Posted by aftermathemat  1/28/2018 1:53 pm | #1 |
Either PSR is necessarily true, or it is necessarily false.
If PSR is necessarily true, then brute facts are impossible because everything must of necessity have some sort of explanation which makes it in some way intelligible.
If PSR is false, then it is necessarily false. This means that the proposition that there are no brute facts is necessarily false. Which means that there are some brute facts of necessity; namely, if some contingent facts are true, some of them will be brute of necessity.
So at least some brute facts necessarily obtain. And this means that the existence of brute facts is explained by the necessity that some obtain, especially existential facts. But brute facts by definition do not have any explanation whatsoever. Nothing makes them intelligible and nothing could in principle make them intelligible, so this means that brute facts cannot obtain of necessity in any way. Which means the PSR must be true, otherwise brute facts would have an explanation in that they must necessarily obtain, especially for existential facts, because PSR is false.
So brute facts cannot obtain in any case, and therefore the PSR is true either way. Q.E.D.
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Posted by Greg 1/29/2018 4:29 pm | #2 |
aftermathemat wrote:
This means that the proposition that there are no brute facts is necessarily false. Which means that there are some brute facts of necessity; namely, if some contingent facts are true, some of them will be brute of necessity.
From "necessarily, there are brute facts" it doesn't follow that "there is some brute fact which is necessary," that is, that "for some brute fact f, necessarily f obtains". That is a scope fallacy.
And this means that the existence of brute facts is explained by the necessity that some obtain, especially existential facts.
It is questionable that the necessity of some fact always amounts to an explanation of the fact.
Suppose that necessarily f obtains. So f obtains in the actual world. Is the obtaining of f explained by its necessity?
Well, here's one reason to think that f's necessity is useless as an explanation of it. Consider the parallel case of singular and universal claims. Suppose that all fire trucks are red. And suppose a is a fire truck and is red. Is the fact that a is red explained by the fact that all fire trucks are red? That seems doubtful. a may have been painted a minute ago; the explanation of a's being red is that these firemen painted it.
Similarly, why should we accept the fact that f obtains in all possible worlds as an explanation of the fact that it obtains in any particular possible world? (Why not say instead that the necessity of f's obtaining is explained by f's obtaining in each possible world?)
Our notion of explanation is, I think, one of a relation that might obtain between items in a single possible world. Why did this happen? Because of its cause. Facts about other possible worlds seems to have no direct relevance to the giving of explanations about what happens in this possible world.
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Posted by aftermathemat 1/29/2018 4:57 pm | #3 |
From "necessarily, there are brute facts" it doesn't follow that "there is some brute fact which is necessary," that is, that "for some brute fact f, necessarily f obtains". That is a scope fallacy.
Can you elaborate? Considering how the first proposition "Necessarily, there are brute facts." entails that there actually are brute facts, at least if taken prima facie and as standalone, it seems that there should also be brute facts because they must necessarily obtain. Facts about existence are the prime example of this, as they must necessarily obtain if any contingent facts are true, since to say all contingent facts have an explanation would be PSR, and PSR is suppositionally denied here.
Well, here's one reason to think that f's necessity is useless as an explanation of it. Consider the parallel case of singular and universal claims. Suppose that all fire trucks are red. And suppose a is a fire truck and is red. Is the fact that a is red explained by the fact that all fire trucks are red? That seems doubtful. a may have been painted a minute ago; the explanation of a's being red is that these firemen painted it.
Similarly, why should we accept the fact that f obtains in all possible worlds as an explanation of the fact that it obtains in any particular possible world? (Why not say instead that the necessity of f's obtaining is explained by f's obtaining in each possible world?)
Well, first of all I would reject possible word dialectic, and would say that the reason that f obtains is because it must obtain of it's own nature.
Second, your fire truck example is a bit suspicious, because the same concern could be made with other deductive arguments. All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
It would do no good to suggest that Socrates could have been an immortal human-like entity that was somehow downgraded by God into becoming human, as this wouldn't really be a counter-example because the conclusion follows from the universality of the first premise. In the same way, if fire trucks are red by necessity, then that explains why A as a fire truck is red. It wouldn't make much sense to suggest that the fire truck could have been painted, for this is either the reason all fire trucks per universal are red, or it wouldn't actually have been a fire truck before it was painted. It would have been an unfinished fire truck, a regular non-intentional vehicle that wasn't designed for use but was due to circumstance forcibly appropriated for the mission, etc.
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Posted by Greg 1/29/2018 6:47 pm | #4 |
Can you elaborate?
Yes. You said, "the proposition that there are no brute facts is necessarily false." I interpret this as: "Necessarily, there are brute facts." More formally: (1) "Necessarily, there exists some x such that x is a brute fact." That just means that each possible world contains a brute fact.
Next, you said, "Which means that there are some brute facts of necessity; namely, if some contingent facts are true, some of them will be brute of necessity." The claim is that the italicized bit follows from (1).
But how? In (1), the necessity operator is adverbial, taking an entire proposition as an argument, whereas now you are writing of facts "brute of necessity." I am not sure what that means, but it is not clear how it is related to the adverbial use. My guess was that what was intended in the italicized bit was this: (2) "There exists some x such that necessarily x is a brute fact." That in the next paragraph you apparently take "some brute facts necessarily obtain" to be equivalent to this, seems to jive with this reading. But the inference from (1) to (2) is not valid. (1) only says that each possible world contains a brute fact; for all (1) says, it could be a different brute fact in every possible world.
But maybe (2) was not what you intended. The bolded bit glosses the italicized bit. Maybe the idea is that there is a necessary entailment between f's obtaining (for some contingent fact f) and f's being brute: (3) "There exists some x such that necessarily (if x obtains, then x is a brute fact)."
But that doesn't follow from (1) either, and it doesn't fit with the remainder of the argument.
Or perhaps when you say "some brute facts necessarily obtain," you mean nothing more than (1). Then the inference is not a scope fallacy, and the question is whether we can make sense of the suggestion that the existence of a brute fact is explained by the fact that necessarily there are some brute facts. I don't see why we should think so. Suppose, for instance, there were two brute facts. Then of neither one is it true that it must be there or else there should be no brute facts. So it is not clear that we can say that the necessity of there being some brute facts is an explanation of any one in particular, since the necessity claim does not actually necessitate that either one obtain--and the thought was that necessitating was what is important.
Well, first of all I would reject possible word dialectic, and would say that the reason that f obtains is because it must obtain of it's own nature.
I don't think my points really ride on possible world semantics.
The more general problem is that your conception of necessity becomes obscure. Is the suggestion that necessity claims like "necessarily, f obtains" are most perspicuously reformulated as "f must obtain of its own nature"? Then it is not at all obvious that you can coherently formulate your argument in those terms. (For instance, "necessarily, some brute fact obtains" could only be reformulated if the obtaining of some brute fact were itself a fact with its own nature, but that is not really clear. And what then does it mean to say that PSR is "necessarily" true or false?) There is nothing wrong with trying to work out a possible-worlds-free modal semantics, and I'm indeed sympathetic to the view that necessity should principally be predicated of, say, objects rather than sentences, but you are using "necessarily" much too casually for it to be clear what you mean.
Second, your fire truck example is a bit suspicious, because the same concern could be made with other deductive arguments. All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
There's nothing wrong with that argument, and my fire truck example does not imply that there is. There is a difference between explanation and logical consequence. That all fire trucks are red and that a is a fire truck certainly imply that a is red; they just don't explain it.
In the same way, if fire trucks are red by necessity, then that explains why A as a fire truck is red. It wouldn't make much sense to suggest that the fire truck could have been painted, for this is either the reason all fire trucks per universal are red, or it wouldn't actually have been a fire truck before it was painted. It would have been an unfinished fire truck, a regular non-intentional vehicle that wasn't designed for use but was due to circumstance forcibly appropriated for the mission, etc.
Well, in fact not all fire trucks are red. Some are yellow, for instance. So it is not necessary that something be red if it is a fire truck, and we cannot say of some red fire truck that it would cease to be a fire truck if it ceased to be red, nor can we say that of some non-red vehicle that, by virtue of being non-red, it cannot be a fire truck.
So I take it that all yellow and other non-red fire trucks could be painted red. Then it would be the case that all fire trucks are red. But this fact obviously doesn't explain the redness of particular fire trucks; rather, it is more appropriate to say that the fact that all fire trucks are red is explained by the fact that the ones that weren't have been painted.
(Of course, this has nothing to do with fire trucks. For my example, I just need there to be two predicates which are not in fact coextensive but could be imagined to be.)
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Posted by aftermathemat 1/30/2018 8:56 am | #5 |
Yes. You said, "the proposition that there are no brute facts is necessarily false." I interpret this as: "Necessarily, there are brute facts." More formally: (1) "Necessarily, there exists some x such that x is a brute fact." That just means that each possible world contains a brute fact.
My bad. I realised the mistake I made a day or so after I posted the OP, but a part of the argument still seems valid. Namely, if PSR is true, then all contingent facts must have an explanation, if any of them obtain. If PSR is false, then if any contingent facts obtain, some of them must of necessity be brute, the existential ones that is. Thus, existential contingent facts will be necessarily brute, which would explain why they are brute, which would go against the definition of brute facts as inexplicable. One problem with this, though, is that this only answers the question of why existential facts are inexplicable, not why a certain existential fact exists, so this may undercut the objection that this contradicts the definition of brute facts.
That all fire trucks are red and that a is a fire truck certainly imply that a is red; they just don't explain it.
I think a saying such as the following might be applicable here: All implications are explanations, but not all explanations are implications.
Well, in fact not all fire trucks are red. Some are yellow, for instance. So it is not necessary that something be red if it is a fire truck, and we cannot say of some red fire truck that it would cease to be a fire truck if it ceased to be red, nor can we say that of some non-red vehicle that, by virtue of being non-red, it cannot be a fire truck.
This would then expand the universal of fire truck to include non-red trucks as well, which would undercut the painting example since the necessity is not in the redness.
So I take it that all yellow and other non-red fire trucks could be painted red. Then it would be the case that all fire trucks are red. But this fact obviously doesn't explain the redness of particular fire trucks; rather, it is more appropriate to say that the fact that all fire trucks are red is explained by the fact that the ones that weren't have been painted.
But this wouldn't follow of necessity then, wouldn't it? It would be like saying that all non-mortal humans could lose their immortality and that would bring them into the universal of men and thus entail their mortality. It wouldn't make mortality a strictly necessary part of the universal then.
Last edited by aftermathemat (1/30/2018 8:57 am)
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Posted by Greg 1/30/2018 4:02 pm | #6 |
But this wouldn't follow of necessity then, wouldn't it? It would be like saying that all non-mortal humans could lose their immortality and that would bring them into the universal of men and thus entail their mortality. It wouldn't make mortality a strictly necessary part of the universal then.
My apologies if I was unclear: necessity is not at work in the fire truck example, just universality.
Possible worlds are a way of attempting to make a form of intensional talk (about necessity) clearer by formulating it extensionally, that is, as just being about a set of objects. Some of our problems would be made easier if we could read "Necessarily, b is red" as a claim that b is red in each possible world in which it exists; it wasn't clear what the first sentence meant, but now we can reduce the question of whether it's false to the question of whether there is a possible world in which b is not red.
There might be objections to be made at any point here. The question will still remain as to what a possible world is. But my thought was this. The crassest reading of modal statements will just say that what it means to say that necessarily, b is red is to say that in each possible world, b is red. This is to say that modal claims are simply extensional. And necessity claims are just universal generalizations over the set of possible worlds.
If that's what one thinks (neither you nor I think that way, though), then it is very dubious that the necessity of something can explain its actuality. For universal generalizations don't seem to (or need not) explain their instances. If modal claims are just claims about sets of possible worlds, then necessities don't seem to explain actualities.
I think that this remains a problem even for those who are more uneasy about possible-worlds talk. There are different views:
(1) Even if possible worlds don't actually exist, possible worlds are abstract entities, and modal claims are still claims about those entities.
(2) Even if possible worlds neither actually or abstractly exist, we can use possible-worlds talk to ensure that our possibility claims remain consistent; thus modal claims imply claims about possible worlds.
(3) There is in fact something distorting about possible-worlds talk, and it must be avoided.
On (1), my worry is very alive, and it is unclear how the necessity of something can explain its actuality. On (2), which I think is a plausible view, there is at least a question which remains. Necessity claims will imply claims about the set of all possible worlds, and the latter claims cannot explain actualities; so then what do necessity claims add?
I think a saying such as the following might be applicable here: All implications are explanations, but not all explanations are implications.
I don't think this'll work. There are mutual implications, for instance p if and only if q. It presumably cannot be the case that p explains q and q explains p. And of course every truth implies itself, but we shouldn't say that every truth is self-explanatory.
My bad. I realised the mistake I made a day or so after I posted the OP, but a part of the argument still seems valid. Namely, if PSR is true, then all contingent facts must have an explanation, if any of them obtain. If PSR is false, then if any contingent facts obtain, some of them must of necessity be brute, the existential ones that is. Thus, existential contingent facts will be necessarily brute, which would explain why they are brute, which would go against the definition of brute facts as inexplicable. One problem with this, though, is that this only answers the question of why existential facts are inexplicable, not why a certain existential fact exists, so this may undercut the objection that this contradicts the definition of brute facts.
This formulation is improved, but I still don't know what it is to say that "a fact of necessity must be brute."
Now, I am also doubting this claim: "If PSR is false, then if any contingent facts obtain, some of them must of necessity be brute, the existential ones that is." PSR presumably says something like "Necessarily, every contingent fact has an explanation." The denial of this is "Possibly, some contingent fact does not have an explanation." This does not imply anything about the contingent facts which actually obtain. PSR, so formulated, could be false, even if every contingent fact that actually obtains has an explanation.
Of course, one might think that it would be enough for a cosmological argument that every contingent fact be explained in some possible world, so you could set up a dilemma. But some argument would be required there, and it wouldn't be trivial.
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Posted by aftermathemat 1/30/2018 4:26 pm | #7 |
I think that this remains a problem even for those who are more uneasy about possible-worlds talk. There are different views:
(1) Even if possible worlds don't actually exist, possible worlds are abstract entities, and modal claims are still claims about those entities.
(2) Even if possible worlds neither actually or abstractly exist, we can use possible-worlds talk to ensure that our possibility claims remain consistent; thus modal claims imply claims about possible worlds.
(3) There is in fact something distorting about possible-worlds talk, and it must be avoided.
On (1), my worry is very alive, and it is unclear how the necessity of something can explain its actuality. On (2), which I think is a plausible view, there is at least a question which remains. Necessity claims will imply claims about the set of all possible worlds, and the latter claims cannot explain actualities; so then what do necessity claims add?
I would accept something like 3, mostly because I see possible worlds talk as just being overly complicating something that needn't be complicated, and as being largely dispensable considering possible worlds seem to be reducible to nothing more than logical possibilities.
Or, at least, logical / metaphysical possibilities are a much better way of talking about modality than possible worlds are.
This formulation is improved, but I still don't know what it is to say that "a fact of necessity must be brute."
Now, I am also doubting this claim: "If PSR is false, then if any contingent facts obtain, some of them must of necessity be brute, the existential ones that is." PSR presumably says something like "Necessarily, every contingent fact has an explanation." The denial of this is "Possibly, some contingent fact does not have an explanation." This does not imply anything about the contingent facts which actually obtain. PSR, so formulated, could be false, even if every contingent fact that actually obtains has an explanation.
Of course, one might think that it would be enough for a cosmological argument that every contingent fact be explained in some possible world, so you could set up a dilemma. But some argument would be required there, and it wouldn't be trivial.
Well, consider existential contingent facts. If even one contingent fact about the existence of anything (or everything!) had an explanation, this could only be a necessary explanation. But to say that existence has an explanation would be the same as PSR because then no brute facts could exist, because existence as such is explicable. It then universalises explicability to all things that have existence.
The only way to deny PSR would be to say that the existence of anything whatsoever must of necessity be a brute fact, otherwise PSR would necessarily follow. So every contingent fact relating to the existence of anything contingent must be brute, otherwise one must admit the PSR. This means that we already know that certain contingent facts are brute, and this without even delving into new existential brute facts that could obtain, or non-existential brute facts (if there is such a thing, because a good argument could be made that any brute fact that could possibly obtain must involve existence in one way or another, thus making all possible brute facts be existential ones).
And the plus side on this is the fact that we can easily conceive of an explanation for existence and the exact nature of that explanation as well as further reasons of why contingent facts need an explanation, or at the very least know that if there is an explanation it must be necessary, which puts a lot of doubt on the idea that existence is necessarily brute, lending more credibility to the PSR.
Last edited by aftermathemat (1/30/2018 4:30 pm)
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Posted by Greg 1/30/2018 6:02 pm | #8 |
I would accept something like 3, mostly because I see possible worlds talk as just being overly complicating something that needn't be complicated, and as being largely dispensable considering possible worlds seem to be reducible to nothing more than logical possibilities.
Or, at least, logical / metaphysical possibilities are a much better way of talking about modality than possible worlds are.
I am not sure what you mean by "logical / metaphysical possibilities" such that they are not possible worlds in a sense consistent with (2).
(3) is a view that really calls for a lot of explicit justification before it would make sense that someone would hold it.
Say I have a pretty adequate conception of some form of possibility, say natural possibility (assume I'm speaking univocally of one kind of modality in what follows). Then I might adopt the convention "If possibly p, then say: in some possible world, p." So far, possible-worlds talk is dispensable, but that isn't to say objectionable. But it might be useful. It might be that I want to say that p is possible and q is possible, but p & q is not possible; thinking about possible worlds just as maximal possibilities is just a good way to try to think clearly about compossibility. A possible world is just "a way things could be," where "could" corresponds to whatever kind of modality you like. So there are no presuppositions here of their being merely possible. And if you think that what is possible is substantially more restricted than what a lot of other philosophers think is possible, then you can register your disagreement by denying that there are certain possible worlds.
Well, consider existential contingent facts. If even one contingent fact about the existence of anything (or everything!) had an explanation, this could only be a necessary explanation.
Again, you need to be careful with the word 'necessary'. What does it mean to say that something has "a necessary explanation"? That what explains it is a necessary truth, a necessary fact, or a necessary object? Or that the proposition "this explains that" is necessary?
I presume you mean the latter. But why is that obvious? First, it seems to depend on the essentiality of origins, that if nothing which didn't have the same origins (or, in this case, explanation) could be the same thing. I find that somewhat plausible, but it isn't obvious and some philosophers reject it.
But it also does seem to depend on explanation as necessitation. You previously wanted to deny that wherever there is explanation, there is implication. But if it is necessary that this explains that, then it is impossible to have this without that. But it seems that, say, causal relations don't have to necessitate.
But to say that existence has an explanation would be the same as PSR because then no brute facts could exist, because existence as such is explicable. It then universalises explicability to all things that have existence.
I don't see how you are moving from "some contingent fact about existence has an explanation" to "existence as such has an explanation"?
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Posted by aftermathemat 1/31/2018 8:10 am | #9 |
Say I have a pretty adequate conception of some form of possibility, say natural possibility (assume I'm speaking univocally of one kind of modality in what follows). Then I might adopt the convention "If possibly p, then say: in some possible world, p." So far, possible-worlds talk is dispensable, but that isn't to say objectionable. But it might be useful.
I would agree with that. Possible worlds are dispensable, and in my view unecessarily complicated, and are easily replaced with talk of logical possibilities, which are more clearly based and derived from the actual world.
Again, you need to be careful with the word 'necessary'. What does it mean to say that something has "a necessary explanation"? That what explains it is a necessary truth, a necessary fact, or a necessary object? Or that the proposition "this explains that" is necessary?
Poor wording, sorry. What I mean by that is that the explanation for existential contingent facts, and ultimately for contingent facts as a whole, can only be rooted in something necessary if there is to be any explanation of them. That is what I mean by " a necessary explanation." I was talking about the nature of the explanation.
I don't see how you are moving from "some contingent fact about existence has an explanation" to "existence as such has an explanation"?
Well, if an existential contingent fact had an explanation, that explanation would have a necessary nature / be rooted in a necessary being. But if even one contingent fact about existence had an explanation, then PSR would be vindicated and this would mean that all contingent facts have an explanation. Because once you say questions about the existence of things have an answer, that means that existence is ultimately intelligible and explicable, which means brute facts are not possible.
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Posted by Greg 1/31/2018 5:56 pm | #10 |
Well, if an existential contingent fact had an explanation, that explanation would have a necessary nature / be rooted in a necessary being.
But why? Here's an existential contingent fact, I think: The birdhouse in front of me exists. But here's its explanation: I made the birdhouse in front of me. That explanation is contingent.
Maybe that explanation is somehow rooted in a necessary being, or perhaps there's some sense in which the true explanation of the existential contingent fact (perhaps differently construed) is a necessary one. In fact, I think those claims are both true. But they aren't easy to see.
