God, Possibility, and Evidential Support for Non-Contingent Propositions

Mike Valle gave a presentation yesterday before the ASU philosophy club on the skeptical theist response to the evidential argument from evil.  A good discussion ensued among Guleserian, Nemes, Lupu, Reppert, Valle, Vallicella, et al.  Peter Lupu made a comment that stuck in my mind and that I thought about some more this morning.  For what puzzles him puzzles me as well.  It may be that we are both just confused.

1. Let us assume that our concept of God is the concept of a being that has a certain modal property, the property of being such that, if existent, then necessarily existent, and if nonexistent, then necessarily nonexistent. Call this the Anselmian conception of deity.  It follows that God exists, if true, is necessarily true, and if false, necessarily false.  Simply put, the proposition in question is either necessary or impossible, and thus necessarily noncontingent.

2. Peter's question, I take it, was: how can such a noncontingent proposition have its probability either raised or lowered by any empirical consideration?  In particular, how can considerations about the kinds and amounts of natural and moral evil in the world lower the probability of God exists?  If true,then necessarily true; if false, then necessarily false.  Peter's sense -- and I share it -- is that evidential considerations are simply irrelevant to the probability of noncontingent propositions.

3. The problem -- if it is one -- arises in other contexts as well.  I once argued that conceivability does not entail (broadly logical) possibility.  I got the response that, though this is true, conceivability of p raises the probability of p's being possible. That is not clear to me.  Assuming the modal system S5, if p is possible then necessarily p is possible, and if p is necessary, then necessarily p is necessary. (The possible and the necessary do not vary from world to world.)

I happen to think that S5 caters quite well to our modal intuitions.  Assume it does.  Then It is possible that there be a talking donkey is necessarily true, if true.  If so, how can the fact that I (or anyone or all of us) can conceive of a talking donkey raise the probability of the proposition in question?

4. Reppert made a comment in response to Lupu about the probability being epistemic in nature.  I didn't follow it.  If p is noncontingent, and we are concerned with the probability of p's being true, and if truth is not an epistemic property (i.e., a property reducible to some such epistemic property as rational acceptability), then I don't see how evidential considerations are relevant.

The ComBox is open if Victor or Peter want to add to their remarks. 

 

 

Comments

[John]

Bill,

Upon reading your remarks here, I had a reaction similar to Reppert's: the issue raised by evidential considerations pertains in the first instance to epistemic possibility.

I assume that the idea here would be the following. Yes, the proposition that God exists is necessarily noncontingent; if true, it is necessarily true, and if false, it is necessarily false. So evidence of evil can have no impact on the truth or falsity of that proposition. But if we move from logical or metaphysical possibility to the notion of epistemic possibility, then the situation changes. Say that a proposition p is epistemically possible for an agent S just in case, given what S knows to be true, it might be that p. Say that a proposition q is epistemically necessary for an agent S just in case, given what S knows to be true, it must be that p. I take it that evidential considerations regarding evil would suggest that the proposition that God exists is certainly not epistemically necessary for any of us, and that those same considerations would have implications regarding whether or not the proposition that God exists is epistemically possible for us.

This is only a rough-and-ready sketch of what I take to be the thought behind Reppert's reaction. But the idea is just that evidential considerations are important for determining the epistemic - but not metaphysical - possibility that God exists. And none of this, I take it, need be committed to the view that truth just is warranted assertibility.

[Bill Vallicella]

Good comment, thanks. That God exists is epistemically possible for us in that the existence of God is logically consistent with what we know: it is not logically ruled out by what we know. Nor is it logically ruled in by what we know. So we can say that the existence of God is epistemically/doxastically possible for us but not epistemically/doxastically necessary for us.

That is just a fancy way of saying that what we know neither entails that God does not exist, nor entails that God exists.

But now how exactly does probability come into this? What is the probability a probability of?

[John]

Bill,

I am not sure how probability comes into it. But my suspicion is that some people think that evidence of evil shows that the proposition that God exists is not epistemically possible for us, and so that in some way the likelihood that the proposition that God exists is true goes down. We are faced with two possibilities: the proposition that God exists is (necessarily) true, and the proposition that God exists is (necessarily) false. If that proposition is not epistemically possible, then it's more likely that the latter possibility obtains: the proposition that God exists is (necessarily) false. There is some relation between epistemic and metaphysical possibility here, such that the decreased epistemic possibility of God's existing suggests that it is more likely that the proposition that God exists is necessarily false. In other words, though we are faced with the aforementioned two possibilities, they are not equally likely; it's not like the case of a coin, where the probability that it will land on heads is 50% and the probability that it will land on tails is 50%. Given our verdict on epistemic possibility, it might be that the probability that one of the two possibilities with respect to God's existence is not equal in this way: maybe it's more like 10% likely that the proposition that God exists is (necessarily) true and 90% likely that the proposition that God exists is (necessarily) false.

Maybe this is incoherent. I don't know enough about epistemic possibility to say. But I suspect that something like this might be behind Reppert's response.

[bob koepp]

While there is a distinction to be made between epistemic and metaphysical possibility, I don't see how it bears on the question about possible evidential support for a non-contingent proposition. The propositions expressing the evidence are, presumably, themselves contingent. What theory of evidential relations could license inferences (even proababilistic inferences) from contingent premises to non-contingent conclusions?

[T. Hanson]

Don't objective or non-epistemic probabilites only apply to frequencies - random experiments where you calculate the relative frequency of a certain number on a roulette wheel, say?

Since "Necessarily God exists," is not an event occuring in a sequence, it would seem only evidential, or Bayesian probability applies here, where evidence for or against affects the probability of the the truth of the claim.

[Account Deleted]

T. H.

You are correct to distinguish between objective or frequency interpretation of probability vs. subjective or degree-of-belief or Bayesian interpretation. The former, as you note, is inapplicable to "Nec God exists" etc.

However, your further claim regarding Bayesian or subjective probability does not seem to me right. You say that such probability "applies here, where evidence for or against affects the probability of the the truth of the claim."

Subjective or Bayesian probability can only say something about the degree of belief regarding the truth of a proposition, given evidence. However, I fail to see how such a notion of probability can apply to the truth, per se, of necessarily true or necessarily false propositions.

Consider a simple example. The proposition 'P & ~P' is necessarily false. Does it makes sense to say that the falsity of this proposition has a high probability based upon evidence consisting of a large number of instances of the same form all of which were found to be false?

I don't think it makes sense to say that.

[Jan]

Good question. I do not think it is more difficult than the question of the meaning of (epistemic) probability of a given event of the past. I can answer neither of them satisfactorily. This comment screams: "I know nothing of epistemology". Read at your own peril.

Let's say I see a person on the bus who I think might be my old friend Fred. When I come home I ponder the proposition p: 'the person I saw is Fred'. Clearly, an event in the past either occurred or did not, and its probability is either 1 or 0. Nevertheless, it seems one can assign to p the (epistemic) probability r ∈ ]0,1[. The person had a characteristic scar that Fred has, which increases r - this is common sense. Echoing the question of dr. Vallicella: what is r the probability of? In particular, what is the probability space (http://en.wikipedia.org/wiki/Probability_space)?

It seems that the elementary outcomes here are possible worlds. The sample space - the space of the elementary outcomes - is the ensemble of all the possible worlds. Our question is: what is the probability that, given all that I know of the actual world W, W is s.t. the person sitting on the particular chair on the bus b at a time t is Fred. In other words, we ask about the conditional probability. Let A denote the set of all the possible worlds consistent with all that I know (W ∈ A). In particular, I know that there was a person on the bus resembling Fred and the person had a characteristic scar. Let B denote the set of all the possible worlds s.t. the person in question is indeed Fred. Then r = P(B|A), where P is the probability measure - a function assigning probability to events. This is completely clear, but useless - we do not know what is the measure on the ensemble of the possible worlds.

(One might try to give a simpler definition of r. Take n random possible worlds consistent with all that I know. Denote the number of those n worlds s.t. the person is Fred by t. Define r := lim t/n with n->inf. The problem here is that the expression 'a random possible world' is meaningless without a measure on the space of all the possible worlds. Compare http://en.wikipedia.org/wiki/Bertrand_paradox_%28probability%29. )

The problem of giving meaning to the probability of a proposition p that is true or false necessarily is analogous. The question is not about picking the actual world W from the ensemble of all possible worlds, but about picking the ensemble of all possible worlds E from the ensemble of all ensembles of worlds (not necessarily possible). That is, what is the probability that, given all that we know of the ensemble of all the possible worlds E, E is s.t. p is true for all the worlds in E. This seems to me conceptually clear and in this model knowledge of contingent propositions ("E is s.t. in one of its worlds q obtains") can change the (epistemic) probability of E being such that p is true in all of its worlds. Again, the fatal flaw is the lack of a measure on the ensemble of the ensembles of worlds.

The only way I can give r a meaning is the following. Let's say I am pondering the truth of a proposition p. Let n denote the number of situations in which I had a 'similar level of (subjective) certitude' that a certain proposition (other than p) is true, and such that eventually I ascertained the truth of the proposition in question. Let t denote the number of times I was right. Then I will say that the probability of p being true is r := t/n.

PS. Even mathematicians talk about the probability of a given not yet proved theorem being true ("the theorem is probably true"). Obviously, mathematical theorems are true or false necessarily. The heuristic assessment is based on broadly aesthetic grounds - how the theorem (or its negation) harmonises or fits with what we already know.

[Account Deleted]

Jan,

I think that your last note that even mathematicians speak about mathematical theorems as in "the theorem is probably true" can be interpreted as "such and such persuades me towards thinking it is true".

But they do not take the "such-and-such" as a proof or as conclusive evidence that it is true (or false). Rather they mean it as a claim about their subjective leaning towards the truth or falsity of the theorem. An actual proof is required in order to determine whether it is true or false. And mathematical proofs are the sort of things that entail the truth of mathematical statements.

[T. Hanson]

Peter writes: "Consider a simple example. The proposition 'P & ~P' is necessarily false. Does it makes sense to say that the falsity of this proposition has a high probability based upon evidence consisting of a large number of instances of the same form all of which were found to be false? "

But we know a priori that 'P & -P' is false.' No evidence is required. But we don't know a priori that God exists whether as a necessary being or contingent one; so counter - evidence like the existence of evil could weigh on the negative side of. God's necessity or contingency don't even seem to be relevant to the issue. The probability we are talking about is whether a being exists, and that depends on evidence.

You reply to Jan, "But they do not take the "such-and-such" as a proof or as conclusive evidence that it is true (or false)."

But we don't have conclusive proof that a necessary supreme being exists either.

I don't see a problem here, but I might be missing it ;-)

[Bill Vallicella]

Bob Koepp,

Excellent point. That is indeed part of the puzzle. 'There are evils that are not explainable by free human agency' is an empirical, contingent proposition. 'There is no God' is a necessary proposition if true. What inference principles could license the move from the first to the second?

[Bill Vallicella]

T. H.,

LNC we know a priori. That God exists we do not know a priori. Granted. But we do know a priori that either God is necessary or God is impossible. And we know a priori that either Goldbach's Conjecture (Every even n > 2 is expressible as the sum of two primes)is either necessarily true or necessarily false.

So Peter's problem arises: How can empirical evidence be relevant to deciding either of these questions?

[Bill Vallicella]

Suppose God exists. Then he nec. exists. It follows that any evil there is just has to be logically consistent with the existence of God.

Now turn it around the other way. Here is some evil that cannot be laid at the doorstep of a free agent, e.g. Bambi being burned alive in a forest fire. Assume that this is indeed an evil, and assume that God is noncontingent. How can this natural evil provide any evidence for the nonexistence of God? If God exists, then the counterevidence is merely apparent. If God does not exist, then he is impossible. But how can I infer the impossibility of God from a mere contingent fact, namely, that there is natural evil?

[bob koepp]

I'm not enough a modal logician to proffer any substantive response/rejoinder to the problem that Peter Lupu has discerned. But I want to suggest that we're getting just a glimpse of the profoundity (I think that's the appropriate term) of the Anselmian conception of diety. Thank you, Peter.

[Account Deleted]

Gentlemen,

Perhaps this could be a solution to the problem of the present thread. Consider a non-contingent proposition P:

(1) If P is true, then necessarily P is true.
(2) If not necessary that P is true, then it is not the case P is true (Equivalence to (1)).
(3) ~Nec P iff Possible not P (Definitional equivalence between necessary and possible)
(4) If possibly ~P, then it is not the case that P is true. ((3) and substitution)

Now, we can have evidence that possibly ~P if we can get evidence that ~P is true in the actual world. For evidence that ~P is true in the actual world is evidence that Possibly ~P.

What do you think?

[David]

Alvin Plantinga mentions this in an article available here:

www.springerlink.com/index/m58515015517173n.pdf

"But if this is so, then G is a necessary truth, in which case E (and every other proposition) entails G. But if E entails G, then the denial of G is not probable with respect to E--not, at any rate, if the axioms of the probability calculus govern the relationship the atheologian claims that G and E stand in, when he claims that G is improbable with respect to E."

Ibid. (1979). The Probabilistic Argument From Evil. Philosophical Studies 35 (1).

[Bill Vallicella]

Peter,

Your logic is impeccable, but how do we get evidence that ~p when p is noncontingent?

[Nick]

I've only scanned the comments so forgive me if this has been covered. Could I suggest the following? The evidential argument from evil, at least in Rowe's formulation, has been called a deductive argument with an evidential premise (the premise in question being that there are gratuitous evils in the world). It strikes me that probability considerations can affect an evidential premise, which, if accepted, would, in conjunction with another premise (or premises) form a deductive argument against God. So evil does not count against God, it rather counts in favour of a premise in an argument that would rule out God's existence deductively. Likewise, most of the arguments for God are deductive in nature, but often follow from an (extremely plausible) empirical premise that is susceptible to evidential considerations - that the universe is fine-tuned, or that the universe began to exist.
What I think might make this interpretation persuasive is if we look out how Swinburne's arguments work. Swinburne's arguments are inductive, not deductive with evidentially supported premises. However, Swinburne is anxious (a) not to affirm the ontological argument, and (b) not to understand God's necessity in a very strong way. In fact (although my memory is hazy on this), he understands God's necessity as being the ultimate (simple) brute fact.
From this point of view we might see the sceptical theist as denying that the major premise of Rowe's argument can attain evidential support. Any thoughts?

[Account Deleted]

Bill,

My assumption is that to say that p is non-contingent is to say that

(1) If p is true, then p is necessarily true;
&
(1*) If ~p is true, then ~p is necessarily true.

But now this seems to be very strange for in two quick steps you get from (1*), for instance, to

(2*) If possibly p is true, then p is true.

But (2*) is certainly not a theorem of modal logic, so far as I recall (certainly not of S5), and it is clearly counterintuitive. So perhaps non-contingent truths are not captured by propositions such as (1) and (1*). I don't know what to think?

[T. Hanson]

Bill and Peter, your comments helped. So it looks like together with your Anselmian assumption, any possible experience, (not to mention all inductive arguments, and sacred texts) are irrelevant to the probability of God's existence. This is quite a consequence, if true. Thanks.

[Jan]

Firstly, (1) ∧ (1*) of Peter Lupu is indeed equivalent to (2) ∧ (2*) [(2): If possibly ¬p, then ¬p]. It is easily seen. If p is necessary, it is either true in all the possible worlds, or untrue in all the possible worlds. Therefore, if p is true in one of the possible worlds (in other words, p is possible), then p is true in all the possible worlds (in other words, p is true). This might seem counter-intuitive if one confuses modal possibility with epistemic possibility.

The conclusion here seems to be that contingent facts have no bearing on the existence or non-existence of beings defined to be necessary. This does not seem right. 'P exists necessarily' is a stronger claim than 'P exists'. Therefore it is easier to disprove. Clearly, contingent facts can have bearing on the truth of 'P exists'. Here is what I think the main confusion: to disprove the existence of a being whose necessity is a part of its definition, and to prove a necessary non-existence of a being whose modal mode of existence is not known. The first is comparatively easy. It suffices to show its non-existence in one world (that it is possible it does not exist). The second is difficult, and merely contingent facts will not do, as is the common intuition here. One has to show that P does not exist in any world (that it is not possible it exists). Obviously, the case of Christian God is of the first kind.

Dr. Vallicella asks how can one infer the non-existence of a being that is defined to be necessary from contingent facts. Here is how. Let P denote a being whose existence is necessary. Let p denote 'P exists'. Our task is to ascertain whether p is true or untrue in all the possible worlds. Let q denote any contingent proposition that is true in the actual world W. That is, q is true in W and untrue in some other world W'. Consider the proposition ¬p∧q. Suppose it is found to be true in W. It follows that ¬p in W, and from that ¬p in every possible world. ¬p∧q is contingent, because it is false in W', where q is false. Therefore, we have concluded that P does not exist based on two contingent propositions. There is a subtlety here that warrants further thought though: the modal status of ¬p∧q is not known before its truth-value in W is known.

Hopefully this clears the matters of modal possibility at least a little. The murky waters of epistemic possibility still await.

[Bill Vallicella]

Jan writes, "If p is necessary, it is either true in all the possible worlds, or untrue in all the possible worlds." That is not quite right. A noncontingent proposition is either necessary (true in all worlds) or impossible (true in no world). A proposition that is untrue in all worlds is not necessary but it is noncontingent in virtue of being impossible.

First we distinguish the contingent from the noncontingent, and then we divide the noncontingent into the necessary and the impossible. A contingent proposition is one that is true in some, but not all, worlds. A contingent individual is one that exists in some, but not all, worlds. It is important also to realize that contingent propositions and individuals need not actually be true or actually exist.

[Jan]

I stand corrected that the proper language is 'noncontingent' dividing into 'necessary' or 'impossible', and not 'necessary' dividing into 'necessarily true' or 'necessarily false'. The content of my comment stands unchanged.

[Jan]

Is my comment possible to follow with this qualification? If not, I can repost it changing 'necessary' to 'noncontingent' where... needed.

[Bill Vallicella]

But Jan is completely right against Peter when Jan writes, "Therefore, if p is true in one of the possible worlds (in other words, p is possible), then p is true in all the possible worlds (in other words, p is true). This might seem counter-intuitive if one confuses modal possibility with epistemic possibility."

Contrary to what Peter says, there is nothing strange or counterintuitive about *Poss p --> p* when p is noncontingent. If p is noncontingent, then it is either true in every world or in no world. So if there is a world in which p is true (i.e., if p is possible), then it is not the case that p is true in no world. It follows that p is true in every world, which implies that p is true in the actual world, which is to say that p is true simpliciter.

[Bill Vallicella]

Jan writes, " Consider the proposition ¬p∧q. Suppose it is found to be true in W." But that is the whole problem. How do I come to know that ~p is true? For example how do I come to know that *God does not exist* -- which is necessarily true if true -- is true on the basis of some merely contingent fact such as that there are evils not ascribable to human free agency?

[Jan]

Dr. Vallicella,

I am not sure what you mean by "how do I come to know that ~p is true". I attempted to show that it is in principle possible to deduce the truth of a non-contingent proposition from contingent propositions. Do you perhaps mean that to establish a proposition of the form p∧q one needs first to establish p and q separately? This is certainly false if both p and q are contingent or non-contingent.

I suspect it is also false in the case when p and q have different modal status, though I do not yet have an counterexample for this case.

[Bill Vallicella]

Nick,

Thanks for your comments. When Mike V read his paper he made it clear that Rowe's argument was a deductive one with a premise supported by empirical evidence. I took the argument to be of the form Modus Tollens:

1. If God exists, then there are no gratuitous evils
2. There are gratuitous evils.
Therefore
3. God does not exist.

Cases like Bambi the fawn suffering horribly in a forest fire are then brought in as evidence for (2). So what you say in your comment is right and helpful. But I wonder about " So evil does not count against God, it rather counts in favour of a premise in an argument that would rule out God's existence deductively."

One question is how the Bambi example provides any evidence of GRATUITOUS evil. Let's agree that the suffering of the fawn is evil (not exactly obvious, but close enough) and let's agree that the suffering -- the felt suffering, not mere behavior -- is empirically detectable. It seems to me that the GRATUITOUSNESS of the suffering is not empirically detectable. After all, if God exists then there cannot be any gratuitous evils. What is empirically detectable is the same whether or not the sufering is gratuitous. To say of some suffering that it is gratuitous is equivalent to saying that the universe is godless.

So what I quoted you as saying doesn't seem quite right. The only evil that can count against God is gratuitous evil, but gratuitousness is not an empircally detectable feature.

Please note also that one who holds, as I do, that the concept of God is the concept of a noncontingent being is not committed to the soundness of the ontological argument, though he may be committed to the validity of the modal OA.

[Bill Vallicella]

Jan,

No need to repost.

[David]

My reading of Rowe's argument for P2 comes from Peterson's "Contemporary Debates in the Philosophy of Religion."

1. If there was a justifying reason for E, we would probably conceive of it
2. We can't conceive of a justifying reason for E
3. Therefore, there probably isn't a justifying reason for E

Skeptical theists deny the first premise and theodicists attempt to deny the second premise. Rowe seems to assume we can detect gratuitousness; he asserts that we should be able to conceive of outweighing goods or evils that couldn't obtain without E. I'll raise a concern with that later.

In the argument I studied, Rowe avoided deductively concluding that God doesn't exist. Instead he concludes this:

4. Therefore, putting aside all other arguments for G or ~G, the existence of many gratuitous evils lowers the probability of G

This is what Rowe seems to conclude, and perhaps he purposely weakens it to avoid the ontological argument?

All that aside, where is the skeptical naturalist in this discussion? Even if theism doesn't entail that we should conceive of justifying reasons for the variety of evils we find in our world, does naturalism provide us with the epistemic equipment with which to judge goods and evils and the relationship they have to other goods and evils? What kind of evolutionary advantage could such cognitive capacities possibly derive from?

Enough of my ranting, I'll stop stirring you gentlemen off course. *grin*

[David]

*Steering. Better not mix my metaphors...

[James Anderson]

I don't have an explanation as to how noncontingent propositions could enjoy evidential support, but I don't share Peter and Bill's sense that "evidential considerations are simply irrelevant to the probability of noncontingent propositions." Consider Goldbach's conjecture. If true, it is necessarily true. It remains unproven, yet it seems to me that its verification (to date) for integers up to 1.6 x 10^18 is good evidence that it is indeed true (perhaps conjoined with certain basic intuitions about mathematical order and simplicity). In other words, if I were a betting man, I'd bet on its being true. Wouldn't you?

[Bill Vallicella]

Welcome back, James. Funny, I was just thinking about the GC along those lines before seeing your comment. Your challenge is a good one. I have two responses.

What puzzles Peter and me is the notion that a noncontingent proposition can gain evidential support from contingent propositions. But the evidence you cite, based on individual calculations, results in a series of necessary truths, e.g. '4 = 3 + 1', '6 = 3 + 3', '8 = 5 + 3', and so on. So your response does not seem relevant.

Second, if there is an actual infinity of natural numbers, then the fact you cite about verification having proceeded very very far out does not amount to GOOD evidence that the GC holds for all aleph-nought of the naturals.

It is not at all clear that it is a good bet! It is arguably a very bad bet given how tiny is the proper subset you mention as compared to all the naturals.

You may of course wish to contest the very idea of actual or completed infinities.

[Bill Vallicella]

David,

Thanks for your comment. Perhaps I can get to it tomorrow.

[Account Deleted]

James,

Good *seeing* you again.

You say regarding Goldbach's Conjecture that based on a large number of positive cases that "if I were a betting man, I'd bet on its being true. Wouldn't you?"

Perhaps you would so bet. But that would simply reflect your subjective degree of belief based upon a large sample. But what I find difficult to understand is how degree of belief can constitute evidence for something that is necessary.

Consider the following contingent proposition: All ravens are black. Suppose that we find a huge number of ravens (select your favorite number) that are black and none that are white. Surely this would be strong evidence in favor of the truth of the proposition. Moreover, we would hardly expect a better confirmation of the truth of the proposition than what we have already obtained in our examined sample.

But this is not what happens in the case of mathematical propositions. Regardless of how large is the number of integers for which GC was shown to be true, we still require a proof that it holds for all integers, a proof that will rule out any *possibility* of a counterexample. So while the large number of positive cases may induce a high degree of belief in its truth, high enough to bet on its truth, it cannot ever replace a proof. Why is that?

[David]

Given how sloppy my original post was, I won't fault you for not responding at all!

I should have said: "outweighing evils/goods that would/wouldn't obtain without E"

[Bill Vallicella]

Pter,

Glad we agree about Anderson's response. But I need to have your agreement on this as well:

For any noncontingent proposition p, *Possibly p* entails *p.*

[Bill Vallicella]

Jan,

I wonder if you can state your argument more simply and clearly. I don't think I understood it.

David,

If it is probable that there are no justifying reasons for E, then it is probable that there are some gratuitous evils. But how do we get from the probability of some gratuitous evils to the necessary nonexistence of God?

[Account Deleted]

Bill,

I feel somewhat reluctant to accept the following two principles regarding noncontingent propositions:

1) Possibly p, then p;
2) p, then Necessary p.

The reason is that for all propositions, including noncontingent ones, the following two principles hold:

3) p then Possibly p;
4) Necessary p, then p.

But now (1) and (3) entail:

5) p iff Possible p;

and (2) and (4) entail:

6) p iff Necessary p.

Thus, it follows that for noncontingent propositions truth/falsity and modality collapse. That is a strange consequence. On the other hand, I cannot see how else to characterize noncontingent propositions except by (1) and (2).

[David]

Perhaps I am unable to grasp this issue enough to grapple with it. Rowe states that he is starting with a .5 probability of G. This already contradicts what can be said of the objective probability of G--if G were necessarily true of false then the probability should be 1 or 0. Is he saying that E lowers the subjective probability of G? Setting aside the endless debates about whether or not subjective probabilities conform to the axioms of probability calculus, I come up empty handed. Rowe’s argument doesn’t seem to work if your modal properties are granted. Very interesting!

[Jan]

Dr. Vallicella,

Here is my core argument. It is very simple. You say: "how can I infer the impossibility of God from a mere contingent fact". I understand you to hold (or seriously consider) the following proposition:

(*) One cannot even in principle deduce the truth value of a non-contingent proposition from contingent propositions.

I think (*) is false and provide a counterexample - two contingent propositions that imply the truth of a non-contingent proposition.

1) Let p denote a non-contingent proposition truth of which is unknown.
2) Let q be any contingent proposition true in the actual world W.
3) Suppose the proposition r := ¬p∧q is true in W. Note that r is false in a world where q is false and thus r is contingent.
4) From q true in W and r true in W one easily deduces ¬p true in W. Thus, ¬p simpliciter.

[Bill Vallicella]

Peter,

The second of your principles doesn't hold. If p is impossible, then of course it cannot be necessary. Also, (3) doesn't hold. Suppose p is impossible.

(5) is not problematic given that p is necessary. (2) is false so the argument to (6) is unsound.

I don't understand what that collapse is supposed to be. If a proposition is necessary, it is true in every world; if impossible, then false in every world. What's the problem?

[Bill Vallicella]

Jan,

Your reasoning appears correct, but it is not relevant to my concerns. I was not talking about deduction but about evidential support. *God exists* if true is necessarily true. If false, necessarily fale. OK? Now the question is how any contingent empirical fact such as the fact that there is a lot of evil in the world could count as evidence of the falsity of *God exists*. How could that evidence lower the probability of the truth of that proposition?

[Paul]

Guys, I have a question: couldn't the contingent evidence be used to show that a God of a certain sort of conception doesn't exist? So far our conception of God is: "the concept of a being that has a certain modal property, the property of being such that, if existent, then necessarily existent, and if nonexistent, then necessarily nonexistent. Call this the Anselmian conception of deity." But the evidential argument from evil isn't meant to show that that God doesn't, but rather one that is also purported to be all-good, all-knowing, and all-powerful.

For example, what if one's concept of God was that he is necessarily truthful, along with the above attributes. Now, suppose this God revealed that *I* did not exist. If I exist, that's contingent. And I do exist (I hope!). So this would be contingent evidence which lowers the probability of that God existing. Or, suppose this truthful God says he raised Jesus from the dead. but what if we find the bones of Jesus. Would that be contingent evidence against a certain sort of God that is also purported to be necessary? It wouldn't show that there is nothat alleged necessary being aint it. Thoughts?

[Paul]

Sorry, my second to last sentence, "It wouldn't show that there is nothat alleged necessary being aint it" should be "It wouldn't show that there is no necessary being, it would show that that alleged necessary being (probably) aint it."

[Luke Gelinas]

Why can't the evidential arguer just state the argument as an attempt to show that the evil we find in the actual word renders God's existence in the actual world implausible?

It seems the discussion might be in danger of saddling the evidential argument with assumptions it doesn't need (S5, that God either exists in all worlds or none, etc). I don't see why the argument can't just aim to conclude that God's existence in the actual world is improbable, and let us conclude what we may from this. Also, wouldn't the line being pushed rule out any kind of non-a priori argument *for* God's existence as well?

[Bill Vallicella]

Paul,

I didn't mentiion the standard omni-attributes, but that was just to save keystrokes. The reference to Anselm ought to have sufficed to make it clear which conception of God is in play.

Luke,

Everything hinges on one's conception of God. A contingent god is not God.

[Luke Gelinas]

I'm not sure everything turns on this. Even if you believe that God necessarily exists, can't there be evidence in the actual world that God doesn't exist at the actual world?

On classical theism, shouldn't the extent to which evil in the actual world lowers your credence that God exists in the actual world be the extent to which your credence that God exists at all, in any world, be lowered? Since God either exists in all worlds or none, why wouldn't evidence that God doesn't exist in the actual world be evidence that God doesn't exist in any, given classical theistic commitments?

[bob koepp]

Luke - I wonder how there could be evidence that God doesn't exist at the actual world. Rather, there would be evidence that this bit of the actual world is not God, and that bit of the actual world is not God, and that bit, and so on. What I don't see is how an accumulation of such evidence could bear on the question of whether God exists at the actual world.

[Paul]

Bill:

I think some hold to Anselm's conception but differ on some of the omni-attributes. I'm not sure it follows from the claim that God is a necessary being that he is therefore "omnibenevolent" (and worse, you'd have to cash out what that means, there are different understandings even here). So I'm wondering why contingent evidence can't be used to show that God, if he exists, is probably not all-good/loving on some ostensible conception?

Furthermore, much trades on how one understand the claim that God is good. Does this mean he would not allow any evil whatever, and instance of gratuitous evil, etc? If my view is that God would not allow any instance of gratuitous evil, and then someone offers a case that is "probably" gratuitous evil, how does that not support a conclusion that my conception of God probably doesn't exist?