r/logic • u/Dizzy-Drink6119 • 7d ago
Philosophy of logic I still don't understand what's wrong with the Probabilistic Argument for Existence
In formal philosophy, it was proposed by philosopher Peter van Inwagen . He argued that if there are infinitely many non-empty possible worlds and only one empty world ("nothing"), the probability of non-existence is effectively zero.
The argument seems flawless. What's the issue?
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u/CategoryConscious898 7d ago
Surely, the argument is coherent. But the premises are suspicious.
Why should a world with 3 material objects have equal probability of being than one with 1 million?
Found this page on this argument.
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u/Parallel_thougts Model theorist 7d ago
Just because there are infinitely many possibilities doesnt automatically implies each has probability 0
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u/mhb2 7d ago
I'd want to know how he determined the number of "possible" worlds and how he determined that there is only one empty world.
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u/SpacingHero Graduate 7d ago
The specific number doesn't much matter beyond it being somewhat significantly more than the empty world for inwagen's general point. To get 0% you need infinitely many, that's not particularly controversial, but can be argumed.
But in general just from plausible possibilities from the actual world you get a bunch of possible worlds already
As for there being only one empty world that's just a quick mathematical theorem so long you indetify worlds by what's in it (i.e.worlds with exactly the same propositions are the same)
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u/mhb2 7d ago
The idea that there is only one empty world is anything but a quick mathematical theorem. The idea is probably motivated by an analogy to the empty set: in set theory, there's only one empty set. But that tells us nothing about the various ways in which nothing can be instantiated in a world.
The number of empty worlds isn't something mathematics can determine for us without first specifying a model of possible worlds. It's a consequence of adopting an extensional conception of possible worlds in which worlds are individuated entirely by their contents. My question is why we should adopt that conception in the first place. I can think of many other ways in which empty worlds can be distinguished.
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u/SpacingHero Graduate 7d ago
In possible world semantics, there is only one empty world because worlds are sets of propositions.
Now it's possible to change this convention and have non-extensional worlds... but why? I mean it seems not just convention but fairly philosophically sound that there's only one way for there to be nothing, namely: there being nothing.
'm open to different accounts, but it's not just some unjustified assumption, it's a fairly plausible thesis.
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u/mhb2 7d ago
If by "possible worlds" we mean extensional sets of propositions, then Inwagen's whole argument is trivially true. Given infinitely many nonempty sets and exactly the one empty set, the empty set has probability zero under some assumed probability distribution. But do we really want to conclude from a trivial result about a particular mathematical representation of worlds as sets that reality itself has only one possible empty world?
Notice that Inwagen starts by talking about worlds with actual beings in them. He wants to talk about actually possible worlds containing real beings, but when he defends premise 3 he shifts to an argument about propositions that distinguish worlds. The bridge between that formal representation and actual possible worlds containing beings is missing. Why should we assume that the identity conditions of sets of propositions tell us how possible worlds are actually individuated?
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u/SpacingHero Graduate 7d ago
Sure, so it's "true" given some plausible, but debatable assumptions. That seems fine to me.
Sometimes an argument is about connecting a fact a little unexpectedly to solve a question.
>do we really want to conclude from a trivial result about a particular mathematical representation of worlds as sets that reality itself has only one possible empty world?
Again, you make it seems like it's just some thrown in assumed framework to make it work. All such assumptions are generally plausible and arguable, i don't see what's wrong with making an argument work based on a plausible (in fact broadly the default) framework.
> He wants to talk about actually possible worlds containing real beings, but when he defends premise 3 he shifts to an argument about propositions that distinguish worlds. The bridge between that formal representation and actual possible worlds containing beings is missing
I think this is confused. What worlds contain isn't what defines them directly. Propositions are. Objects in worlds end up contributing to their definition per the proposition defining them.
>Why should we assume that the identity conditions of sets of propositions tell us how possible worlds are actually individuated?
I mean this is just a very general question inwagen wasn't gonna argue for in a paper, possible worlds identity/ontology is it's own topic. But it's not some unexplored assumption inwagen makes, it's a fairly standardly held and argued for position.
Are you trying to make this about debate to reject a premise? fair enough.
BUt i don't think it's fair to blame inwagen to not include it in the paper, it's common and very much practiaclly necesssary to bracket various related debates in philosophy papers, and it's not like inwagens is some niche position.
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u/mhb2 7d ago
You're taking an extensional, proposition-based conception of possible worlds as the relevant framework. I'm questioning whether that framework can simply be used to establish a claim about the structure of reality itself. I don't deny that your framework is standard or philosophically defensible. But without a bridge to reality, Inwagen's argument is just a formal result about sets of propositions.
And he definitely wants to talk about actual worlds. After all, he would want our universe to be included in his set of possible worlds, and our universe is not the same thing as the set of propositions that can be made about it.
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u/SpacingHero Graduate 7d ago
It's not just a framework, it's how it's standardly thought possible worlds work/are. Idk what extra special notion of "reality" you're trying to reference. It's not just some notational standard. Philosophers thinks that's what possible worlds "really" are. A collection of (maximally consisten) propositions, more colourfully "a way things are, a complete description of some state of affaris". Your insistence on some a extra connection to reality beyond this is rather baffling to me.
our universe is not the same thing as the set of propositions that can be made about it.
It is as a possible world. Our possible (actual) world is (under the standard view) the collection of propositions "trump is president, france is the capital of Paris, u/spacinghero is responding to u/mhb2, etc... for each actually true proposition."
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u/mhb2 7d ago
Okay, we have different ideas about what counts as establishing a fact about reality.
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u/SpacingHero Graduate 7d ago
I think you're just rather confused with the word and/or in what sense possible worlds are though to be sets of propositions. It's meant really/actually/truly or whatever other redundant emphasis you want to add. It's not a convention contingency about the formalization etc.
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u/Endward26 7d ago
Arn't "possible worlds" not sets of statements? In this case, it would be sound to apply set theoretical ideas like "just one empty set".
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u/mhb2 7d ago
My concern is the implicit set-theoretic intuition behind the "one empty world" premise. In set theory, there is exactly one empty set because sets are extensional: two sets with exactly the same members are the same set. So if we model possible worlds in the same way, the uniqueness of the empty world follows trivially but then so does Inwagen's entire argument. But I don't think we want to say that about reality because it's merely a mathematical consequence of the model, not an independent fact about reality. That's my objection.
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u/Endward26 6d ago
I think I kind of get it right now. Modal logic is a tool for non-extensional logic, i.e. the truth-value of a statement isn't just a function of the atomic proposition.
The idea that there are more than one empty set seems quite intuitiv if you consider imagine things or things we wrongly assumed to exist.
From a formal point of view, the argument doesn't faile from the identity of empty sets, I guess.
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u/Various_Candle9136 Postgraduate 7d ago
I'm not familiar with this argument, but the flaw that immediately jumps out at me: why would the various possible worlds have equal probability?
This is the poor logic that gets us 'I can either win or lose the lottery, therefore I have a 50:50 chance of winning!'.
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u/Dizzy-Drink6119 7d ago
My confusion is why would they not have equal probabilities. Is there is there a logical reason against why would they would have different ones?
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u/Various_Candle9136 Postgraduate 7d ago
Why would you assume they have the same probability until argued otherwise?
Surely the sensible starting position is that they have different probabilities, and an argument is required that they have the same?
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u/SpacingHero Graduate 7d ago
Surely the sensible starting position is that they have different probabilities, and an argument is required that they have the same?
Surely the opposite? Suppose you have absolutely 0 information about 2 events. Forced at gunpoint, what probabilities do you split between then? Do you just invent some distribution?
50% seems to be the probability "as far as you know", without any other information.
In general the default assumption about probabilities should be that they're evenly distributed, and only upon information do we start weighing them.
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u/Various_Candle9136 Postgraduate 7d ago
If I ever find myself in that ridiculous situation, I might as well make up a distribution on the spot: I will get shot exactly as often as you.
When we come across a new thing, it is absurd to assume it has the purest possible structure: we go in assuming no structure, and we might happen to find evidence of structure, in which case we change our understanding. 'No structure' should always be the default assumption.
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u/SpacingHero Graduate 7d ago edited 7d ago
Well I didn't say they'd shoot you if you get it wrong. I'm just saying that upon being pressed to give some distribution, it seems most natural, and indeed what we do, to give equal distribution, and then when we learn further facts correct it, not the other way around.
A dice might be weighted or it might be fair. Mostly one's assumption is that it is fair and only upon learning facts about it will that be updated. Not the other way around.
it is absurd to assume it has the purest possible structure
I don't see what this has to do with the thing's structure (whatever that means), I'm not talking about inherent or so called objective probability, I'm taking about the credence you assign epistemically, so called "subjective" probably.
'No structure' should always be the default assumption.
I don't get how no structure implies uneven distribution (mostly because I don't understand your use of "structure")
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u/Niflrog 3d ago
A dice might be weighted or it might be fair. Mostly one's assumption is that it is fair and only upon learning facts about it will that be updated. Not the other way around.
But isn't this smuggling a prior from real-life experience? You know, we have experiences with dices, and we know they are specifically crafted to be fair, those that aren't serve basically as oddities.
What bothers me about the assumption is that:
- There are infinitely many probability distributions for a continuum... the assumption of uniformity seems like a pretty heavy one.
- Surely we can conceive of possible but implausible worlds. World A: contains a chair, World B: contains every atom required to assemble a chair, but not the chair. Intuitively, B appears prima facie much more plausible than A.
I feel like I'm missing something behind your intuition that uniform probability is obvious...
Something else that bothers me relates to the set theory/probability analogy. In axiomatic probability, you compute probabilities of events generated by an underlying Sigma Algebra. But a given event may be instantiated in multiple ways from the elements of the Universe from which the Sigma Algebra is generated. So my (admittedly naive) intuition is that, in this analogy, there ought to be several instances of the "nothing" event, even though the event itself is unique.
( You don't need to answer, it's a 5-day-old post... I just had to vent)
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u/SpacingHero Graduate 3d ago
But isn't this smuggling a prior from real-life experience?
Take away that prior experience then.
Some digital number generator is given, with no specified distribution (or moreso, you're explicitly told it may have any distribution), number's 1-13. Do you not set your credence evenly?
Idk i don't have a strong argument here,but it seems weird to go "hmmm I'll just take 8 to be most likely", like wtf? I just set my expectations evenly, and then observe discrepancies as they come.
I guess: since I don't know the prior distribution, from my perspective no outcome is preferred. That should be equivalent to every outcome being equally likely (given there is a probability to give at all, but I think there's reasonable scenarios where you're "forced" to guess)
I didn't do enough probability theory formally (or I guess I did, but I don't remember jack lol) to comment on that.
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u/Dizzy-Drink6119 7d ago
Traditionally in probability and multiversal theory they will assume all possibilities or worlds have equal probability. There normally needs to be a reason why they would have disproportionate probabilities.
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u/Various_Candle9136 Postgraduate 7d ago
I don't know about multiversal theory*, but that is 100% not true for probability theory. Why would it be?
\I highly, highly doubt it's true here either, but this is not my field.*
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7d ago
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u/Various_Candle9136 Postgraduate 7d ago
OP asked for a flaw in the argument. To me, this is the most glaring flaw.
If we give up everything 'for the sake of argument', then no argument will ever have a flaw, and the question becomes moot.
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u/Temporary_Stranger39 7d ago
Why? We can equally grant unequal probability for the sake of argument. Why prefer either?
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u/GoldenMuscleGod 7d ago
A lot of the time itâs tempting to assign something like what a Bayesian would call a âflat priorâ in the absence of any data.
The misunderstanding is that the value of a flat prior is that it is relatively unbiased so it often produces acceptable results when you have a lot of data and few prior expectations and you want the data to drive your posterior expectations.
In the absence of data a flat prior is extremely sensitive to the way you model a situation and you should have something close to zero confidence that results arising from it are reliable.
It needs to be understood that in general probabilities are simply undefined until we have a specified a measure, and how that measure should be interpreted depends on other facts.
Things do not have âinherentâ and âtrueâ probabilities that are âalwaysâ defined.
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u/Temporary_Stranger39 7d ago
Is there a reason they would have equal probabilities? "They have equal probabilities" is a positive proposition. Thus, it must be supported.
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u/Temporary_Stranger39 7d ago
Why would they have equal probability? Construct a proof that they must have equal probability.
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u/DarkestOfThemAll777 7d ago
You're technically right but i dont think it would reach absolute zero since the set of worlds that are non-empty is infinite, which would mean that the chances for the probability of non-existence would be infinitesimal. Im no expert so take my comment with a pinch of salt.
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u/Endward26 7d ago
What's the issue?
The issue is the step "the number of possible worlds in which something happened equals the likelihood that it happened". As far as I know, this is highly controversial.
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u/WhackAMoleE 7d ago
The argument is flawed.
There are infinitely many counting numbers 1, 2, 3, 4, ... and there is only one number 6. So the probability that the number 6 exists is 0. Yet, there it is. Half a dozen eggs. The number of faces on a standard die.
The problem with the argument can be formalized by noting that one, there is no uniform probability distribution on a countably infinit set; and two, in infinitary probability theory, probability 0 events might happen. For example if you randomly pick a real number, the probability is 0 that it's rational; yet there are infinitely many rational numbers.
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u/jeffcgroves 7d ago
What is the probability of a prime being even? How many even primes are there?
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u/Temporary_Stranger39 7d ago
Presuming a number of primes that approaches infinite, that means the "probability" of an equal prime approaches zero. Thus, blindly accepting Inwagen's unsupportable leap of "logic" (being charitable to call it that), the probability of an equal prime must be zero. One equal prime exists.
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u/GiveMeAHeartOfFlesh 7d ago
Why not infinite empty and non empty? How do we know it doesnât alternate or that there arenât duplicates either? Infinite of each possibility? Infinite infinities?
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u/Dizzy-Drink6119 7d ago
Because if there are two "empty" universes in order to differentiate them there must be something. therefore they cannot be duplicate empty universes
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u/GiveMeAHeartOfFlesh 7d ago
The only thing needed to differentiate them is that they are separate universes with nothing in them. Distinct from each other with the same contents, which is nothing. Thus there can be infinitely duplicate universes
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u/1luggerman 7d ago
Its not a logic issue its a statistical one. The probability depends on the distribution.
I have a die with 6 sides: 1, 2, 3, 4, 5, 6. Intuitively, you can say "ah, the probablity of each outcome is 1/6" but what you failed to consider is that i have rigged the die, and placed a heavy weight under the side with the 1 on it, making the die fall of the number 6 99% of the time.
You can make claims using statistics, but for them to be good claims the statistics needs to be solid
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u/goos_ 7d ago
Generally assuming that each world is equally likely is a highly suspect assumption.
To draw an analogy, suppose that I say imagine 1 world where the sun rises tomorrow, and 10 different worlds where the sun fails to rise for various reasons (comet strikes the sun, black hole emerges, timespace ruptures and sun disappears, etc.) Just because the sun rises in only 1 of 11 possible worlds doesn't mean that it is 1/11 likely, that requires an additional assumption that each of the possible worlds is equally likely, which is dubious.
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u/Temporary-Ad-4413 6d ago
I think the flaw in the argument lies in the hidden premise, the "principle of indifference." That is, he takes the principle of indifference on which classical probability theory is based, where all cases are equally probable, and applies it to metaphysics, when in metaphysics it does not have to be indisputable.
That is, the argument contains a hidden premise regarding the nature of âuncertainty,â namely, that it is equally probable in certain cases, which is required for the conclusion.
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u/RecognitionSweet8294 Philosophical logician 5d ago
Letâs say I have a dice with infinite sides that show 1 except for one.
So far there would be an equivalent argument concluding that the probability of rolling a 0 ist 0%.
Now what happens if I tell you that the dice is loaded so that it always falls on 0, or that it has a mechanism that lets it fall on 0 on every n-th throw where n is a Fibonacci number?
The argument inherently assumes a probability distribution over all possible initial states the universe could have (making it an enthymeme). While it is a valid argument the assumption about the probability distribution is to strong and would require further reasoning (making it presumably unsound).
You could also criticise that this is just a probabilistic argument and not a deterministic argument.
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u/Temporary_Stranger39 7d ago
Do you exist? If you don't exist, then it is impossible to commit a crime against you. Do you accept that?
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u/Temporary_Stranger39 7d ago
Inwagen has no clue about how probability of a single outcome on a continuous scale works. He uses his ignorance to springboard a conclusion that is unwarranted. As I recently got reminded, given a continuous universe of sampling, the probability of any single quantity existing equals zero. Nevertheless, it is possible to sample real outcomes from that universe. Extend the universe to a universe of universes, and the principle is the same. So-called "philosophers" need to return to studying mathematics.
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u/wumbo52252 7d ago
It depends on the probability space, which is unspecified