The Probabilistic Argument for Why Anything Exists At All Examined (van Inwagen, Nozick)

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Curious

7 min readJan 3, 2021

Perhaps the biggest question in all of philosophy is “why is there something rather than nothing?” or better put as discussed in the first video in this series, “why is there anything at all?”

What if the answer is that it’s just more probable that we exist rather than there being nothing at all?

If an infinite number of possible worlds could exist, and there is only one type of world with absolutely nothing in it, then it’s most likely that something will exist rather than nothing.

Imagine a dartboard that contains all possible combinations a universe can be. The very middle is a world that’s totally empty with no concrete or abstract concepts. If you close your eyes and throw a dart, chances are you’ll hit a world that isn’t totally empty.

This is called the probabilistic argument for existence and I’ll be covering the arguments for it from Robert Nozak and Peter van Inwagen, as well as the main refutations of it.

The probabilistic argument for existence is a necessitarian type response to the fundamental question which means it can be answered and there’s a logical explanation to the question. Something exists because it is a necessary truth.

Nozick’s Probabilistic Argument

Robert Nozick 1938–2002 — Professor of Philosophy at Havard — Image from Wikimedia Commons

Harvard philosopher Robert Nozik first made the probabilistic argument in his book Philosophical Explanations. In it, he actually gives several explanations for why there’s something rather than nothing, not because he necessarily thinks he has the answer, but as more of an exercise to shake up how we approach the question.

Nozik outlined two types of responses to the question “why is there something rather than nothing?” which he called egalitarian theories and inegalitarian theories.

An egalitarian theory means that all states are equal in the sense that they all require an explanation. For example, the state of nothing requires an explanation for existence just like the state of something.

An inegalitarian theory means that only some states need to be explained, while others are treated as “natural” states.

An example of an inegalitarian theory is classical mechanics, where rest is a natural state requiring no explanation, while something like acceleration has to be explained by citing the action of forces.

“Inegalitarian” theories use methodologies from physics and apply them to metaphysics incorrectly.

Now, I won’t go into Nozak’s inegalitarian theories for the fundamental question, mainly because the inegalitarian concept doesn’t make logical sense and seems to use methodologies from physics and applies them to metaphysics incorrectly.

Basically, one can’t make sense of the idea of a natural state unless we make sense of the forces that are supposed to bring the universe out of its natural state. But, no theory for what such a force might be was put forth.

Plus, I think maybe, Nozak seems to realize this and really tries to set us up for his egalitarian solution to the question which is taken more seriously.

Remember, this is the answer that states that all states are equal in their need for an explanation.

Because of this, we can assign the principle of indifference from probability theory to all states meaning nothing and something are equally probable.

The most extreme version of egalitarianism, which Nozick calls the “principle of fecundity”, states that “all possibilities are realized”, meaning every way a universe could exist does.

What does this mean?

First, since the principle of fecundity itself could probably exist, it would create itself since all possibilities of universes now exist. In some universe the principle of fecundity is true.

Then, since every probability exists and there can only be one type of probability in which there’s completely nothing, there is something rather than nothing since the probability of there being nothing is incredibly small.

Van Inwagen’s Probabilistic Argument

Peter van Inwagen 1942- Philosophy at the University of Notre Dame (Image from https://philosophy.nd.edu/)

Another version of the probabilistic argument for existence came from Peter van Inwagen in 1996. It basically claims the same thing but is outlined a little differently.

His argument goes as follows:

There are some beings.
If there is more than one possible world, there are infinitely many possible worlds.
There is at most one possible world in which there are no beings.
For any two possible worlds, the probability of their being actual is equal.

Basically, we know there are some beings since we exist and there is a possible world in which there’s absolutely nothing. Both of these can equally exist. Plus, if there’s more than one possible world, which there is, there are infinitely many possible worlds. Therefore, it’s more likely something exists rather than nothing.

If you have an infinite lottery the chance that you win is 0, he argues. If there are infinitely populated worlds, the probability of a world that’s populated is equal to 1. An empty world with absolutely nothing in it can exist but is as improbable as you can ever get.

Now, if you’re clever, you realize that according to van Inwagen’s own logic, it’s just as improbable that we draw our own world in the infinite lottery as the ‘nothing’ world. But, he says he understands this and just set out to prove that it’s more likely that there should be something rather than nothing.

Do These Arguments Explain Existence?

So, does a probabilistic argument for existence make sense? Is this a reasonable answer to why there is something rather than nothing?

I see two main issues with this argument.

The first is an issue with assuming probabilities. Philosophers such as Matthew Kotzen argue that it’s not logical to treat each possible world as equiprobable. Wouldn’t a world that has 3 material things be more likely to exist than a world with 1 million material things? What about worlds where there aren’t any material things but instead abstract objects and concepts. What about worlds where there’s absolutely nothing?

We have to know something about the operations of how the probabilities are distributed in the first place, which is impossible. Thus, the argument fails.

Plus, some probabilities exclude others. If there’s a possibility that nothing exists in this infinite multiverse then other things can’t exist. You can’t have one universe of nothing and one universe of something because that cancels out the universe of nothing.

Nozick acknowledged this issue and suggested that these universes exist in independent noninteracting realms. But this doesn’t really solve the issue because it makes his principle of fecundity no longer hold across all realms or universes.

The other reason, explained by philosopher Gonzalo Rodriguez-Pereyra is that both these probabilistic arguments actually fail to answer the question ‘why is there something rather than nothing’ in the first place.

All the argument does is make the question more complicated because instead of explaining why there’s one universe, ours, we have to explain why infinitely more universes exist.

Imagine someone asking, why is there a bird outside? It doesn’t make sense to answer “a bird exists outside because there exists another bird alongside it outside; hence there’s no good reason to ask why one bird is outside”.

It’s sort of like asking “how do you catch a bird” and answering “you catch two birds and let one of them go”.

Basically, the premises in both arguments are flawed and the argument doesn’t hold.

In Conclusion

So, hopefully, that explained the probabilistic argument for existence and in future articles, I’ll dive into better reponses to the fundamental question of existence.

Let me know what you think below and make sure to follow me on Medium.

The Rest of the Articles in This Series Including the Best Answer:

Part 1. Questioning the Question and Types of Responses:
https://thinkingdeeply.medium.com/the-types-of-answers-to-why-is-there-something-rather-than-nothing-7360f54253f

Part 2. The Probabilistic Argument for Existence (Nozak & Van Inwagen): https://thinkingdeeply.medium.com/the-probabilistic-argument-for-why-anything-exists-at-all-examined-van-inwagen-nozick-6fd7f209d11d

Part 3. Modal Realism and Probable Worlds Argument (David Lewis): https://medium.com/curious/does-modal-realism-explain-why-anything-at-all-exists-db3c43a45df9

Part 4. Necessitarian Theistic Argument (Leibniz & Craig) https://thinkingdeeply.medium.com/does-god-explain-why-there-is-something-rather-than-nothing-1ba79fd90639

Part 5. The Brute Fact Argument (Hume & Russell) https://thinkingdeeply.medium.com/does-the-brute-fact-argument-explain-why-is-there-something-rather-than-nothing-189eb0289aa9

Part 6. Axiological Arguments (Leslie, Rescher, Tegmark) https://thinkingdeeply.medium.com/do-abstract-objects-explain-why-anything-exists-at-all-axiological-arguments-for-existence-fc9b194a3af9

Part 7. Is the Question Meaningless? (Wittgenstein, Edwards, Positivism, Smith) https://thinkingdeeply.medium.com/is-the-question-why-is-there-anything-at-all-actually-meaningless-1c8f2ce96703

Part 8. The Best Response: https://thinkingdeeply.medium.com/why-is-there-something-rather-than-nothing-the-best-answer-e568f468459a