I'm about to head off to the Scotus Congress in a few hours, so I thought that I'd jot down this thought before I go and absorb the subtle doctor for 4 days. It's probably something that has been noted before, but it has struck me as new, so you can smile and nod and play along for a couple minutes. There are two principles in philosophy which play a significant, though controversial, role. One is the principle of sufficient reason (PSR), which more or less states that there's got to be a reason for everything. On the other hand, there is the principle of parsimony (PoP) (also called "Ockham's Razor," "Scotus' Rule," and most likely other things) which says that we shouldn't postulate more entities than we need. Which therefore makes it the contrapositive of the former (and thus logically equivalent). Observe (where "E(x)" is "x exists" and "R(y)" is "there is a reason that y", ~ is not, and -> is implication):
PSR: E(x) -> R(E(x))
PoP: ~R(E(x)) -> ~E(x)
Granted, PoP is sometimes epistemological (don't postulate more entities than you have found a need for), but this seems to piggyback on the metaphysical claim (why should we choose the simpler explanation unless this gets closer to the reality of things?) So, on that note, if we expect the world to be strongly rational, then it also needs to be as simple as possible.
Now, maybe we think that PSR is too strong; maybe we want WPSR, the weak principle of sufficient reason, which can be stated as "if it is possible that there is a reason for x, then there is a reason for x." What would we get for an equivalent WPoP (where P is possible and N is necessary)?
WPSR: P(R(x)) -> R(x)
WPoP: ~R(x) -> ~P(R(x)); ~R(x) -> N(~R(x))
So, whatever cannot be explained, necessarily cannot be explained. I'm not sure that this is terribly profound; it seems like what it means for something to be explainable. But if WPoP is trivial, that means that WPSR is true.
The above seems to make R somewhat similar to the necessity operator (and WPSR smacks of a cross between an ontological and a cosmological argument), which I find intriguing, although I do note that ~R(x) isn't interchangeable for P(~x) (in fact, God is the main possibly-unexplainable entity, and I certainly don't want to say that God can't exist). So what are the relations between explainability (as an ontological feature, where things really do have some such relation between them) and necessity?
And now I'll let the reader make something coherent and profound out of the above, and attribute it to me (let me know about it). Ah, the rewards of obfuscation and pedanticness.
7 comments:
I certainly have never thought of the principle of parsimony and the principle of sufficient reason as being contrapositives, or otherwise mutually implicatory. I remember briefly discussing Christian Wolff on PSR for a History II paper for your uncle years ago, that it was somehow connected in Wolff's thought with the principle of noncontradiction, and that Dr. C wrote a comment on my paper emphasizing the importance of this point.
My more recent brush with PSR is in William Rowe's discussion of the cosmological argument. He argues we don't have to accept PSR, and that the cosmologicaly argument has no persuasive force if we don't accept PSR. He thinks that an infinite chain of entities, one causing another, is possible if not plausible, but that PSR still demands an answer to the cosmological question: Why does this chain of entities exist? But the atheist can brush that off by saying it is merely a "brute fact", i.e., not something they're going to ask the cosmological question about.
If you're right about PSR being implied by PoP, that would make for an interesting response to Rowe's argument.
I heard from a friend that there's a book that recently come out, called _The Principle of Sufficient Reason: A Reassessment_ by Alexander Pruss, which is good. I haven't read it myself. I like the weaker version better, which acknowledges potential brute facts; the brute facts just can't be thing which could possibly be explained. Given WPoP is true (which I think may be analytic, or at least close to it), then this principle must be true.
So, the possibility of a first cause (a reason for everything else) would entail that the first cause exists. This at least makes theism equally probably as atheism; it won't convert an atheist, but it keeps theism a viable option in the meantime. More work could be done on why the concept of a first being would be possible. I know Scotus has some stuff on that, but I'm not sure how it would fly in contemporary arguments (being based on the notion of infinite being).
I need a richer concept of what it is for there to be a reason for something--your R(x)--before I can determine whether your WPoP is analytic. First of all, I think I understand the claim that there is a reason for something to exist--your R(E(x)). What is the difference in meaning between your R(E(x)) and your R(x)?
Also, is there any reason why we shouldn't treat "having a reason" as a predicate, instead of treating it as an operator? I'm assuming that you did not intend to use existence as a predicate in your discussion, but that you were using E as the existential quantificational operator.
It what follows I am going to use E for the existential quantifier and Rx to symbolize "there is a reason for the existence of x".
(Ex)~Rx
would entail the contradiction of PSR as I understand it. It states that there is at least one brute fact.
I am having some difficulty trying to state PSR without using existence as a predicate. I think I can do it by making a universal statement about predicates as follows:
(F)(x)[(Ex)Fx->Rx]
The existential quantifier inside the square brackets governs the bound Fx, not the implication.
I'm sure there's something wrong here, but I'm not going to bother trying to figure out what that is right now...
Keith Yandell gives a couple of versions stated as such:
(PSR1) If it is logically possible that something depends for its existence on something else, then it does depend for its existence on something else.
(PSR2) What begins to exist must have a cause of existence.
I think that PSR1 is more or less my WPSR. I think this provides more for what "reason" means, without making existence a predicate (at least as far as I can tell).
Would you say that the two statements are more or less the same?:
(1) Existence is not a predicate.
(2) Existence is not something that is added to/composed with a thing's essence (as an abstract intelligible which is what a thing is)
Yandell's PSR2 obviously has to do with the Kalaam argument, and I really don't see any connection between this and the principle of sufficient reason.
I think that saying existence is not a predicate is exactly the *opposite* of saying that existence is not something that is added to a thing's essence (what it is).
Something's essence is what it is (or what it would be if it were?). That a thing exists is a completely different claim than that its essence has a certain property. It doesn't change what a thing is (it's essence) to say that it exists or that it doesn't exist.
Rereading your two propositions, I see that you used the phrase "composed with"--I guess I agree that if existence is not a predicate that existence is not something that is composable with the things properties to make up its essence.
Maintaining the difference between "There is at least one x such that..." and "x is F" parallels in my mind the difference between asserting that p, and p.
On second thought, I'm not entirely sure what I said in my last paragraph works...
An existential proposition is a proposition; I can entertain the proposition "x exists" without asserting it. So I'm not sure that I was right to make an analogy between "x exists" to "x" and (assertion) that "p" and "p". The assertion of p is not a proposition, it is an illocutionary act.
Still, there's something in this analogy I want to hang on to...
Actually, I think that Henry of Ghent would want to make exactly that same analogy, only as a metaphysical statement. He wants to say that essential being, the being of an essence, comes from being a divine exemplar (a thought, even a mental word perhaps, in the mind of God), while existential being comes from the willing, the expression of that thought (not that this is terribly original with HG, but he lays it out the most specifically). I believe this ends up getting tied into his Trinitarian theology as well, though I haven't read the primary sources on that yet. I'm not quite sure how this fits with the assertion of p rather than an illocution, but I'm working on that.
As for PSR2, I think that it doesn't have to be associated with the Kalaam argument; all it states is that every temporal thing needs a reason for its existence (for Yandell, this would be opposed to abstracta), not that a temporal series needs a beginning in time. Now, in order to get an argument for God's existence out of it, you need to assume either a way of getting to the start of a temporal series (and so the Kalaam argument), or alternatively something which would show the inadequacy of a purely temporal infinite causal chain of providing the necessary reason for the existence of any part of it (which could still allow the possibility of the infinite chain, just not as the only fact).
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