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For me, intuitively the answer seems to be yes. But I don't know how this could be justified a priori. The hypothesis "x does not exist" seems not to be simpler than the hypothesis "x exists". By the principle of indifference, both options should therefore be assumed to be equally likely. But this doesn't seem right to me.

The question also could be equivalent to this one:

Is it, a priori, more likely that the complexity of the universe is smaller than larger?

Because a universe where less exists is presumably less complex and vice versa.

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    How unknown is the object? If nothing is know at all this becomes is it more likely that there is something rather than nothing, and I'd say that it is overwhelmingly more likely that there is. And sorry, but I am missing why the boldface question is equivalent to the title one, or even how they are connected at all.
    – Conifold
    Sep 13, 2017 at 23:07
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    "Unknown" says it all: unknown. But if you are nitpicking, ask yourself what the word "likely" means. I do not know, but I think this seemingly trivial subject is huge.
    – George Chen
    Sep 14, 2017 at 13:51
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    You will be hard pressed to find a philosopher today who believes in Kantian style justificatory a priori. The "a priori" recognized today are fallible presuppositions, loosely based on past experience, used to build hypothetical explanations and models. The order of justification is reversed, it is the a posteriori success of explanations that justifies the "a priori". If you start from blank slate then the principle of indifference will tell you that x existing and not are equiprobable, but unless you can use this to explain something it goes nowhere.
    – Conifold
    Sep 14, 2017 at 20:01
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    pray tell, what on earth does "a priori an unknown object does not exist". can you see the problem? the propososal ("unknown object") already assumes what you're trying to establish. your question is perfectly meaningless.
    – user20153
    Sep 14, 2017 at 20:23
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    i.e. "an unknown object" already tells us there must be such an object - otherwise it could not be an unknown object.
    – user20153
    Sep 14, 2017 at 20:26

4 Answers 4

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Frequentist approach
Hypotheses x exist and x does not exist are complimentary: the object either exists or does not exist with probability 1 (i.e., 100%)

In research context, if trying to show existence of something, we would take x does not exist as the null hypothesis and x exists as the alternative hypothesis. We then would then collect data and estimate (using some model) the probability of the null hypothesis being true. Provided that this probability is lower than a priori significance threshold (which we agree upon before collecting the data), we would reject the null hypothesis.

Bayesian approach
In Bayesian approach probability is simply our belief in something, which we adjust according to the evidence available. The set of all the things actually existing can be thought of as a subset of all the things imaginable - that is, the subset of the actually existing this is "smaller". We could even strengthen the relation between these two sets by stating that to any actually existing object corresponds an infinite number of imagined ones. That is an arbitrary fruit of imagination, like the notorious Invisible Pink Unicorn are more likely not to exist than the other way around.

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Well the issue with the principle of indifference is that it only applies if there can be only one item in a set. For instance if you have 4 possibilities that all contradict each other, and thus only 1 can be true, you're looking at a situation where most are false, and it is most likely any one is false. However if you take 4 possibilities that do not contradict each other, and multiple can be true, it is also possible that most or even all of the possibilities are true, and thus you cannot say that it is unlikely for any particular one to be true.

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  • But that's the point. We actually have here two contradicting possibilities, haven't we? "X exists" and "X doesn't exist" contradict each other for any X.
    – Max
    Sep 14, 2017 at 7:42
  • That isn't really the meaning of this rule though, and given two possibilities you would only get that there is a 50% chance of something existing, which does not indicate it probably does not.
    – Braydon
    Sep 14, 2017 at 12:59
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    But that's exactly what I was asking about: Can it really be rational to treat the hypothetical existence of some x as equally likely as it's hypothetical non-existence, as the principle of indifference seems to suggest? I don't know if you share this intuition, but to me it seems much more likely that an object, of which you do not know anything about whether it exists, does not exist than that it does. To put it in another way: Can it really be rational to expect the hypothetical existence of infinitely many unknown hypothetical objects with probably 50% each?
    – Max
    Sep 14, 2017 at 14:37
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Before answering this question, one must ask what it means. What does it mean to calculate the probability that A exists? If it is unknown, should it even be given a non zero probability?

It seems to me that the only correct answer is to say that the question itself is vacuous and the answer doesn’t seem to map into reality in any meaningful way. For example, if I said that there is a 40% chance aliens exist. What does that mean?

If you take a frequentist approach, it’s clearly meaningless. We don’t have multiple “trials” or worlds where we can test whether or not 40% of them have aliens in them. If you take the subjective approach, which is how much of a belief you should have, you still deal with problems. How, or in what way, can you map your subjective credence into reality? If a person feels like there is a 40% probability that aliens exist, how does this translate into reality? And how does one determine their credence?

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  • vacuous is a good word in this context.
    – Marco Ocram
    Jul 5 at 11:17
  • The world is full of one-off events, nonetheless you successfully assign probabilities to them all the time.
    – Max
    Jul 6 at 10:21
  • Define successful
    – thinkingman
    Jul 6 at 23:42
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There are two contexts in which this question can be posed : (1) in your own case and (2) in the case of an agent without experience. 'Unknown' can mean 'unknown that it is' or 'known what it is'. I take it that both senses are implied.

1 If 'a priori' means 'prior to or independent of experience', then (I think) you cannot properly ask the question concerning yourself since you already have experience, and specifically experience of coming to know objects previously unknown in your experience. Inductively, but not a priori, this gives you good grounds for supposing that if you have encountered previously unknown objects in the past then you will also encounter them in future.

2 In the case of someone who has no experience of knowing any objects, I don't see how this person could have any idea of the probability or otherwise of there being unknown objects since no known object has been encountered. 'Unknown object' contrasts with 'known object' but ex hypothesi for this person there are no known objects to contrast with.

3 I think there is a general problem with a priori probability if we take a priori in anything like its standard sense (as above). Probability - likelihood - is probability on the evidence or given certain data :

P (A|B) - the probability of event A, given event B. But a priori, no events are or can be given or any relevant experience. So much is contained in the very idea of the a priori. So while it is interesting to speculate on the probability of there being unknown events, I don't think the a priori is the standpoint from which to approach the question.

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