A Default Argument for Atheism
Michael Tooley (2008) argues that atheism is the default position. His argument is simple and can be strengthened. I will state his argument briefly and then strengthen it. I will then discuss a few responses that one might make to the strengthend argument, and, following this, offer a few reasons to doubt that these responses are successful. My conclusion will be a rather strong one: we should be atheists.
Tooley's Argument
Premise One: The prior probability that God exists is 1/3.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.
An Argument for (P1)
Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
Premise Two*: If (P1*), then the prior probability that God exists is 1/3.
SubConclusion: The prior probability that God exists is 1/3.
An Argument for (P1*)
Premise One**: A being that is jointly omnipotent and omniscient will be either (a) morally bad, or (b) indifferent, or (c) morally good.
Premise Two**: The prior probabilitity that a being that is jointly omnipotent and omniscient will be morally good = the prior probability that he will be morally indifferent = the prior probability that he will be morally bad.
Premise Three**: If (P1**) and (P2**) are true, then the prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
SubConclusion: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
An Argument for (P2)
Premise One***: If the prior probability that God exists is 1/3, then we should believe it is 1/3 likely that God exists before considering any other evidence.
Premise Two***: If we should believe it is 1/3 likely that God exists before considering any other evidence, then were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist.
Premise Three***: If were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist, then atheism is the default position.
SubConclusion: If the prior probability that God exists is 1/3, then atheism is the default position.
That's the argument. Note, too, that it is assumed throughout the argument that God exists iff God is jointly omnipotent, omniscient and morally good. Now, I don't think that believing it is 1/3 likely that P makes it reasonable to believe that not-P. But Tooley can concede this point and simply stipulate that by 'default position' he means simply that, were we forced to gamble as to whether God exists, prior to obtaining further evidence, we should gamble that God does not exist.
This is an interesting argument and what seems to me even more interesting is that it can be significantly strengthened. We can partition degrees of moral goodness more finely than Tooley does. That is, assuming that (a) moral goodness comes in infinitely many quantities and (b) God exists only if he has exactly the highest possible quantity of goodness, and (c) there is a highest possible quantity of goodness, we get the conclusion that the prior probability that God exists is either zero or infinitesimal. If the prior probability is zero, no evidence can raise the probability that God exists. If it is infinitesimal, then it would take, well, a whole lot of evidence to raise the probability that God exists. We have no such evidence (even fine-tuning wouldn't get us this) and so we should be atheists.
The Strengthened Argument
Premise One: The prior probability that God exists is 0 or infinitesimal.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.
An Argument for (P1)
Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good to the highest possible degree is 0 or infinitesimal.
Premise Two*: If (P1*), then the prior probability that God exists is 0 or infinitesimal.
SubConclusion: The prior probability that God exists is 0 or infinitesimal.
I won't repeat the rest of the defense. The defense is relevantly the same. But here is another way to make the point in the form of an argument from analogy.
Suppose a solid were to pop into existence moving at a constant velocity. Let's say the solid is the referent of 'Fred' iff the solid has a mass of exactly 6 units, a volume of exactly 6 units, and a velocity of exactly 6 units. Suppose now that, in fact, a solid pops into existence in front of you and you can see it and watch it moving. What is the prior probability that that solid is Fred? The idea is that the prior probability is either 0 or infinitesimal. In order to be Fred the solid must have a precise combination of three properties, each of which comes in infinitely many quantities. Since any combination is, prior to evidence, just as likely as another, the probability that the solid is Fred = 1/infinity (which means it is either 0 or infinitesimal depending upon which math is correct). Thus, we should think that it is very likely indeed that the solid we are looking at is not Fred. What's more, it would take a whole lot of evidence to make it reasonable to believe the solid is Fred. The same goes for God.
Response One:
Surely we could get evidence that I exist (just look at me) and we could know that I have some exact quantity of a variety of properties that come in infinite quantities. So, can't the same be true of God?
No. God is defined as a being with the highest quantity of omniscience, omnipotence, and moral goodness. Unlike God, I am not defined as such a being. We could get evidence that I exist without getting evidence that, for some particular weight, I have that weight. This is not so for God. If we get evidence that God exists, then we must get evidence that a being with the highest quantity of those three properties exists.
Response Two:
We could still get evidence, even if this argument is sound, that there is a being that is jointly omniscient and omnipotent is also very morally good, for some range of quantities of goodness.
Yes. I am assuming that God, if He exists, has the highest of such a range. A being that has less than the highest degree of goodness, I am assuming, is unfit to be the referent of 'God'.
Response Three:
But it seems possible to get evidence that the solid is Fred. Couldn't God tell you this? And couldn't you imagine a possible instrument that could, having measured the solid, make it reasonable to believe the solid is Fred. And so, shouldn't we say the same for God?
First, supposing this is right, what premise is false? Second, perhaps we should simply say that 'no' we could not get such evidence and that's just a strange, but correct consequence of dealing with properties that admit of infinitely many quanitities. Infinitity is strange, but notice, even the theists trafficks in infinity talk and so she should be the last person to doubt the intelligibility of its application.
So, what do you think readers?
Tooley's Argument
Premise One: The prior probability that God exists is 1/3.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.
An Argument for (P1)
Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
Premise Two*: If (P1*), then the prior probability that God exists is 1/3.
SubConclusion: The prior probability that God exists is 1/3.
An Argument for (P1*)
Premise One**: A being that is jointly omnipotent and omniscient will be either (a) morally bad, or (b) indifferent, or (c) morally good.
Premise Two**: The prior probabilitity that a being that is jointly omnipotent and omniscient will be morally good = the prior probability that he will be morally indifferent = the prior probability that he will be morally bad.
Premise Three**: If (P1**) and (P2**) are true, then the prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
SubConclusion: The prior probability that a being that is jointly omnipotent and omniscient is also morally good is 1/3.
An Argument for (P2)
Premise One***: If the prior probability that God exists is 1/3, then we should believe it is 1/3 likely that God exists before considering any other evidence.
Premise Two***: If we should believe it is 1/3 likely that God exists before considering any other evidence, then were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist.
Premise Three***: If were we forced to believe that (a) God exists, or (b) God does not exist, we should believe that God does not exist, then atheism is the default position.
SubConclusion: If the prior probability that God exists is 1/3, then atheism is the default position.
That's the argument. Note, too, that it is assumed throughout the argument that God exists iff God is jointly omnipotent, omniscient and morally good. Now, I don't think that believing it is 1/3 likely that P makes it reasonable to believe that not-P. But Tooley can concede this point and simply stipulate that by 'default position' he means simply that, were we forced to gamble as to whether God exists, prior to obtaining further evidence, we should gamble that God does not exist.
This is an interesting argument and what seems to me even more interesting is that it can be significantly strengthened. We can partition degrees of moral goodness more finely than Tooley does. That is, assuming that (a) moral goodness comes in infinitely many quantities and (b) God exists only if he has exactly the highest possible quantity of goodness, and (c) there is a highest possible quantity of goodness, we get the conclusion that the prior probability that God exists is either zero or infinitesimal. If the prior probability is zero, no evidence can raise the probability that God exists. If it is infinitesimal, then it would take, well, a whole lot of evidence to raise the probability that God exists. We have no such evidence (even fine-tuning wouldn't get us this) and so we should be atheists.
The Strengthened Argument
Premise One: The prior probability that God exists is 0 or infinitesimal.
Premise Two: If (P1), then atheism is the default position.
Conclusion: Atheism is the default position.
An Argument for (P1)
Premise One*: The prior probability that a being that is jointly omnipotent and omniscient is also morally good to the highest possible degree is 0 or infinitesimal.
Premise Two*: If (P1*), then the prior probability that God exists is 0 or infinitesimal.
SubConclusion: The prior probability that God exists is 0 or infinitesimal.
I won't repeat the rest of the defense. The defense is relevantly the same. But here is another way to make the point in the form of an argument from analogy.
Suppose a solid were to pop into existence moving at a constant velocity. Let's say the solid is the referent of 'Fred' iff the solid has a mass of exactly 6 units, a volume of exactly 6 units, and a velocity of exactly 6 units. Suppose now that, in fact, a solid pops into existence in front of you and you can see it and watch it moving. What is the prior probability that that solid is Fred? The idea is that the prior probability is either 0 or infinitesimal. In order to be Fred the solid must have a precise combination of three properties, each of which comes in infinitely many quantities. Since any combination is, prior to evidence, just as likely as another, the probability that the solid is Fred = 1/infinity (which means it is either 0 or infinitesimal depending upon which math is correct). Thus, we should think that it is very likely indeed that the solid we are looking at is not Fred. What's more, it would take a whole lot of evidence to make it reasonable to believe the solid is Fred. The same goes for God.
Response One:
Surely we could get evidence that I exist (just look at me) and we could know that I have some exact quantity of a variety of properties that come in infinite quantities. So, can't the same be true of God?
No. God is defined as a being with the highest quantity of omniscience, omnipotence, and moral goodness. Unlike God, I am not defined as such a being. We could get evidence that I exist without getting evidence that, for some particular weight, I have that weight. This is not so for God. If we get evidence that God exists, then we must get evidence that a being with the highest quantity of those three properties exists.
Response Two:
We could still get evidence, even if this argument is sound, that there is a being that is jointly omniscient and omnipotent is also very morally good, for some range of quantities of goodness.
Yes. I am assuming that God, if He exists, has the highest of such a range. A being that has less than the highest degree of goodness, I am assuming, is unfit to be the referent of 'God'.
Response Three:
But it seems possible to get evidence that the solid is Fred. Couldn't God tell you this? And couldn't you imagine a possible instrument that could, having measured the solid, make it reasonable to believe the solid is Fred. And so, shouldn't we say the same for God?
First, supposing this is right, what premise is false? Second, perhaps we should simply say that 'no' we could not get such evidence and that's just a strange, but correct consequence of dealing with properties that admit of infinitely many quanitities. Infinitity is strange, but notice, even the theists trafficks in infinity talk and so she should be the last person to doubt the intelligibility of its application.
So, what do you think readers?
posted by Christian at 8:40 PM
7 Comments:
Hi Christian,
I have an initial thought that may not be relevant to some variants of your argument. Some people think that a being that has some divine attributes has to have other divine attributes as well. for example, if a being is omnipotent and omniscient, then (some might think) he has to be perfectly morally good. Here is the thought. If a being is omniscient, then he is a rational being that knows all the moral truths. Given that he knows all the moral truths and that he is rational, he must want to act in accordance with those truths. But, he is also omnipotent. So, he is able to do what he wants. So, he is able to act in accordance with all the moral truths. So, an omnipotent and omniscient being must also be perfectly good.
If this kind of argument is correct, then Premise One* in your argument is false. I do admit that this is a rather controversial kind of response and I also admit that a simple modification to your argument might be able to avoid this kind of response (for example, you can focus on gradations of omnipotence rather than goodness).
Hey Joshua,
I agree and I agree.
For example, if we assume a certain view of "Motives Internalism" then Premise One* is false. And my response is exactly what you indicate, i.e., to move to omnipotence or omniscience rather than moral goodness. I think these other arguments are just as strong.
I don't think that Motives Internalism is true though. I'm convinced by the case of the amoralist. It seems possible to me that someone could know what the right thing to do is, but simply fail to have the motivating desire to do it. I think I should be giving much more money to charity, I think I know this is the right thing to do, but I am miserable, I lack the relevant desire.
Christian,
I thought that you would respond the way that you did. However, I just wanted to clarify one thing. I am not sure how you would formulate the view that you call 'motives internalism'. However, I think that the thesis I was relying on is weak enough that it should not be threatened by the possibility of a amoral person who knows what is morally right.
Here is the thesis that I was considering:
For any S and any A, if (i) S's knows that doing A is not morally permissible, (ii) S has no reason in favor of refraining from doing A, (iii) S can do A, then S acts rationally only if S does A.
I was assuming not only that God knows all the moral truths but that God is also fully rational.
I also have a worry about Premise Two*. The word 'God' is used in lots of different ways. It seems, though, that grammatically, it is a proper name. If that is the case, then even if God happens to be the one and only omnipotent, omniscient, perfectly good being and even if the prior probability of there being such a being is 1/3, it might still be the case that the prior probability of God existing is greater than 1/3.
Here is an analogy. Suppose that Christian happens to be the one and only being that fits perfectly description D. Suppose also that the prior probability of something fulfilling description D is 1/3. It might still be the case that the prior probability that Christian exists is greater than 1/3. After all, given that it is a prior probability, it seems that it should be a probability taken independently of our belief (or lack thereof) that Christian is D. Perhaps, given a principle of indifference the prior probability of Christian existing is 1/2.
Similarly, we might think that the prior probability of there being an omnipotent, omniscient, perfectly good being is 1/3, yet the prior probability of God existing is 1/2. Of course, given these two values, the probability that God exists and that God is omnipotent, omniscient and perfectly good might still be significantly less than 1/2.
Yo Joshua,
Let me consider this principle:
For any S and any A, if (i) S's knows that doing A is not morally permissible, (ii) S has no reason in favor of refraining from doing A, (iii) S can do A, then S acts rationally only if S does A.
I think there's a 'not' in clause (i) that needs to be taken out. Having taken it out, though, I think there is a counterexample.
I know that wearing a white t-shirt rather than a black t-shirt today is morally permissible. I have no reason for refraining from wearing my white t-shirt, and I can. The principle above implies that, in this situation, I act rationally only if I wear my white t-shirt. But I think that's wrong since I could act rationally by wearing my black t-shirt.
I think there is a simple way of making degrees of moral goodness not probabilistically independent of degrees of omniscience. One of many good-making properties of a being is that she knows the moral truths, and so, being perfectly omniscient entails this property. But, if P entails Q, then Q is not probabilistically independent of P.
Your second worry is similar to one that has been bothering me and I'm unsure that my answer will seem satisfactory, but here's a go. In my argument I assumed that God exists iff a being that is jointly omniscient, omnipotent, and morally perfect exists. But, as you say, we might think the prior probability that God exists is greater than the prior probability that a being with these three properties exists. We could think the former is 1/2.
My claim is that this leads to probabilistic incoherence. I think that, as a general rule, if it is believed by S that (P iff Q), then if the prior probability of Pr(P) for S = n, then the prior probability of Pr(Q) for S = n. If you want me to prove this I think that I can, but I'm pretty lame at proofs, and it would take me a few days to do it right. I'm very confident that this principle (or a version of it) is widely accepted.
What's important, I think, is that the biconditional: God exists iff there exists a being that is jointly omnipotent, omiscient, and morally perfect takes no stand on the semantic question. Let the description give the meaning of 'God', or fix its reference, or unpack a mode of presentation (I don't know, maybe there are other options too), but all I need is the truth of the biconditional.
But suppose I'm just wrong. Won't this point leave unaffected an argument formally similar to the one I gave, but where 'God' is replaced with 'A being that is jointly omnipotent, omniscient, and morally perfect'? Then, I could add as a premise:
Premise n: If Atheism about a being that is jointly omnipotent, omniscient, and morally perfect is the default position, then atheism about God is the default position.
Christian,
I'm very sorry, my principle has several mistakes in it. I was thinking of two different ways of formulating it and mixed them up. Here is what I'd like it to say:
For any S and any A, if (i) S knows that doing A is morally obligatory, (ii) S has no reason in favor of refraining from doing A, and (iii) S can do A, then S acts rationally only if S does A.
This should not fall prey to your counterexample.
I am surprised to learn that this is a widely accepted principle:
"if it is believed by S that (P iff Q), then if the prior probability of Pr(P) for S = n, then the prior probability of Pr(Q) for S = n"
Isn't a prior probability supposed to be a probability assigned when there is a certain lack of evidence. If a person believes (or at least rationally believes) that P iff Q, then that person should have evidence that bares on the issue of whether P is true and whether Q is true. So, shouldn't he assign a posterior probability to P and Q? Moreover, shouldn't the posterior probability for P be the same as Q?
Joshua,
The new principle is better:
For any S and any A, if (i) S knows that doing A is morally obligatory, (ii) S has no reason in favor of refraining from doing A, and (iii) S can do A, then S acts rationally only if S does A.
I'd like to remain agnostic about it. For all I can tell, it's correct. But I think there are many conceptions of rationality, and I can't tell whether it's correct given each kind of rationality that may be substituted in your principle. But, that being said, now I'm dubious that the truth of the principle is a problem for my argument.
The idea is that clause (ii) in the principle does not follow from any of my assumptions. Clause (i) follows from omniscience, and (iii) follows from omnipotence. Let me take forgranted the claim about rationality. But what of the claim in (ii), is it to be a stipulation?
If so, then I won't make that stipulation in my argument. My idea is that knowledge and omnipotence place no constraints on the desires of anything that has them, and desires can provide reasons in favor of refraining from doing what's morally obligatory. So, even if your principle is true, it doesn't apply to the being my argument is claiming is unlikely to exist. If your principle did apply to this being, then it would be claiming that it didn't have such desires, but nothing in my argument entails this. And I don't mean to include this.
Isn't a prior probability supposed to be a probability assigned when there is a certain lack of evidence.
Yes and this is an interesting worry. Suppose I grant this point and include in my evidence only the claim that God exists iff a being that is omnipotent, omniscient and morally perfect exists. I then change the argument to being about posterior probabilities, but only when this one proposition is taken as evidence, and then say atheism is the default position when this is taken into account. It seems to me, right now, that the argument still goes through. Moreover, we will still be considering something very much like a prior probability, it will be a probability before considering any evidence other than this one biconditional.
On the other hand, maybe we should simply include in our priors certain biconditionals, namely, those are stipulated. I don't yet see any problem for doing this. We could call stipulations 'evidence', but in an important sense they are not. If they were, at any rate, then it would be too easy to get evidence, i.e., just sit around and stipulate willy-nilly and you get evidence. That seems wrong to me. That is, it seems to me that the notion of 'evidence' at work in the prior/posterior distinction is not that kind of evidence.
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