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Posted by on Jul 20, 2007 in Dawkins, McGrath | 20 comments

Dawkins vs. McGrath – probability

Here’s what I think is wrong with McGrath’s move (see previous post) in the video at 9mins 15-55secs.

He says that whilst God may be highly improbable, the question is: Does God exist?

After all, you and I are highly improbable (probability that our parents should meet, that exactly that sperm should fetilize that egg, etc.). Yet we can be rightly confident that we exist, can’t we?

The implication is that, whether or not Dawkins is right about God’s probability, we might still be rightly confident of God’s existence.

Seems to me McGrath here trades on an ambiguity, that between epistemic and objective improbability.

Objective vs epistemic probability

Philosophers often distinguish objective and epistemic probability.

Objective probability is the probability of X occurring given Y. E.g what’s the probability of a lightening strike hitting just this spot (given the laws of nature plus these initial conditions), or this dice coming up six if we roll it?

Epistemic probability is the probability of a claim’s being true, given the available evidence/grounds.

Something may be objectively improbable but epistemically highly probable. E.g. my existence is objectively improbable, given certain facts (what are the chances of just that egg and sperm meeting?). But the epistemic probability that I exist is very high indeed (for me at least – cogito ergo sum!).

McGrath’s sleight of hand

In the context in which McGrath makes his move, the relevant notion is epistemic probability. Dawkins is suggesting the epistemic probability of God existing is low. It’s unlikely God exists, given the evidence. Belief in God is not well-founded.

It’s this claim McGrath should be dealing with.

McGrath’s counter is to say, in effect, “But something can be very improbable, yet we can still be justified, or have fairly good grounds, for supposing it to be true!” His illustration of this point is: the existence of he and Dawkins is very improbable, yet that they exist is a well-founded claim.

It’s clear, isn’t it, that McGrath is muddling probabilities?

McGrath pretends Dawkins is talking about objective probabilities, when Dawkins is actually (here) talking about epistemic probabilities.

Showing that something can be objectively improbable yet well-founded does nothing to deal with Dawkins’ contention that belief in God is epistemically improbable, i.e. not well-founded.

McGrath’s attempt to disarm Dawkins only looks plausible if we fail to notice this unacknowledged slide from one notion of probability to the other.

Dawkins on the objective improbability of God

Actually, Dawkins does also argue that God is objectively improbable. He argues that the objective improbability of eyes, fine tuning, etc. is not reduced by invoking God, for then we have merely replaced one objectively improbable thing with another.

I’ll discuss that another day.


  1. > Something may be objectively improbable but epistemically highly probable…yech. I’d appreciate some clarification on this point:Are these two probabilities different because they are of different types (epistemic vs. objective)?Or are they different because they’re actually different probabilities? (i.e. they condition on different things)In the example you give ( P(my existence | X) ), you substitute different things for X in the epistemic / objective cases. In the epistemic case, you condition on experiential evidence of your own existence (Cogito ergo sum!), which is obviously going to make it a much higher probability.Can the same thing be analogised to the EoG case as McGrath implies? On re-reading, it seems all he’s claiming is that “there might be things that if we conditioned upon them, the probability of EoG would become very high”. And I don’t think anyone would deny this. They just have trouble coming up with the right things that would convince all reasonable people to the point where they would accept it as true.A further question is: how do we make our epistemic degrees of belief coincide with objective probabilities (presumably measured using statistical techniques). It seems intuitively desirable that the two systems of probability should coincide, provided the same things are conditioned upon.Of course, not all probabilities lend themselves to objective statistical analysis: the EOG for starters. My point (which I think I expressed rather badly before) was that I find it much easier to come up with an epistemic probability that’s already highly conditioned on tons of stuff. In which case, the epistemic prior EOG is simply uninteresting.Appreciate your thoughts on this – it’s an area that interests me.snafu

  2. I find the argument from probability (either objective or epistemic) entirely unconvincing.I don’t want this to turn into an inordinately long tome that no one will read anyway, but I find both arguments lack what I consider the necessary amount of absolutism.I keep reading and hearing about the “lack of evidence” for God. Fine: lets do a Design of Experiments (DOE) to test for God. What do we need? Well, any experimenter worth their salt will tell you, that to produce a “well designed” experiment, you need:1. Objective factors that you are going to measure. These factors must have context and meaning, and its important that you don’t create too big of a factor matrix, which could yield unwieldy amounts of data.2. You need to make certain that you have randomization and blocking in your experiment: This is done to remove (or at least mitigate against) experimenter bias.3. You need to control noise in the experiment. If the noise cannot be controlled, it must at least be accounted for.4. Create a probability model. This model must have an adequately defined probability space, including well-defined states of nature (outcomes) and the events to which a probability is assigned. What objective means is one going to use to assign the states of nature? In none of Dawkins arguments (nor anyone else that I have seen) is there this type of scientific rigor. Dawkins simply speculates. Probabilities are assigned with no rational justification apart from his pre-bias. There is no numerical analysis, nothing that could even remotely be considered “scientific.”YET he (and others) say “there is no evidence.” Well, no, OF COURSE NOT: The heavy lifting has never been done. So, ultimately, to me, the “no evidence” claim is pretty hollow. Note that I’m not attempting to defend theist nor atheist, but I think the argument as presented by Dawkins (et. al.) lacks requisite rigor to be considered “science” or “scientific.”

  3. Yes, please could you discuss Dawkins’ argument of the objective improbability of God one of these days.I think it is actually Dawkins’ central argument against God (although I agree that the he is talking about the epistemic probability at the point in the video which you highlight).I find the topic fascinating but complicated…and any illumination would be gratefully appreciated!

  4. Steve: You say you think the “no evidence” argument for god is unconvincing. Do you have any evidence?I would be convinced if God wrote in letters of fire “Hello everyone, I exist” above major cities, and predicted with perfect accuracy several natural events that no human could control.

  5. I agree that the probability argument is a bit flaky. I find the problem of evil similarly suspect. They can be argued either way.It’s sometimes helpful to distill philosophical arguments down to what they’re actually saying. Here’s three, in what I feel is the correct order of merit:Decartes: I think therefore I am.Manning (Bernard, RIP): She’s blonde therefore she isn’tMcGrath: I believe therfore He is.

  6. cagliost said…Steve: You say you think the “no evidence” argument for god is unconvincing. Do you have any evidence?I’ll just HOPE that was intended as humor…

  7. Steve, the ‘no evidence’ argument is merely a counter to the many unsubstantiated claims for the existence of god. I agree with Dawkins point in The God Delusion, “None of us feels an obligation to disprove any of the millions of far fetched that a fertile or fecitious mind might dream up.” The existence of god hypothesis is about as far fetched as any, and when you add all the baggage of religion, as pointed out by Dawkins in the interview, it all seems to be just a crazy idea – no evidence, circular arguments, unreasoned faith. The ‘no evidence’ argument isn’t claimed to be a clincher. Think of it this way, with the following hypotheses. Hypothesis H1: God exists.Hypothesis H2: God does not exist.All arguments used are not conclusive about either point. Everyone agrees that both hypotheses can’t be proved. Arguments tend to be supportive of some derived hypothesis:H3: There is no good reason to accept H1.The ‘no evidence’ argument doesn’t provide strong support for H2, but it does provide strong support for H3. Ocham’s razor and the ‘no obligation’ argument above also support H3.H4: There is good reason to accept H1Theists’ support for H4 typically consist of: faith (I believe therefore He is); the inadequacy of science (god is outside the scope of science); the removal of the requirement for reason (god is above reason). Funny though how reason is used to argue against the appropriateness of reason.H5: There is good reason to accept H2Atheists struggle to support H5, often relying on arguments such as the probability and the problem of evil. Even if these argments are intended to support H5 theists interpret them and respond to them as if they are supporting H2.H6: There is no good reason to accept H2I don’t think I know of any arguments used to support H6Personally I think H3 is the atheist’s strong point, and I think the theist doesn’t have a strong point at all.

  8. Exactly. Atheists don’t believe that God definitely doesn’t exist (I’ve never met a “strong atheist”), just that there’s reason to believe it does.

  9. I agree that McGrath appears muddled (although he was addressing someone he shares few metaphysical presuppositions with, so that’s perhaps understandable, cf. Dawkins’ concept of God), but incidentally your existence is objecively certain, now (and was only objectively improbable in the past if indeterminism is true). Anyway, since epistemic probabilities are inevitably different for different points of view, for different presuppositions, Dawkins’ assertion that God is highly improbable is presumably, even when taken epistemically, connected to his view of God’s objective improbability.

  10. Ron Murphy said…H1: God exists.H2: God does not exist.H3: There is no good reason to accept H1.H4: There is good reason to accept H1.H5: There is good reason to accept H2.H6: There is no good reason to accept H2. … and …Steve, the ‘no evidence’ argument is merely a counter to the many unsubstantiated claims for the existence of god … The ‘no evidence’ argument isn’t claimed to be a clincher.Ron: Personally, I don’t see how any of these may be considered anything but speculative in the absence of a rigorous experiment along the lines of what I enumerated previously. The “no obligation” argument strikes me as rhetorical flourish by Dawkins, and brings nothing substantive to his thesis: I wouldn’t consider it to be “supportive” of anything. All one has, in the absence of an experiment, is no data. The claims are NEITHER “unsubstantiated” nor “substantiated” because there is no objective data. Philosophical verisimilitude may appear to be internally consistent in principle, but lacking any hard data, it’s still speculative, and speculation always occurs through the lens of culture, language and bias. It’s not objective.

  11. Hi Steve,I agree completely with your point. The whole god issue has no data either way, and so can’t be examined until such data is collected. And what data is required, etc.? But I don’t see Dawkins or anyone else suggesting that the god exists/doesn’t exist debate has any data – in other words Dawkins isn’t trying to prove H2, or provide conclusive evidence for it, or even to disprove (falsify) H1.There’s no data, but in the mean time we’re left to live our lives and have to make decisions. In this context the main focus is on moral decisions, the source of moral codes used to make those decisions. And, it’s not only the obvious moral dilemma we need to resolve – is it ok to kill on a whim, in self defence, as the result of a ‘just war’, etc.? Allowing religions to indoctrinate children is thought to be immoral by many humanists. The arguments that ensue in this regard innevitable lead to the consideration of H1 and H2, and on the basis of that conflict being insoluable the more reasonable hypotheses to be considered are H3 and H4:H1: God exists.H2: God does not exist.H3: There is no good reason to accept H1.H4: There is good reason to accept H1.We don’t have the scientific experimental data – I agree, and we’re unlikely to get it any time soon. Surely that’s the problem that philosophy has had to contend with from its beginnings. Over the centuries science has moved some subjects out of the philosophical domain and into the science domain*. Reason is all we have to guide us in the face of the lack of data and in the assessment of any data we do have.Although many of the arguments for H3 (no evidence, no obligation) are not falsifying H1 or even H4, that doesn’t mean they are not good arguments. They are common and reasonable arguements used throughout philosophy and science. There purpose is to provide a good guide until more data, evidence, experimental results are available.The scientific method may require that a scientific hypothesis can be tested, as you describe; so in that sense all the above hypotheses aren’t scientific ones. But they are philosophical ones and are subject to reason, and subject to judgement as to their ‘reasonableness’ (*I’m not referring to the strict boundaries of the NOMA principle – which I disagree with. I mean more in the simple sense that we are so familiar with and had sufficient data on many topics that were once philosophically challenging are commonly accepted sufficiently to obviate the need for serious argument.

  12. Steve: “test for God. What do we need?””I’ll just HOPE that was intended as humor…”No, I was dead serious.How would you test for God? It’s all very well to say any experiment would need to mitigate against experimenter bias, control noise and create a probability model, but what “objective factors” did you have in mind?

  13. cagliost said…”what “objective factors” did you have in mind?”Presumably, I can surmise that you have missed my point, given a question like this.

  14. Could you draw attention to the point you think I have missed? Maybe a one-sentence summary. You say:”YET he (and others) say ‘there is no evidence.’ Well, no, OF COURSE NOT: The heavy lifting has never been done.”No. The heavy lifting could not be done. There is no evidence because either God doesn’t exist or hasn’t provided any. Things that could be tested, like prayer, have been, and have been found wanting.In the absence of evidence (such as predictions written in the sky with fire), it is unreasonable to believe in God. That really is all there is to it. McGrath says, correctly, that God may be improbable but still exist. But he still has no reason to believe in God.Some more:”I’ll just HOPE that was intended as humor…” Why? “but I think the argument as presented by Dawkins (et. al.) lacks requisite rigor to be considered ‘science’ or ‘scientific.'” Well it’s not. It’s philosophy, not science.

  15. Steve’s point and the recent responses to it appear to have hijacked Stephen Law’s blog topic. Still, following the discussion with Steve on the usefulness of some arguments that do not constitute scientific arguments – not based on experimental results, I’ve just spotted this on Philosophy Bites: Any thoughts Stephen?

  16. Mr. Atheist:When I read your site I am sickened by your bitterness and unsensoredhatred. All you damned atheist think you know it all don’t you? WellI got news for you: you don’t!If you don’t accept Jesus in your heart now/today/this minute you’llbe facing eternal punishment. You know in your heart God and Jesusare real. We all feel it deep inside and cant deny it unless we tella lie. That’s right you’re lying and sinning each time you say thereisn’t a God. I can’t help wondering how good life would be in ourwonderful country if you atheists didn’t infultrate the government andtake away the great Christian nation that our founding fathers gaveus. You people have killed this country you know that! Do you thinkGod let 9/11 happen because of all the good Christians? My friend,you and I both know deep down why 9/11 happened. Atheists and queersand witches are turning this whole country against God, and God triedto show you some of the things to come. 9/11 was a glimpse into thefuture. Think! It is so obvious! What is life like over there inIraq and all those other countries over there? Terrible that’s whatit’s like! Know why? Because they reject Jesus Christ as their Lordand Savior! You KNOW this and I know you know it. We all know it butwe can’t say it because it isn’t politically correct–one of the worstatheist liberal inventions ever. Politically correct.What about God and morals and the Ten Commandments? Do you want tolive a life like those lost souls in those other countries? FindJesus, if you don’t youll suffer and always regret it.I don’t even want to know how much you hate yourself and your lifebecause you’re an atheist. Life must be so pointless to you. I betyou amke your family miserible. That’s another thing. I read yourrant diary thing and I’ll tell you what: that premature baby you got?I want you to know you did it. You almost killed your own babybecause you reject the One True God! The sins of the father will fallunto his flower I tell you that much! How does that make you feel toknow that because you hate God that you caused this tragedy in yourfamily? If you still have a little spark of Jesus you should feel badright now. If not it might be too late for you becaue the Devil haseaten your heart to peaces.

  17. It’s clear, isn’t it, that McGrath is muddling probabilities?Absolutely!Thanks for linking to DC.

  18. cagliost said…”No. The heavy lifting could not be done. There is no evidence because either God doesn’t exist or hasn’t provided any. Things that could be tested, like prayer, have been, and have been found wanting.”Some points:1. As the experimenter, it is up to me to to do my own design of experiments. If I’m characterizing a transistor array, it’s not going to provide me with any insight until I execute a measurement or observation. If I never do so, for WHATEVER reason (including the intractable nature of the measurement) at the end of the day, I have no data.2. I notice from this comment that you are more interested in debunking monotheist religion than you are in debunking God.cagliost also said…”…Well it’s not. It’s philosophy, not science.”…and as such is speculative, not objective.

  19. Just wanna point out right away that I am not the same anonymous who provided us with the hate filled ‘find Jesus’ post. Anyway…Steve,I have to agree with Cagliost on this. You say:”1. As the experimenter, it is up to me to to do my own design of experiments. If I’m characterizing a transistor array, it’s not going to provide me with any insight until I execute a measurement or observation. If I never do so, for WHATEVER reason (including the intractable nature of the measurement) at the end of the day, I have no data.”In your example you are talking about characterizing something that you know to exist. Thats the whole problem with science investigating God.Assume God does not exist. What observations can possibly be made to prove this? Assume God exists. What observations can possibly be made to prove this? This is a philosophical problem because it is outside the scope of science to prove or disprove. Just because we cannot provide concrete objective proof or even strong objective evidence does not render any argument for or against God worthless or beneath consideration. Philosophical arguments certainly should be reasoned arguments, not just wild unjustified opinion. I would like as much as anyone else if we could perform experiments that would provide strong if not conclusive evidence for or against the existance of God. Devising such an experiment would like trying to show experimentally that there is not an invisible intangible hamsterster controlling George bush from inside his own head. – thought there may be some circumstancial evidence to support this hypothesis. You say arguments about this topic are speculative – I agree that is the case. You suggest that there is some manner of experimentation that can be done to provide objective evidence – That seems more like wishful thinking.

  20. What probability are we really discussing? Which concept of God are we examining? Talking about the probability of God should begin with some concept of the type of deity in question. There are multiple gods for multiple purposes in some religions. There are very personal gods and a single god that occupies the opposite pole: an initial creator of mass, energy, and the laws of physics. If all of these gods did not exist, how would the world, solar system, galaxy, or universe differ from what it appears to be?

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