# Generating the simplest sort of Cosmological Argument

First, I am not a philosopher, but rather an applied mathematician. However, the Cosmological Argument has always intrigued me. At times I feel that all attempts are necessarily hopeless, at other times I feel that a clever argument could actually get somewhere. Trying to read the literature on this is daunting: Continuous back and forth arguments and counter-arguments, and as a non-professional, finding time to keep up is difficult.

In any case, my hope is to simplify matters for myself to see how far we can even go with one assumption, and was hoping that somebody could check my logic.

Assumption 1: Principle of Sufficient Reason (PSR): For every entity X that exists, either X causes itself, or some other entity Y causes X.

Now, I am not schooled on the metaphysics of causality, but if we're using human intuition as a guide, I assume we can talk about this in a semi-acceptable way. Anyway, the argument is as follows:

Given that the universe exits, we begin by asking what caused the universe U. If the universe didn't cause itself, then something, call it external cause C1, causes the universe, and and we write C1<U to mean that C1 caused U. Then either C1 causes itself, or some external cause C2 exists and causes C1, in which we write C2<C1<U to mean that external cause C2 causes U.

Now, if there are a finite amount of external causes, at least one causes itself, as you cannot have a finite amount of entities, each with an antecedent, and not have a loop (such as Cn<C'<...<C''<Cn.)

Contrapositively, if no external cause causes itself (neither directly nor through a loop), you must have an inifinite chain of such causes (with no loops).

Hence, it seems that with only the PSR, we are left with three distinction options:

1. The universe caused itself.
2. There's an infinite chain of causes which did not cause themselves (either directly or through a loop).
3. There exists at least one external cause (other than U) which caused itself (either directly or through a loop).

Making no other assumptions, this seems to be the choices we are given. Of course, proponents of the Cosmological Argument will have reasons to exclude possibilities 1 and 2. But am I on decently solid ground at least narrowing this down to these three choices, given that we buy the PSR? Thanks in advance!

• Re assumption 1: Why does this argument always assume there is a single cause for each event, like a line of falling dominoes? Surely a casual glance at the world shows this to be false. A million tiny little things have to happen for my parents to meet and make me and then I live my life and had breakfast this morning. It's more like a network or graph than a linear chain of causality. The linear causality model is a discrete sequence of events, like video frames. But there's no evidence that reality works that way. Perhaps causation is continuous and not discrete. Assumption 1 is unproven. Apr 30, 2021 at 21:25
• What if I weaken "cause" to "plays a role in causing"?
– Mark
Apr 30, 2021 at 21:34
• I'm not sure. If each event has multiple causes, you end up with a network or a graph. The infinite regress argument probably still works and my objection fails. My other scenario is continuous causality. Like a differential equation. You can approximate it discretely, but fundamentally it is never a frame-by-frame. So if you know the state at time t0 you can determine the state at time t1, but you can never enumerate all the uncountably many intermediate states. In this case I don't think the argument can be salvaged. And consider the open interval (0,1). Every point has uncountably many ... Apr 30, 2021 at 22:13
• (continued) predecessors, there is no first cause or first event, yet the entire chain of causality is bounded below. Perhaps God is more like a limit point in a topological space than the first natural number in Peano arithmetic. Continuous versus discrete. Apr 30, 2021 at 22:16
• You do not need PSR, self-cause is not relevantly different from no cause, and it is not specific to causation and the cosmological argument. These three options (infinite chains, dead ends and loops) can be formulated as a theorem of graph theory, and a version of it (with justifications instead of causes) goes back to ancient times. It is known as Agrippa's trilemma. For the cosmological argument specifically you need more even if 1 and 2 are ruled out, to rule out multiple dead ends in 3 and get to a single first cause. Apr 30, 2021 at 22:33

The version of the Cosmological Argument you present is a caricature that no significant philosopher ever defended. This isn't your fault. The version you describe is basically the version that is presented in most modern books and classrooms; it is what most modern philosophy professors think is the cosmological argument, but it isn't a serious argument that anyone serious ever made.

If you think about it for a minute, you can probably see that this must be the case. The Cosmological Argument is a part of a tradition of two thousand years of some of the best academic minds in Europe and the area around the Mediterranean. The very idea that a product of that school of thinkers would have produce an argument so dumb that it can be shot down by freshman taking their first philosophy class--that's an absurd idea.

One of the problems is that the Cosmological Argument depends crucially on the metaphysical foundations of the argument, and few people today really study medieval metaphysics, so they don't even understand the words that are being used in the argument. For example, "cause" very often doesn't mean what it means in modern language. It might not even be something that happens temporally before the effect; it might mean something more like "that which sustains the existence of a thing" (it means different things in different versions of the argument).

Also, any criticism of the Cosmological Argument that begins with "he just assumes" is wrong. The medieval scholars didn't "just assume" anything. They argued for each point extensively, often for dozens or hundreds of pages. These things they supposedly "just assumed" were consequences of a very detailed metaphysical theory, and if you want to refute one of these points, you have to first understand their argument for the point--and you won't get that argument in a one-paragraph summary of the "the Cosmological Argument".

I don't know if it's worth discussing the Cosmological Argument today, but I'm certain that it's not worth discussing a version that no significant philosopher ever defended.

• Thanks for your reply. I admit, I am not a significant philosopher. In the premise of my post, I simply wanted to carry out the exercise of narrowing down the logical possibilities as much as possible with the least amount of beginning assumptions possible, which I took to be the PSA.
– Mark
May 1, 2021 at 12:54
• 'The medieval scholars didn't "just assume" anything. They argued for each point extensively, often for dozens or hundreds of pages.' Scholastic thinkers would argue for their points extensively given the premises of Aristotelian metaphysics, but they didn't really argue for the soundness of Aristotle's metaphysics of substantial forms, the four causes, etc. May 2, 2021 at 1:15
• (cont.) Robert Pasnau is a prominent scholar of Scholastic metaphysics (see this revew of his book on it), see his comments at the bottom of p. 32 here: 'Because substantial forms were not challenged within the Aristotelian tradition, they were not defended or explained in any detail until the Renaissance. No consensus ever developed about what substantial forms were, and not even the most articulate of Aristotelians, medieval or Renaissance, explained the theory very clearly.' May 2, 2021 at 1:17

The possibility that something causes itself should be excluded as a cause would need to exist first before it could cause anything. This would apply also to the notion of creation.

The idea that A causes B is essentially ordinary physical causality, which is irrelevant here.

Thus, the notion of cause should be further specified as A causes B to exist, i.e., "A created B", which I think is the relevant sense of cause. We also have to specify that anything that exists was caused to exist by one cause only.

Given this, the first alternative offered in the question is trivially excluded. Several possibilities remain:

1. A finite chain of causes with no initial cause.
2. An infinite chain of causes with no initial cause.
3. A finite set of causes with one initial cause
4. An infinite chain of causes with one initial cause.

All these alternatives are compatible with both the existence of some god and the non-existence of any god. Without going through all the possibilities, we can say that all alternatives are compatible with the notion that a god created our world. However, they are also all compatible with the notion that something else created God, and something not necessarily god-like. They are also compatible with no god at all.

The reason that people exclude some of these possibilities is that they admit of non explicit assumptions that make their conclusion necessary. There is no mystery in logic and if it is not logical, it is not worth discussing since you can then admit it without discussion.

For example, if we assume that it is possible for something to create itself but that only a god could do that, then the conclusion follows that the universe ultimately was created by some god. Nothing really worth discussing.

Personally, I don't see any logical reason to exclude the possibility that something could exist that was not created by something else. Indeed, this seems true of reality itself, which exists without possibly having been created (by something else).

We could always assume that reality is God, but then this is just making the discussion not worth having, since we are unable to justify excluding the possibility that reality is not a god.

• I find the exercise interesting because of the logical consequences. Even if we exclude god from the discussion, you hope to get down to two rather mind-blowing possibilities: either something created itself, or there is a literal infinite of causes with no end. I don't know which of those I find more incredible. But the point of my exercise was just to logically get to those possible conclusions.
– Mark
May 1, 2021 at 12:57
• Also, how does your first possibility remain? If we have a finite collection of causes, either at least one causes itself in a loop of causation, or there is an initial cause. Certainly if we have a causal loop containing say "cause A", then A has played a role in its own creation, and we can in some sense say that A has created itself.
– Mark
May 1, 2021 at 14:03
• @Mark "something created itself" Personally, I exclude that possibility. You need to exist if you are to create anything and so self-creation is a logical impossibility. However, and this comes to broadly the same idea, it is logically possible that something exists without having been created. It may be for example a non-devine reality or it may be a devine one, i.e. God, who at some point decides to create our universe. May 1, 2021 at 16:56
• @Mark "there is a literal infinite of causes with no end" Logically possible but all alternatives I mentioned are equally logically possible. May 1, 2021 at 16:57
• @Mark "If we have a finite collection of causes, either at least one causes itself in a loop of causation, or there is an initial cause" No, why? In a finite chain of causes with no initial cause, the first cause is not caused. It exists without having been caused, just like God presumably would but without necessarily being God or God-like. You could say it is a first cause but because it is itself uncaused, the whole chain of causes exists and is uncaused, so we can also say that there is no initial cause. May 1, 2021 at 17:07