Monday, July 12, 2010

Science, Religion And Two Very Silly Claims Often Made By Agnostics

If the people running the atheist bus campaign had asked me, I would have balked at the word 'probably' and pushed for something like, "We Can Be As Sure Of The Non-Existence Of God As We Can Of Anything, So Stop Worrying And Enjoy Your Life." Then they would have pointed out that my version is a lot clunkier than theirs, and that it would be harder to fit on the side of a bus in letters big enough for people to read as it rolled down the street, and I would have said, OK, despite my deep commitment to fallibilism about absolutely everything (and, yes, that includes fallibilism, and no, you can't run a self-refutation argument against fallibilism on that point, unless you want to beg the question by simply assuming that certainty is a requirement for knowledge), I'm slightly uncomfortable with the word "definitely", but I'll accept it as a necessary simplification for the sake of space.

As it happens, Richard Dawkins, being prominently involved in the project, actually did argue for the phrasing "almost certainly." Whether or not this is equivalent to my "as sure as we can be about anything" formulation presumably depends on whether Professor Dawkins thinks that we can be absolutely certain about anything. (I'm not sure.) My position, at any rate, is that (a) the Stone Paradox is just as much of a logical problem for the claim that an omnipotent being exists as Russell's Paradox is for naive set theory, (b) we have powerful empirical evidence against the existence of God in the form of the Problem of Evil, and that, (c) given the total absence of anything resembling evidence for the existence of God, even if there were no evidence against the existence of God, and theism were a logically coherent position, and we were in an "all else being equal" situation, atheism would still win hands down as a matter of sheer ontological simplicity.

(If I tell you that an invisible three-inch-tall elf is jumping around on my right hand as I type, tap-dancing and singing show tunes at a frequency that no human or piece of recording equipment can detect, your response will obviously and correctly be active disbelief. No rational person would respond with, "well, it's probably wiser for us all to be humble and admit that no one really knows whether or not there's an elf....")

Despite all of this, a lot of nice enlightened tolerant liberal agnostic types balk at the claim that we can be confident about the non-existence of God, citing the deeply silly and confused claim that "you can't prove a negative." A related and equally silly objection comes from people who, often in the context of tut-tutting at the involvement of folks like Dawkins in things like the atheist bus campaign, say (often in a tone that indicates that they take themselves to be delivering a great insight) that "there can't be a conflict between science and religion because they concern different subjects."

(Note that, while I have heard one or two people who do philosophy for a living express similar sentiments--even the best of us have days where we haven't had enough coffee in the morning to think straight--I'm mostly talking about "the folk" here, or rather a certain very recognizable subsection of the folk who read the New York Times, listen to National Public Radio and studiously avoid having "extreme" or "strident" opinions about anything.)

The force of that second objection, of course, relies on playing with an ambiguity about the word "science." If by "science", you mean to narrowly refer to chemistry, physics, biology and so on, then, sure, it's true that there's no direct logical conflict between theism itself and the deliverances of these fields. Of course, many religions do make specific claims that can and do conflict with the findings of physics, chemistry, biology and so on--creationism being only the most obvious example--but other religious views are specifically designed to avoid such conflicts, and certainly the claim "an all-powerful, all-knowing, all-good being exists" doesn't by itself directly conflict with the findings of any of those fields.

If, however, by "science", one means to refer more broadly to the overall project of trying to understand the world in a rational, evidence-driven way--with chemistry, physics, biology and the rest being important elements of that project, but not the whole of it--then, yes, "science" in that sense does indeed conflict with religion, in so far as the Problem of Evil gives us an extremely convincing empirical, evidential argument against theism, there's no evidence for the existence of God, and the sorts of considerations of simplicity, non-adhocness and so on that necessarily drive theory selection in every part of the overall project should lead us to favor atheism.

The first objection is even stranger. Of course you can prove a negative. I'm constantly amazed by the number of otherwise bright, college-educated people who have somehow gotten it into their heads that it's impossible to do so. If by "prove," one means "show by means of evidence," then, remember, Sir Karl Popper thought that the whole of science was a matter of disconfirming theories--conjectures and refutations--and never a matter of confirming them. Even if one isn't willing to go quite that far, it's still indisputably true that we often have evidence that shows us that certain things are not the case. If a consequence of Astronomical Theory A is that such-and-such planet will be at such-and-such position at a certain time, and at the relevant time, we observe the relevant position and the planet isn't there, that's evidence against Astronomical Theory A. (Similarly, an obvious consequence of theism is that unnecessary suffering shouldn't exist, but it does exist, in great quantities, and the theist has no convincing way to explain it away. This is evidence against theism.) Without this sort of negative evidence, the process of doing science would be unrecognizable.

(Also, of course, given the logical law of double negation, any evidential confirmation of any claim P is also a confirmation of the negation of ~P.)

If by "proof", one does not mean "demonstration by evidence" but "proof" in the strict sense used by mathematicians or logicians, then the claim that "you can't prove a negative" becomes, if possible, even sillier and stranger than it was when we understood "proof" evidentially. There are simple, elegant and decisive proofs of the fact that there's no largest prime number, that there's no set of all ordinal numbers, and so on. So, whether one means "prove" in this narrow sense or in a broad enough sense to include evidential confirmation, the claim that one can't prove a negative is bizarre.

Still, can we specifically prove this negative (that God doesn't exist), in the strict, narrow sense of "prove" just discussed? I think so, yeah.

One of the most famous negative proofs in the history of philosophy and mathematics is Bertrand Russell's refutation of naive set theory, which goes like this:

Start with the claim that, for every description you can come up with, there's a set of all and only and only the objects that match that description. Question: What about the set of all sets that are not members of themselves? Is it a member of itself? If it is, it isn't, and it isn't, it is. Either way, we've got a contradiction.

Here's the equivalent for God:

Start with the claim that a being exists who can do anything. Question: What about creating a stone so heavy that He Himself cannot lift it? If He can create it, then there's something the being that can do anything can't do (create the stone), and if He can't, then there's something the being that can do anything can't do (lift it). Either way, we've got a contradiction.

"But, wait," you say, "can't we just be more careful and re-define omnipotence to avoid these problems? Let's just say that God can do pretty much anything, but there are some limits imposed by logical possibility."

Sure, you can say that. Similarly, the naive set theorist could respond to Russell's Paradox by being more careful about how to express their unrestricted comprehension axiom. They could just say that for pretty much any description we can come up with, there's a set of all and only the objects that meet the description, but that there are some restrictions on this imposed by logical possibility. Or they could reject one of the logical laws used to derive the contradiction. Or they could pull a Modus Ponens where everyone else opts for Modus Tollens, and take Russell's Paradox as an argument for the existence of true contradictions. (Graham Priest does, in fact, take precisely this line, and people who've read this blog before know that, while I disagree with Priest, I take his argument very seriously.) There's a general lesson here: given a conflict among one's beliefs, there are always many different ways of changing those beliefs to resolve the conflict. The process of rational belief revision is all about carefully weighing the options and choosing the best and most plausible alternative. Considerations of simplicty, non-adhocness and so on will come into play, and no solution can be absolutely ruled out in advance.

....which brings us back to where we started. Can we be absolutely certain that God doesn't exist? Nah. But we can be as sure about that as we can about anything, and the bus-campaigner's adjective "probably" severely understates the case.


Colin said...

Hey Ben, first of all: congrats on the shiny new job! Onto the post. I don't substantively disagree with anything you say, but I tend to self-identify as an agnostic about these matters and I was wondering if we might get to the heart of this difference in attitudes. I am mainly curious about the generalization you make that religion conflicts with science in the broad sense. I'm not sure that's true, especially if we allow for religion in the broad sense. The end of the religious spectrum which interests me is the possibility of a more personal, less doctrinal kind of spirituality which is fundamentally concerned with liminal experiences. This sort of thing is often called 'mysticism' and it typically involves the idea that borderline experience plays an essential role in a process of spiritual liberation or enlightenment. I raise this case because what is most philosophically distinctive of mysticism is the claim that the content -- and thus, the significance -- of liminal experience can only be grasped by acquaintance, it cannot be adequately described to someone who has not experienced it (though it can perhaps be metaphorically described, etc...). I have long been fascinated by such views, even tempted to believe versions of them. What is vexing about mysticism from a philosophical/scientific point of view is that one can seemingly have no reason to believe the 'enlightenment myth' is true until one has already experienced it first hand. On the other hand, this also seems to save it from refutation by apriori or empirical argument. What do you think?

Aaron said...

I just believe there are things that outrun our conceptual capacities, (perhaps except for our concept of "existence," so long as you take this to be logically unanalyzable) and might be candidates as answers to some of our largest cosmic questions, if we could know better and know how to conceptualize the right questions. I have a sort of a Kantian position. If you equate God with the noumenal, there you go. That's the extent of my agnosticism. Ok, yeah, yeah, I know, that's not how ordinary religious folk think of God. I should remind you though that there's extensive literature among medieval philosophers as to whether God is even knowable, and I think this has filtered down into part of the modern Christian sentiment.

Ben said...


Thanks, man. As far as mysticism goes, I'm not sure I have anything too interesting to say about it.

(The post itself is about conventional religion and classical theism, since that's what the atheist bus campaign's 'probably' is about and what ordinary western agnostics are agnostic about.)

Basically, my impulse is to separate the questions of (a) whether transcendent experiences might be interesting and valuable, and whether the search for such experiences (through drugs, meditation, study of past mystics, and all sorts of other means) is a worthwhile human activity, and (b) what sorts of metaphysical conclusions one comes to at some point in that quest. I'm actually quite sympathetic to (a), but my instinct is to be at least initially quite suspicious and cautious about conclusions people come to about how the world is on the basis of experiences inaccessible to the rest of us. Of course, that's a fuzzy sort of posture, not a worked-out position.


(1) Equating "God" with "the noumenal" strikes me as so distant from the ordinary meaning of the term as to be not so much an interpretation as a dramatic change of subject. (Certainly unless you take "the noumenal" to have created us, rule the universe, reward and punish us after we die and so on.) Similarly, if I equate "God" with my minivan, then the rationality of theism starts to look pretty different from how it works now.

(2) For familiar reasons, I'm very suspicious of the prospects for cashing out the claim that "there are things that outrun our conceptual capacities" in a remotely coherent way. (In a way, Graham Priest's book "Beyond the Limits of Thought" is an excellent critique of that whole program, although I'd Modus Tollens the sorts of things he Modus Ponens.) Saying that there's way to rule out the possibility that there might be things that outrun our conceptual capacities is one thing, but making a positive claim that there are such things, that you somehow have epistemic access to that fact, strikes me as an extremely strange thing to claim. How do you know? And if we can be aware of at least some of their properties--that they exist, that they outrun our conceptual capacities--doesn't that mean that they don't quite outrun our conceptual capacities?

(3) The Via Negativa isn't quite the same thing as equating God with the noumenal, but I think it faces quite similar coherence problems.

Unknown said...

I think you may need to weaken (C) (in the statement of your position). Anyone who thinks our perceptual/intellectual seemings have prima facie epistemic merit, and recognizes that events in the universe that were not initiated or orchestrated by human agents sometimes appear, nonetheless, to be purposeful, would have to back away from claiming the "total absence of anything resembling evidence for the existence of god". I'll note here that I am an atheist, and think that the prima facie merit of such seemings is overridden.

I also think you may be dismissing responses to the Stone paradox a bit too quickly. Take the sentence "God can create an object so visible that even he can't see it." It seems like a problem with that is a failure to successfully designate an activity-type, and that we wouldn't want to fault omnipotence.

Additionally, I think you need to revise the presentation of the Stone paradox to account for the modal stuff: A being is omnipotent if it can do anything. So if we allow that "creating a stone so heavy an omnipotent being cannot lift it" designates an activity, the being can do that activity. It does not quite follow from that alone that there is something the being can't do, because the stone in question doesn't exist. There is no stone that the being is unable to lift. So, either you want to focus on the being's status in a world where the power to create the stone was exercised (in which case you need to attribute necessary omnipotence), or you need to focus on the activity "create a stone so heavy even omnipotent beings cannot lift it and then lift it". I'm not a hundred percent sure about what happens to the paradox when you rework it in either of those two ways.

Unknown said...

Sorry, I meant to ask (re: the "object so visible" case) whether you agree that that constitutes a "God can ..." we'd refrain from affirming, and whether that is a problem for the hypothesis of an omnipotent being.

Simon Bunckenburg said...

Hi, re your treatment of the problem of evil. I'm suprised you do not mention Platinga's free will response? seems to make sense to me.

ombhurbhuva said...

Is there a fallacy where you refute a position your opponent never held? Maybe it's the straw man who never was fallacy. I'm thinking about the British intelligence coup in WW II and the movie The Man who never was. My point is that Christians freely admit that the 'proof' of the existence of God where offered is not like a scientific proof. I am prescinding from consideration the vapouring of fundies in the U.S. who do not represent sophisticated theological thought. Hindus declare that the existence of God is only known from scriptures. I don't believe that the O.T. offers any notion of a rational demonstration of the existence of God. The Catholic Catechism speaks of converging and convincing arguments not proofs. There is no matter of fact that can be probable or improbable. In other words what they hold, religious folk in general, is that this a matter of supernatural reality and that supernatural reality is accessible by faith which is a subjective thing. Again not scientific. It's verification Ben but not as you know it.

The stone that cannot be lifted. Given omnipotence as a starting point then there could not be such a stone anymore than given that someone is a bachelor they might also be married at the same time. Your conundrum never grows legs so to speak.

As you see it you probably cannot afford the down time involved in getting acquainted with palpable nonsense and it is more economical to simply accept the received dogmas of Internet chatter.

Ben said...


(1) On seemings of purposefulness, would you at least agree on a revised version of (c) that was dialed down to something like "no serious evidence"? If a crime has been committed and I have a gut feeling that John committed it, but he left no fingerprints, no one saw him do it, none of the witnesses described the assailant in a way that sounds like John, he doesn't appear on a videotape recorded by one of them and so on, then, depending on how one feels about the evidential value of "intellectual seemings", I might have grounds for objecting to the formulation "there's a complete lack of evidence that John did it", but surely something very very close to that formulation gets things right.

(2) I like your take on the Stone Paradox. I find that theists almost always pick the other horn of the dilemma, arguing that creating such a stone would be logically impossible and that, as such, God's inability to do so doesn't limit his omnipotence. (I.e. their move is to either de facto water down "omnipotence" in much the way discussed at the end of the post, or to, like Swinburne in "The Coherence of Theism," do things like try to argue that logically possibility is somehow contained in the very notion of an "action.") I find your solution (that an omnipotent being could create such a stone, but the mere possibility of that would only make his omnipotence possibly limited, not actually limited) a lot more promising. That said, I'm not sure that the move couldn't be sufficiently accommodated by altering my slopping formulation "lift it" to something like "lift such a stone."


On Plantinga's free will defense:

See today's post, which is going to be entirely about that!


"Is there a fallacy where you refute a position your opponent never held?"

Yup, and you commit it against me in your comment, when you write:

"My point is that Christians freely admit that the 'proof' of the existence of God where offered is not like a scientific proof."

The only place where I mentioned science was to take issue with the claim that science and religion could not conflict because they had different subject matters. Whether any particular Christian takes themselves to have "scientific" evidence for God is totally and obviously irrelevant to that issue.

"Given omnipotence as a starting point then there could not be such a stone...."

Yes, that's the problem. Given omnipotence as a starting point, any possible way of retaining logical consistency in the face of problems like the Stone Paradox imposes limits on God's power. Your solution--to deny God the ability to create such a stone--is hardly a counter-example to this claim.

Emil O. W. Kirkegaard said...

Yes, there are some silly agnostics, and I really do not like these terms as they are confusing. I like the new nomenclature (something like this:

In any case, another interpretation of "cannot prove a negative" is that it means cannot prove that there isn't a being, b, somewhere in the universe. It doesn't get much better than that, and this is a really far out interpretation.

Your stone-paradox argument doesn't work though. Try writing a formal version of it, or read this:

Ben said...


The solution to the Stone Paradox found at your link is precisely the same as the solution that Lewis floats above, and my response would be about the same.