Does the Big Bang prove that the universe had a beginning?

TLDR: No, depending on what you mean by "prove."

Asking somebody to prove something is a way of raising the burden of proof to an unattainable standard. The idea behind our request is that we want the person to demonstrate certainty about their conclusion. That way if there's just an inkling of doubt, we can dismiss their case. In the real world, epistemological confidence (or strength of belief) comes in degrees. There are very few things we can be certain about, but certainty isn't necessary to function in life. We go on less than certainty about most things. Requiring certainty, then, is unreasonable in most cases.

For the purpose of this blog post, let's take it for granted that the big bang happened. I know there's a big stir on the internet about the James Webb Space Telescope calling the big bang into question. I don't think there's any merit to those doubts, but that's not what this post is about, so I won't go into it.

The question for today's post is whether the big bang, if it happened, proves that the universe had a beginning. If we're using "proof" as in establishes with certainty, then my answer is no. If the big bang were proof in that sense, it would mean that it would be impossible for the universe not to have a beginning as long as the big band theory is true. As long as it is possible for the big bang to be true without the universe having a beginning, then the big bang doesn't prove the universe had a beginning.

There are lots of models cooked up by cosmologists that are consistent with the big bang and that do not have a beginning. Most of these models are speculative and untestable. Most of them are probably wrong. But as long as they are possible, they show that it is possible for there to be a big bang without an absolute beginning. And that means the big bang does not show with certainty that the universe had a beginning.

But the fact that the beginning of the universe doesn't follow necessarily from the big bang doesn't mean the big bang isn't evidence for a beginning. Here, I'm using "evidence" to mean any artifact, data, or information that raises the probability of some conclusion. Since the beginning of the universe is more probable given the big bang than it would be without it, the big bang is evidence for the beginning of the universe.

Consider two scenarios - one in which the universe appears to be static and the other in which the universe appears to be expanding. Of these two scenarios, the expanding scenario at least makes it look like the universe had an origin as opposed to the static one which gives no indication. The origin would've been at or near the point in the past at which everything converged to a singularity. As you go back into the past, everything gets closer and closer together. There's a limit to how close things can get. Once they are all located at the same point, they cannot get any closer. If we look at the expanding universe and extrapolate back in time, it points to an absolute origin since everything is headed in the direction of infinite density.

Admittedly, there are horizons beyond which we can't look. One horizon is the epoch of recombination when subatomic particles first formed stable atoms. Before that, the universe was opaque. Recombination was the point at which the universe began to give off its first light. That light still exists as the Cosmic Microwave Background radiation (CMB). We can't see, using electromatic radiation, what the universe looked like before that no matter how powerful our telescopes become because no light was emitted prior to recombination.

We may be able to see earlier than that using gravitational waves, though. Gravitational wave astronomy is still new. I hope it advances to the point of being able to look at the universe earlier than the release of the CMB. There would be a lot we could learn.

Even if that succeeds, though, we run into another horizon. There is a point beyond which not even our best theories in physics can predict what we should expect the universe to be like. In general relativity, Einstein's field equation (and its various solutions) starts to yield nonsensical results when the curvature of spacetime approaches infinity. In quantum mechanics, the Heisenburg uncertainty principle would be violated if things were contricted to spaces smaller than the Planck length. Quantum mechanics and general relativity are two of our most successful theories in physics (and maybe in all of science), but if we try to use them to extrapolate back to a beginning, we run up against a wall.

It may be that we can push beyond this horizon if we can come up with a theory of quantum gravity that reconciles quantum mechanics and general relativity and allows us to describe the universe on scales smaller than the Planck length. But who knows if we will ever have such a theory? It may be that there isn't such a theory or it may be that such a theory is unknowable.

With all this fuzziness about what the universe was like beyond a certain point, it raises a degree of doubt that we can extrapolate from our observations about the universe now, using the known laws of physics, to an absolute beginning. That may always be the case.

I don't think this doubt should prevent us from inferring a beginning of the universe, though. Suppose the universe does not converge all the way to a singularity. Still, there's a limit to how far it can converge. At some point, it can't get any denser. Only one of two things can happen once you extrapolate to the limit of how dense the universe can get. Either whatever is left came into being, or it has always existed. If it has always existed, then why did it just begin to expand 13.8 billion years ago and not any sooner? After all, it would have had an infinite amount of time in which to do so. Whatever the reason or cause for why the universe began to expand when it did, that cause or reason would have always been there. I think the big bang points to a beginning of the universe even if we don't know what the universe was like beyond a certain point.

It may be that the beginning of the universe is the point at which our theories do make sense. The fact that we cannot push them beyond a certain point may be owing to the fact that the universe can't exist beyond that point, which in turn, means that's the beginning. Maybe the universe had some finite curvature and density at its beginning, avoiding all the problems of infinities, and avoiding the violation of any known laws.

This is all speculative, of course, but the speculation that the universe had a beginning is at least based on what we know. Based on what we know about the expansion of the universe and the laws of physics, it looks like the universe had a beginning. The fact that there are speculative models in which the universe didn't have a beginning doesn't change this fact. There's nothing in our evidence that makes it look like any of those speculations are true. There's nothing we can point to that would remotely suggest the universe had some finite density for infinite time before expanding.

So, while I don't think the big bang shows with any certainty that the universe had a beginning, I do think it shows with some positive probability that the universe had a beginning. It at least points to a beginning. It's the sort of thing we would expect if the universe had a beginning. It certaintly makes it look more like the universe had a beginning than it would if the universe was not expanding or contracting. So I think the big bang is evidence for the beginning of the universe even if it's not proof.

Subconscious Reasoning

We are reasoning machines, but most of the reasoning we do isn't explicit and formal. Aristotle attempted to formalize our reasoning methods by recognizing laws of logic, including syllogisms that express laws of logical inference. Using these tools in a formal way allows us to recognize and avoid making mistakes in our reasoning. It also helps us understand what people are saying and thinking if we can formalize what they say.

Consider this conversation:

Sam I Am: I may have had Covid a month ago, but I'm not sure.

Doctor: Oh, if you had Covid, you would know it.

Sam I Am: In that case, I definitely had the flu.

This conversation didn't actually happen, so there's no need to nit pick about the fact that it's possible to have Covid and not know it. That's irrelevant to the point I'm trying to make.

Anywho, it might seem like I made some big leap in logic to conclude that I had the flu from the fact that if I had Covid, I would've known it. But there's some unstated premises in my reasoning as there almost always is in our day to day conversations. If I were to formalize my reasoning, it would look like this:

1. If you had Covid, you would know it.
2. I do not know it.
3. Therefore, I did not have Covid.

1. I either had the flu, or I had Covid.
2. I did not have Covid.
3. Therefore, I had the flu.

Formalizing my reasoning reveals that I used two different kinds of syllogisms. The first one uses the modus tollens syllogism, and the second one uses the disjunctive syllogism. Notice that the second premise in my second syllogisms says the same thing as the conclusion in my first syllogism. That's why the first syllogism comes first. I have to establish that conclusion before I can use it as a premise in my next argument. To simplify this sort of thing, we can combine all the premises and inferences into one argument, which eliminates repetition. In my case, it would look like this:

1. If I had Covid, I would know it.
2. I do not know that I have Covid
3. I either had the flu or I had Covid.
4. Therefore, I did not have Covid (this follows from 1 and 2 by modus tollens).
5. Therefore, I had the flu (this follows from 3 and 4 by disjunction).

Whenever we're talking to somebody, and they seem to make a leap of logic, or they come to some conclusion we disagree with, we tend to want to fill in the gaps where they didn't explicitly state all their permises. If we're charitable, we fill the gaps with whatever we think must be assumed in order to render their argument logically valid. Often, we don't even state the premise ourselves. If we disagree with their conclusion, the reason we give is always some denial of what we think the hidden premise was.

Now consider the following conversation:

Jim: I don't think I had Covid.

Bobe: Why not?

Jim: Because if I had Covid, I would've known it.

Notice that if we tried to formalize this into a syllogism, there would be a missing premise.

1. If I had Covid, I would have known it.
2.
3. Therefore, I did not have Covid.

What is the hidden premise? It doesn't take too much creativity to recognize that Jim's reasoning assumes that he did not know he had Covid since that's the only way to render the reasoning valid. If you were trying to understand Jim, you would likely assume that's his hidden premise. He could've said something like this:

Jim: I don't think I had Covid.

Bob: Why not?

Jim: Well, I didn't have any of the symptoms of Covid.

Bob: It's possible to have Covid without having symptoms.

There are a couple of things going on in this conversation. First, Jim is making an argument to justify his conclusion that he didn't have Covid. Second, Bob is objecting to Jim's argument by denying what he takes to be Jim's hidden premise.

At first glance, Jim's argument might seem unobjectionable, but even this line of reasoning contains a hidden premise, which can be exposed by trying to formalize the reasoning into a syllogism.

1. I did not have any of the symptoms of Covid.
2.
3. Therefore, I did not have Covid.

The best candidate for the hidden premise that jumps out at us is this: If Jim had Covid, he would have had symptoms of Covid. If that were the hidden premise, the conclusion would follow by modus tollens. Since that's the only premise Bob can immediately come up with, he fills in the gap and denies that premise. If the hidden premise is false, then Jim's argument is unsound even if it's logically valid.

Notice that Jim and Bob had this conversation without either of them ever stating the hidden premise in Jim's argument. This sort of thing happens every day. It happens in regular conversation, in heated arguments, and in civil debate and discussion.

There is a danger in filling in the gaps when somebody else delivers an argument with hidden premises. The danger is that you will fill the gaps with the wrong premise. If you do that, and the other person notices, they will think you are misrepresenting them. They may either chalk it up to an innocent misunderstanding, or they may think you're misrepresenting them deliberately. It's hard not to want to fill the gaps when the missing premise seems obvious, but we sometimes fill the gaps with whatever jumps out at us even if there are other options. We do this because we're hasty and sometimes uncharitable.

When I've had formal debates, I've tried two different tactics when responding to my opponent's argument. One tactic is to acknowledge that there's a hidden premise. I'll say something like, "Your argument assumes such and such because that's the only way to make the argument go through." Another tactic I use is to formalize their argument, leave one of the premises blank, and say that unless my opponent fills in the blank, his argument is invalid. I can only remember using that second tactic one time in a debate. I'm reluctant to use that in a formal debates because it requires more back and forth before getting to the point, and there are limited rounds. Usually, I make my best guess at the hidden premise. To avoid being accused of strawmanning their position, I make it known that I'm only guessing what their hidden premise is. Then I'll say something like, "If I've understood you correctly, here's the issue I have with your arugment. . ."

It is interesting to me that in most debates, arguments, and discussions I've seen or been involved in, the disagreements seem to hinge on the hidden premises rather than the explicitly stated premises. It is also interesting to me to recognize that a lot of reasoning - even valid reasoning - happens without even exlpicitly thinking about all the premises we're invoking. We just jump from one fact or observation to our conclusion without explicitly thinking about the hidden premise or the logical rule of inference we used to draw the conclusion from the stated and hidden premise. In many, and possibly most, cases, we reason subconsciously. But formalizing our reasoning can help us be more clear. Formalizing our buddy's reasoning can help us understand him. Formalizing our reasoning can help us recognize and avoid mistakes in thinking. It can also improve our reading compreshension.

We should be thankful for Aristotle.