Posted by aftermathemat  1/22/2018 7:45 am | #1 |
I believe I've stumbled upon an argument for PSR that is quite interesting. Have a look, especially those of you who are fellow theists who are knowledgable in classical philosophy and the literature on the PSR:
Brute facts are things that exist or occur or happen for no reason whatsoever. It is quite obvious then, and has been clearly demonstrated by others (Pruss et al.), that one cannot assign any probability to brute facts. But what is interesting is that this is not a case where brute facts do have an objective probability, but it's just that we cannot know what the probability is. We actually know that, ontologically, brute facts do not have any probability whatsoever.
They are neither likely (>0.5), nor unlikely (<0.5). They are not 50-50, and they also aren't anything left or right of that either. They just don't have a probability, period.
Now, probability is defined as being in an interval between 0 and 1, and let's define it that 0 means a thing cannot happen in principle (square circles) while 1 means that they are absolutely necessary (mathematical truths, laws of logic). Anything that is not 0 or 1, is only possible. But where are brute facts then? They are clearly not anything in the set of <0.1, 0.9> which means that brute facts are either impossible (0) or necessary (1). If the former, PSR is true. If the latter, EVERYTHING is a brute fact. So this puts the PSR denier in a dillema.
Another way to look at this is that possibility implies probability, and if we want to check possibilities, we would have to look at the interval between 0 and 1 because 0 and 1 are logical limits which form the space of possibility. But brute facts are NOT located in this interval, as mentioned earlier. Therefore, brute facts do not belong in the realm of possibility. Therefore, brute facts aren't actually possible. The crucial premises to defend here would be that having a probability of 0 implies impossibility, while 1 implies something like necessity, and that the possibility of a thing does imply something like probability.
What do you think? Some friendly feedback would be appreciated.
Last edited by aftermathemat (1/22/2018 7:47 am)
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Posted by Ouros 1/22/2018 8:03 am | #2 |
Except that an event with a probability of 0 may happen in theory; if you randomly choose a number beetween 0 and 1, the chance that you pick any of them equals zero, but you're sure to pick one of them.
It's a subject for probability theory, with the events that are almost surely, wich mean that they have a 1.0 probability, for example.
That said, I think that there is something to say about your idea that something wich can't even attribute a subjective probability seems like simply impossible.
Also, other consequences with the destruction of probabilities by authorize brute facts is that you can't use induction, abduction, and skeptic scenarios aren't escapables anymore.
Last edited by Ouros (1/22/2018 8:04 am)
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Posted by aftermathemat 1/22/2018 8:25 am | #3 |
Ouros wrote:
That said, I think that there is something to say about your idea that something wich can't even attribute a subjective probability seems like simply impossible.
Also, other consequences with the destruction of probabilities by authorize brute facts is that you can't use induction, abduction, and skeptic scenarios aren't escapables anymore.
Actually, it's even worse then that. We actually KNOW that brute facts by their very definition do not have ANY probability whatsoever. It's not that we can't give brute facts some sort of subjective probability, it is that we positively know that brute facts do not have any objective probability. So it's not merely that brute facts subjectively lack a probability, they lack any actual objective probability as well.
What this means is that we cannot even coherently say that brute facts have a probability of 0. Or a probability of 1. They are neither guaranteed, nor are they impossible. And they are neither bound to happen as in your number scenario, nor are they bound to never happen.
The above actually seems like a denial of the Law of Excluded Middle here, because what alternative is there? How can we even begin to describe brute facts at all now, without doing something analogous to rejecting the LEM when attempting to describe them?
Last edited by aftermathemat (1/22/2018 8:28 am)
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Posted by Ouros 1/22/2018 9:02 am | #4 |
Actually, it's even worse then that. We actually KNOW that brute facts by their very definition do not have ANY probability whatsoever. It's not that we can't give brute facts some sort of subjective probability, it is that we positively know that brute facts do not have any objective probability. So it's not merely that brute facts subjectively lack a probability, they lack any actual objective probability as well.
I'm OK with that, I follow you on 100%. For me, it's just that subjective evaluation was "larger" than objective one. I will think about this.
Now, I think that you didn't prove that "possibility implies probability". You have shown that probability implies possibility, but not the opposite.
Also, maybe it's a little problematic for libertarian free will; if you can't attribute a free action a certain probability, that would also mean that it's illogic, and if you can, then is it a free act?
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Posted by aftermathemat 1/22/2018 9:27 am | #5 |
Now, I think that you didn't prove that "possibility implies probability". You have shown that probability implies possibility, but not the opposite.
I think that something broadly like that can be proven if we take 0 to be impossibility, and 1 to be necessity, and all things in between them to be possibility. In this case, brute facts either wouldn't be in the realm of possibility and would instead be either impossible or necessary, or they would violate the LEM because they would be neither possible, impossible or necessary.
On the other hand, another argument that I think I can see the faint shadow of here for PSR would that, if brute facts were possible, order and chaos would be indistinguishable.
Say for example that PSR is the best explanation for why things don't constantly and chaotically pop into existence, which would be open if brute facts were allowed. A PSR denier could just say that the lack of any new objects and even the appeareance of order is also just a brute fact. The problem with this answer would be that it would still leave open the possibility of things popping into existence brutely, and the fact that both order and chaos could thus be indistinguishable from each other if they could be brute facts.
As for libertarian free will, maybe some solution compatible with probability could be found ala Alexander Pruss' self-explanatory contingent fact proposal?
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Posted by FrenchySkepticalCatholic 1/22/2018 1:55 pm | #6 |
The problem with this answer would be that it would still leave open the possibility of things popping into existence brutely, and the fact that both order and chaos could thus be indistinguishable from each other if they could be brute facts.
I'd bite. What would happen if order and chaos were indistinguishable? Wouldn't we have successfully demonstrated the existence of a "supreme force", namely God?
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Posted by Miguel 1/22/2018 4:58 pm | #7 |
"A PSR denier could just say that the lack of any new objects and even the appeareance of order is also just a brute fact."
That would be a non-response however, since we're not really assuming there can't be brute facts with the argument; all one is using with empirical arguments for PSR is inference to best explanation, which everyone should use. It is bizarre how (if PSR is false) nothing ever seems to pop into existence without any explanation whatsoever, so the best and simplest explanation for that is just that PSR is true. Calling something a brute fact should really be an extreme last resort (IF brute facts are even possible), otherwise we couldn't explain anything for everything could simply be said to happen as a matter of brute fact.
Your argument about probabilities is an interesting one. Maybe you have something there. If they have no objective probability of any sort, then they could be meaningless; not probable, not improbable, not certain... not possible.
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Posted by aftermathemat 1/23/2018 11:46 am | #8 |
That would be a non-response however, since we're not really assuming there can't be brute facts with the argument; all one is using with empirical arguments for PSR is inference to best explanation, which everyone should use. It is bizarre how (if PSR is false) nothing ever seems to pop into existence without any explanation whatsoever, so the best and simplest explanation for that is just that PSR is true. Calling something a brute fact should really be an extreme last resort (IF brute facts are even possible), otherwise we couldn't explain anything for everything could simply be said to happen as a matter of brute fact.
Your argument about probabilities is an interesting one. Maybe you have something there. If they have no objective probability of any sort, then they could be meaningless; not probable, not improbable, not certain... not possible.
The argument would work if the crucial premise that possibility implies probability is correct. Otherwise, it doesn't do the work. We would also have to assign a probability of 0 to logically impossible things and 1 to necessary things, and we would then have to see how the realm of probability would be affected by this, or whether assigning these meanings to 0 and 1 is even relevant to probability or misses the point.
But I do think that there is an argument to be made on the basis of how destructive brute facts are to probability and how they themselves lack probability.
