with both of these ideas: that we may work from first principles, a definite starting point, counting up from zero (or one, historically); but also that we may trace the causes of things to some point, and then later ask how that starting point came to be. But the two ideas are themselves in conflict.

Which is true — that infinite causal chains are impossible? Or that they are necessary? Or are they perhaps possible without being necessary?

Related questions:

• Can we ever know the origin of universe?

• How do proponents of the Cosmological argument respond to the nature of time?

• Is it possible for something to have no cause?

• Why is there something instead of nothing?

• Can there be an infinite regress of Creators?

Answer 1

We must first distinguish between what is physically possible — what it is possible to actually occur — and what is imaginable, or logically possible under certain premisses.

Remarks about the logically possible

Initial approaches

Logic itself — which I will take to mean classical propositional logic — has very little to say about time, or about infinite chains of consequences, either extending forwards or backwards. Indeed, it has nothing at all to say. Logic is merely a tool which we use to investigate topics, but anything it has to say on the subject are from premisses which we supply. So what is logically possible depends on the premisses we adopt.

Obviously, if we assume that there cannot be infinite regresses, we will conclude that infinite regresses are impossible; and if we assume that everything must have a cause, then infinite regress is necessary. Boldly asserting our assumptions is not a form of logical deduction, however. So we must try to avoid doing so if we wish to consider logical possibility or necessity.

We can observe that the two statements — everything must have a cause, and that there cannot be an infinite regress of causes — are in apparent conflict with one another. There is one possible resolution: a cycle of causes, where A ⇒ B ⇒ C ⇒ A, and the like, including potentially complicated networks of mutual-causation. If you find this just as dissatisfying as an infinite regress of causes or an uncaused event, then you may wish to assume that such cycles cannot exist: but then you should remain aware that this is an assumption on your part.

There is absolutely no proposition A that we know of, which "causes" another proposition B to hold — that is, where A ⇒ B — which prevents us from considering yet another proposition Z such that Z ⇒ A, and where we may regard A as true because Z is true. So every proposition can be concieved of as being caused by another. But there is nothing which forces us to formulate such a proposition Z, either. We must move beyond mere sentential logic if we wish to plumb this idea further.

Infinite regresses in mathematics

We may consider what ideas come from mathematics to inform our ideas about whether logical causal chains are possible: mathematics is in effect our most intense testing grounds for logical consistency of ideas. Indeed, in modern mathematics, infinite forward-moving causal chains are common. The simplest example is Mathematical Induction, in which one proves that if some property P holds for 0, and if P(0) ⇒ P(1), and if P(1) ⇒ P(2), and so forth ad infinitum, then P holds of all whole numbers: one essentially completes an infinite chain of implications in one swoop. It is similarly common to build "upward towers" of containments: for example, sets A ∈ B ∈ C ∈ D ∈ ... However, it is unusual to consider chains of conditionals which reach "infinitely backwards", where ... ⇒ Q(3) ⇒ Q(2) ⇒ Q(1) ⇒ Q(0); and in most formulations of set theory, chains of the form ...∈ D ∈ C ∈ B ∈ A are expressly forbidden. We must not mistake this for logical impossibility, however. The axioms of set-theory that we have today were explicitly formulated to avoid confusions of definitions of sets, but they are not the only such formulation: there is a study of so-called non-well-founded set theories in which such "infinitely descending chains" are possible. As to infinite chains of consequences, for any predicate P for which we have an infinite ascending chain P(0) ⇒ P(1) ⇒ P(2) ⇒... of entailments, the predicate Q(n) ≡ ¬P(n) has an infinite descending chain ... ⇒ Q(2) ⇒ Q(1) ⇒ Q(0) by contraposition. So if you admit infinite chains of "logical effects", you must allow infinite chains of "logical causes" as well, or very carefully re-examine your foundations of logic.

Infinite descent is very common in mathematics, of course, if you consider the set of the integers ... < -3 < -2 < -1 < 0 < 1 < 2 < 3 < ..., or similarly if you consider the rational or real numbers ... < 1/16 < 1/8 < 1/4 < 1/2 < 1. Arguing for the fact that these are defined in terms of the whole numbers starting from 0 neglects the fact that we have chosen that starting point for reasons which may be described as simply traditional; the fact that we feel compelled to consider number systems which allow these infinite backward regresses is also a counterpoint.

So much, then, for inspiration through mathematics.

What are the permissible assumptions to use?

It is difficult to see how to proceed without entering the domain of physics (which I will touch on momentarily).

• The Principle of Sufficient Cause is very much in sympathy with determinism; but of course assuming that the world is deterministic does not prevent us from entertaining the idea of a further cause to any particular cause that we might like to imagine — so more physical assumptions beyond mere determinism would be necessary to make the notion of determinism useful.

• Consider an "actual infinity" of regress — that is, where one may not only posit a preceding cause for any cause, but actually entertain a completed chain of causes. One might try to argue that an actual infinity of anything (logical causes or otherwise) is absurd; and while this was an active debate in philosophy of mathematics in the late 19^th and early 20^th centuries, the consensus is heavily in favour of actual infinities; a simple rejection of actual infinities is not likely to be convincing to others. But even if you only admit potential infinities of causes, you still have a potentially-infinite-regress, where the only reason why you don't entertain a cause for some early event is because you get caught up in doing something else instead. (The tendancy for us to do so is a possible reason why the idea of a first cause is so popular in the first place.)

• The fact that there may, or may not be, a largest infinity which describes an infinite regress, is more ambivalent. Few people are terribly concerned about the subject so far as I can tell. However, the fact that one could always posit "a larger infinity", a la Cantor, is no rebuttal against an actual infinity of causes (despite the fact that this is in effect what Aristotle does for his Prime Mover): there is also nothing preventing someone from positing a cause for what otherwise would appear to be a Prime Mover. Whether one prefers a system of reason in which largest possible cardinalities exist, or do not, is a matter of taste; this is an impasse for the debate.

• If you are of a religious persuasion — and in particular, a creationist — then it will seem quite natural to posit that there is a first cause. Suffice it to say that there are many people who will find your arguments unconvincing, if for no other reason than the fact that they do not agree to the assumptions included in your religious background.

I am unaware of any particularly compelling ideas — or for that matter, any particularly interesting ideas — which would decide in favour either of infinite regress, or in favour of the impossibility of infinite regress, as logical necessities. As far as I can tell, both the notion of a first cause and the notion of an infinite causal regress are logically coherent — except if you in essence assume that one of them is false.

It would seem that there is nothing left but to get out of the arm-chair, so to speak, and actually look at the outside world to see what is more likely to be the case.

Remarks about the physically possible

Because this is not the Physics StackExchange forum, we should not pretend to answer definitively what is "actually" possible, which is the domain of physics (or science more generally). However, we may make some observations from what is broadly known in the physics community.

For physical quantities or qualities, such as mass and energy, physicists tend to be skeptical of the idea of infinite quantities, if for no other reason than the fact that some object of infinite magnitude should presumably be easy to spot (if it didn't destroy the universe first). However, things like "age" aren't physical quantities or qualities; the universe may have processes which we can use as reliable time-keeping devices, but time is not written into matter itself, so far as we know.

Remarks on cosmology

Of course, the Big Bang theory is a physical theory, and it posits that our universe has a beginning only a finite amount of time ago. So this supports the idea that the universe does not have infinite causal regresses. But this is an observation, not a theoretical proof: our universe happens to be finitely old, and only so far as we can tell. (As if we could do better than the best of our observations.) When Einstein formulated General Relativity, he postulated a cosmological constant precisely because he thought the universe was in an infinitely old steady state: this is a move he later described as the biggest mistake of his life, but only because his prejudices prevented him from making one of the most astonishing anticipations in the history of science — modern theoretical grounds for a finite age to the universe based on a theory of gravity (which would have been an unanticipated event on the order of magnitude as Dirac's prediction of antimatter). These days, people feel more forgiving of Einstein's mistake, because it would seem that there is a non-zero cosmological constant, just as Einstein thought — only it has the opposite sign to what he thought, so that the universe is not only expanding, but faster than it had before.

The continuity of time

Of course, if time is continuous, there actually are infinite causal chains, but more of a Zeno-like flavour: between every cause and effect which happen at different times, there are intermediate effects and causes, and ones between those, ad infinitum. In the limit of infinite division of causal chains, you can obtain a continuum of intermediate events. Alternatively, between a cause at time t=0 and at time t=1 you may contemplate intermediate events at t=1/2, t=3/4, and so on for all times t=1-2-n for all positive integers n, still giving rise to an infinite chain of events which lead up to the event at time t=1. This is only prevented if there is discrete time; but there's no particular evidence that time is finite. (There is indeed research into such discrete models of time, and although this research sometimes looks interesting and promising, there isn't anything particularly strongly suggestive.)

On determinism and causation

It is possible that we might be able to undermine the Principle of Sufficient Reason, if for instance there are random events. Do they have causes, and if not, can the whole universe (or some powerful entity within it) perhaps be uncaused? Of course, many events which seem random can in principle be predicted if we have enough information about the initial conditions in which the die was rolled. Chaos theory may predict that it is impossible to pin down initial conditions sufficient to predict for all subsequent times, and quantum mechanics suggests that perhaps there is no perfectly defined initial conditions in the way that we would require e.g. in Newtonian mechanics. But so persuasive is the idea that the world acts according to deterministic and causal mechanisms that it is difficult to abandon the idea that everything happens for a reason, and so there are researchers such as those who work on de Broglie-Bohm theory who seek to give a deterministic interpolation of quantum mechanics (as opposed to "an interpretation", speaking here against the common manner of speaking of de Broglie-Bohm theory).

Of course, here too there is an impasse: just because one of our more practical theories can be formulated efficiently as a probabilistic theory, does that mean that therefore there is randomness inherent to nature? But this is just a particular instance of the problems of epistemology: if nature is sufficiently subtle, it can fool us into classifying it differently than we might if we were somehow more perceptive or less biased. As with everything in science, the jury is still out.

In summary

But the state of the art in theoretical physics is that there's no theoretical grounds for ruling out infinite causal chains, even ones which extend into the infinite past: the best we can do is to say that observation suggests. This is ultimately what matters anyway; what is, rather than what might otherwise be.

What observation — and our interpretation of these observations — has thus far suggested that our universe is finitely old, and that it is reasonable to suppose that there are events which are not completely characterized by what came before. However, by the very fact that we have a useable theory of random behaviour in quantum mechanics, no event seems to be "completely uncaused"; and it also assumes a continuous evolution in time, so that there are at least Zeno-like infinite chains of cause and effect.

Answer 2

At the same time, we have gotten a lot of leverage in science from the ideas that everything happens for a reason. This is sometimes described as the Principle of Sufficient Reason. Aristotle also applies this idea, except that the first mover is made an exception, something which exists literally for no reason. Indeed, the emotionally negative way that "no reason" is used in common speech, as something groundless and irrational, indicates how widespread the feeling is that the idea of uncaused events is deeply dissatisfying.

The form of the principle of sufficient reason Hume uses is: No event, of whatever type, can happen at time t without something determining its occurrence at that instant. If the explanation of X is itself necessary and if it is a sufficient explanation of X, then X will be necessary, since X will be a necessary consequence of a necessary proposition. So either X is unexplained or it is necessary. But the principle of sufficient reason tells us that it can’t be that X is unexplained so it must be necessary. So principle of sufficient reason entails that all facts are necessary. Believe it if you can. God isn't free to choose to create one world rather than another. The principle is only justified in the framework of a deterministic conception of natural processes. Contemporary physical theory does not any more support such a conception.

Particles susceptible to radioactive decomposition have taken individually a period of latency whose length is only statistically determined, followed by an instant at which they produce, as an effect, new particles resulting from their decomposition. The step from latency to the actualization of the causal potential of such a particle is ‘‘spontaneous’’ in the sense of being independent of any triggering factors external to the particle. The occurrence of the event at "t" is ‘‘indeterminate’’. Nevertheless, it is preferable to avoid using the term ‘‘indeterminate’’, to the extent that it may give the erroneous impression that the occurrence of such an event is not subject to the laws of nature. Nothing determines which of several possible events occurs at instant "t", as far as an individual radioactive particle is concerned. In this sense it can be said of a given radioactive decomposition event that it is spontaneous although it is also subject to a probabilistic law. This is possible because a probabilistic law does not directly determine the evolution of each individual particle to which it applies, but only the average evolution of a large number of such particles. In the context of a radioactive particle, the term spontaneity is meant to refer to the fact that it is indeterminate which of two possibilities becomes actual. In any case, the behaviour of radioactive particles constitutes a counterexample to the version of the principle of sufficient reason used by Hume: There are events that can happen at time t without something determining its occurrence at that instant.

“When people ask me if a god created the universe, I tell them that the question itself makes no sense. Time didn’t exist before the big bang, so there is no time for god to make the universe in. It’s like asking directions to the edge of the earth; The Earth is a sphere; it doesn’t have an edge; so looking for it is a futile exercise.” “If the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end.” - Stephen Hawking

The question of a finite chain of causes of the universe, itself makes no sense. Why is there something rather than nothing? This is an illogical question because impose an impossible explanatory demand, to deduce the existence of something without using any existential premises. One can not give a imaginary definition of attributes of a being as a timeless or out space being or an uncaused being, as proof of existence. If everything has a cause, then God must have a cause. If there can be anything without a cause, it may just be the universe as God. Of all the approaches to a being’s existence, the deduction is the strategy that we would expect to be successful were there a necessary being. But there are not a valid deduction of a non logical existence, then we can conclude that there is no such necessary being.

Answer 3

Well, here are some different thoughts on this:- One popular variation on the Principle of Sufficient Reason is in the three possible formualtions:

For every Entity X, if X exists, then there is a sufficient explanation for why X exists. [Let us call this the 'X' formulation]

For every Event E, if E actually occurs, then there is a sufficient explanation for why E occurs. [Let us call this the 'E' formulation]

For every Proposition P, if P is true, then there is a sufficient explanation for why P is true. [Let us call this the 'P' formulation]

Note: in each formulation is required a sufficient explanation. It cannot be less than sufficient but, conversely, it need be no more than sufficient.

The creation of the universe: E - an event. There has to be sufficient explanation for why it occurred - not simply that it occurred or how. If we argue, as Hawking does (with Mlodinov) in 'The Grand Design' that the laws of physics and chemistry themselves are sufficient explanation for event E the creation of the universe, then we now have a P formulation requiring explanation. For the laws of physics and chemistry are propositions (in our argumentation here). We might respond that "Because we observe them in action in our universe" is sufficient explanation. But it is not. It is only an explanation that they are true - not why. As we saw, these formulations require explanation of why in each case. WHY are they true? We can respond that they are true because of an entity (X) which brought them into being in order to create this universe (E) and continues to apply them in it (E) (E) (E) ...

Aristotle called that entity (X) the Prime Mover. That Prime Mover, however, is not 'exempt' from this test of logic, and neither does it need to be. We can say that the sufficient explanation for creation of this universe (E) was this Prime Mover (X), external to this universe, yes - but not external to this logic at all; the Prime Mover willed this universe to be (E)- and, indeed, is also sufficient explanation as to why the universe continues and is dynamic (E) (E) (E)- the Prime Mover wills this to be so (this is a new and more cosmic slant on what Aristotle said regarding the Prime Mover as causation in his - now obsolete - physical model of the universe).

Fine - but what is the sufficient explanation for the Prime Mover (X)? Remember: we do not have to explain how or that it exists - and need give only sufficient reason - and no more. We can respond "In order that there be this universe" (E) - and governed by the particular laws of physics and chemistry which we explained (P) above. This will also explain why this particular universe (the only one about which we can truly know anything - any other possible ones being outside this logical discussion). We cannot then ask "Why did there have to be a universe?" or "Why did there have to be this particular universe?" and think we have thus created the famous (or infamous?) 'argument of infinite regress' which Aristotle sought to disprove (he argued against it on a number of grounds including the possibility of it becoming self-defeatingly circular - which, in fact, is one of the big flaws in some of Hawking's arguments). We have closed any possible open loop in our logic - because we can show that there had to be a universe created, and specifically this one (E) governed by these laws (P) ... because we know it is there.

It is only then possible to pull open our logic and demonstrate an 'infinite regress' if we can show either that this universe does NOT (NO E) exist or that it was never created (i.e. truly had no beginning ... a position which very few can defend today) (NO E) or else that these laws which appear to reliably govern it are false or an illusion or else do not exist (NO P). If these last were to be the case then the Hawking/Mlodinov postions would, as it were, 'self-destruct'. I don't see them doing that. So this argumentation stands.

Answer 4

Wow - timely. This topic is really trending lately.

Ok, so rather than write an equation to prove black equals white and endanger myself at the next zebra crossing, I'd like to put forward a couple of logical arguments to highlight some gaps.

1. Where Infinite Regression is impossible

In the research you mentioned above (ie. Aristotle) that the impossibility of infinite regression means that everything must have a beginning, and a prime mover must have been there to create that beginning. Yay prime mover.

2. Where Infinite Regression is possible

However, there an equally logical argument that the possibility of an infinite regression is also the cause of a prime mover. What you can say is that the infinite regression sits in a bubble of time, and outside of this bubble of time sits a prime mover who is without time. Because the universe is subject to time, but there is a hypothetical non-time environment, you can simply have the two sit side by side. The prime mover who is without time doesn't need to have gone back to the infinitely old universe to kick thing off, but was just always there. Yay prime mover.

Back to reality

The human mind is so creative and flexible it can always find a way to justify or explain a prime mover. When arguing against a true believer, it's impossible to win because they will always fall back on 'but god must have created the big bang' type of argument. God as an explanation is like the ultimate set of wildcards - that's why you can't use facts to debunk it.

However, a truly logical mind knows there is no such thing as a prime mover because ultimately the argument isn't about infinite regression, big bangs, physics, or maths.. but comes down to the most beautiful logical statement of all time.. Ockham's razor:

If given the choice between:

1. an amazing strange universe that's been evolving and growing from a spontaneous or infinite point; or

2. an amazing strange universe that's been evolving and growing after being created by another amazing strange prime mover that existed spontaneously or infinitely..

Which is the most likely given Ockhams? It's option 1 of course. The more assumptions you place in your statement, the more unlikely it becomes. The second statement has twice the number of assumptions!

It's not about having a definitive answer, it's not about proof, and it's not about belief. It's about common sense to recognise what's the most probable answer. No-one will ever know for certain because science will always discover more unknowns, and religion will always hijack those unknowns to argue a prime mover.

Footnote: The infinite regression isn't just about stepping back in time to understand the sequence of events for creation and evolved of the universe.. it's also applicable to the logical argument of who created the prime mover, and who created the creator of the primer mover, and who created the creator of the creator .. etc. This is where the requirement for a prime move is equally illogical, irrespective of whether infinite regression is possible or not.

Answer 5

They are impossible.

Suppose they were possible, then you couldnt write down all the causes in a finite space, because if you could, then that description would be a single cause for the whole chain.

This means that if they are possible that you have to expand the meaning of what is a cause into an infinitely long description, essentially taking each step in the causation as an axiom in the definition of cause. So "infinite" chains of "causation" are about as meaningful as stating "A->B, because "A->B". Or "anything happends for a reason, because this is the definition of reason!".

Answer 6

What about the energy associated with each cause or effect?If there has to be infinite cause and effect chain, then there has to be continuous supply of energy associated with each cause creation maintenance and destruction. This would mean there is infinite energy present all the time throughout the chain as a constant irreducible factor.This is in sync that energy is not actually created or destroyed, but it just changes the form.Hence infinite regress is simply morphing of a constant infinite energy!Apparently this single constant, which is present throughout the universe and constantly changing its form.Even for this energy's form change, the energy required has to be from the same infinite source.It is because of this constant's morphing that the infinite chain is perceived.

Answer 7

Wittgenstein famously states that (Tractatus Logico Philosophicus, proposition 5.1361) : "The events of the future cannot be inferred from those of the present." and "Superstition is the belief in the causal nexus."

Later (Propositions 6.37, 6.371 and 6.362) "A necessity for one thing to happen because another has happened does not exist. There is only logical necessity. At the basis of the whole modern view of the world lies the illusion that the so-called laws of nature are the explanations of natural phenomena. So people stop short at natural laws as at something unassailable, as did the ancients at God and Fate. And they both are right and wrong. But the ancients were clearer, in so far as they recognized one clear conclusion, whereas in the modern system it should appear as though everything were explained."

I might be quoting too exstensively, but I wanted to include the passage on God and Fate since it was an issue which was alluded to above.

To summarise, Wittgenstein holds (in the Tractatus at least) that causation (as a law) is an a priori intuition about the possible forms of science, and is useful in making hypotheses, but is not a logical necessity -and thus not a necessity- and tells us nothing about the nature and meaning world in itself.

I cannot, in conclusion, strictly "answer" the question (from the Wittgenstanian point of view), but I can make it go away :-) as causation is not an absolute law, and the problem of infinite regress disappears with this idea.

This is my first answer on this site, and I don't know if anyone will ever read it, but I enjoyed writing it, and I saw that no one had brought up Wittgenstein, whose claims on causation (and the way he pronouced them) really jumped off the page and caught my eye on my first reading of the Tractatus.

Answer 8

Although an infinite regress of causes may sound implausible, it is entirely reasonable, as long as time is continuous. A ball rolling across a table reached the other side because at the halfway point it had the appropriate momentum. But likewise, it reached the halfway point because halfway to the halfway point it had the appropriate momentum, etc., etc., forming a perfectly reasonable infinite regress of causes. (This kind of apparent paradox was of course first described by Zeno.)

Answer 9

I hope I can cut to the chase with the following:

Parmenides (~475 BC): "The all is one." ("ἕν τὸ πᾶν"). There is an implied addition to this axiom: "There is only the all"; hence a more complete: "The All is One; there is ONLY the All."

I call this statement the Prime Axiom. It is an axiom because it can neither be proven, nor disproved, but its truth is evident and hence must be admitted.

The only attributes of the All are Its unity and the fact that it is All. May I also add that there is no, and cannot be any, "not-All". This is the Prime Corollary.

I humbly offer that any other statements/inferences/descriptions/beliefs, etc., concerning the Prime Axiom (the All) are products of the human brain, which is certainly a limited and imperfect tool of investigation. As long as we have words we will probably keep speaking about this, but can never come to any understanding or final explanation of what is clearly beyond us. I don't know where this leads us (probably nowhere), but that's what we must live with. My cat (Buddy) doesn't seem to worry about these things, at least he has never indicated to me that he does. Perhaps this is a human disease; trying to understand what is not understandable. If so, I am certainly smitten with this disease and hope I am cured before this body ceases to function!