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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 '17 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 '17 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 '17 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 '17 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 '17 at 20:26
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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.

  • 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 '17 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 '17 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 '17 at 14:37
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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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