Monday, July 23, 2007

Dawkins' improbability argument

I said I would explain some of my doubts about Dawkins' improbability argument (in The God Delusion, and in the video we are discussing [at 13 mins 45 secs to 14 mins 40secs]). Here goes...

Dawkins presents an improbability argument against the existence of God.

The idea, I take it, is that the fact that God is supposed to be a conscious, knowing, intelligent designing subject means he is himself very far from being “simple”. He must be terrifically sophisticated and complex, in fact.

So,

(i) invoking God to explain complex things like eyes, fine-tuning, etc merely replaces one improbable thing by another (overall, improbability is not reduced), so undercutting the justification for invoking him, and

(ii) God's being highly improbable, it’s highly unreasonable to believe in him, given the absence of evidence for God.

While I, like Dawkins, am not persuaded by intelligent design arguments (and let me stress I am generally in agreement with Dawkins, and in fact am a great admirer of his), I am not sure Dawkins' improbability argument is correct.

Prof Hugh Mellor (philosophy, emeritus, Darwin College, Camb.) distinguishes objective (or, as he puts it, physical) probability and epistemic probability.

The physical probability of an event etc. is the chance of it happening, given certain facts/laws. So, the physical probability of this unloaded dice rolling a six is one-in-six, of it raining today, given the general conditions (high pressure, etc), is very low, and of my dying before I reach 150 is very high.

The epistemic probability of a claim etc. is the probability of its being true, given the evidence. So given the patter against the window, the wet feet of the shoppers, etc. the probability of its currently raining is high. The evidence is good.

Things can be objectively improbable but epistemically highly probable. That this coin landed exactly on its edge is epistemically very probable (I just saw it happen with my own eyes) yet objectively improbable (the chance of it happening, given certain laws/initial conditions, is v. low)

It seems the reason we find things shocking, surprising and standing in need of explanation is that their objective probability seems very low. If someone lives to 300, or if it snows midday in the Sahara, or if my left foot spontaneously combusts, or if a coin lands exactly on its edge, we’ll be amazed, and look for an explanation. An explanation that lowers the improbability of the event (or even shows that it had to happen).

Notice that its objective probability we are talking about here. You can’t explain an event by raising its epistemic probability. I can confirm beyond any reasonable doubt that my left foot has indeed spontaneously combusted. That doesn’t remotely explain why it spontaneously combusted. Here's Mellor making the same point:

Take the probabilistic link between smoking and cancer. My smoking will only explain my getting cancer, if I do, by making it more probable, if that probability is a real physical probability (or chance for short). It is not enough for my smoking merely to raise my cancer’s so-called epistemic probability, the kind of probability that measures how far evidence supports a hypothesis. After all, that probability is also raised by the symptoms which tell my doctor that I have cancer. But these symptoms do nothing to explain my getting cancer, because they are not what raised the chance of my getting cancer in the first place.

Now design arguments for God work by pointing out that something is allegedly objectively/physically improbable, and then explain it by invoking God to reduce that improbability.

Mellor, however, suggests that, when it comes to, say, the character of the universe, it has no objective probability, high or low. Because that would be a physical improbability. And a physical probability is always relative to whatever the physical laws and initial conditions are. So…

the initial state, if any, of a universe, or of a multiverse, which by definition lacks precursors, has no physical explanation, since there is nothing earlier to give it any physical probability, high or low.

Similarly, God would have no objective/physical probability, high or low, on Mellor’s view. It's only things within a given universe that have such physical probabilities.

I suspect Mellor may be correct. That the universe has these laws etc. is neither probable nor improbable, objectively speaking. Nor is there anything remotely surprising - or standing in need of explanation - about it's having just these laws.

Certainly, there's a question here for Dawkins - is God objectively improbable? Or is he neither probable nor improbable, as Mellor would, I think, maintain?

Notice, by the way, Paley's example of the inference about the watch is not threatened by all this. A watch found on a beach is hardly something that purely natural mechanisms are likely to have produced all by themselves. Its spontaneous appearance really is physically improbable, given the laws of nature, etc. So we are justified in invoking an intelligent designer.

But the logic doesn't carry over to fine-tuning. From Dawkins' perspective, the problem with invoking God to explain "fine-tuning" (the universe's laws and initial conditions being "just right" for life) is that we are invoking an improbable thing to explain an improbable thing. From Mellor's perspective, the problem is that the "fine-tuning" is neither probable nor improbable, and so doesn't require an explanation (by means of God, a multiverse, or anything else).

Mellor's paper supplied on request.

21 comments:

The Barefoot Bum said...

Probability is an abstract concept. Doubly abstract, because the linguistic objects of probability are counterfactuals, themselves abstract; probability suffers from the same sort of philosophical issues as counterfactuals in general.

If you want to be very rigorous, there is no such thing as truly objective probability: Things are either true or false. You will either get cancer or you won't. You either will be dealt a royal flush or you won't. Or, to be even more rigorous, it is impossible to distinguish between epistemic probability and objective probability.

As a category of abstractions, though, we can create a distinction between objective and epistemic descriptions of probability.

One informal way to draw this distinction is if we can define an abstract probability space and get a rigorous, well-defined frequentist probability, we're (usually) constructing an objective description; if we're forced to resort to Bayes theorem (Bayesian probability is more general than frequentist probability), we're (usually) constructing an epistemic description. Since Bayes theorem is in fact a theorem under frequentist probability, it is possible to recast any objective description to an epistemic description (but not the reverse).

Dawkins uses existential language—"There is almost certainly no God"—but by the above, this statement is identical to the statement, "We know almost certainly that no God exists." The existential language can be seen as a matter of convenience.

steve said...

The Barefoot Bum said...

"Probability is an abstract concept. Doubly abstract, because the linguistic objects of probability are counterfactuals, themselves abstract; probability suffers from the same sort of philosophical issues as counterfactuals in general.

If you want to be very rigorous, there is no such thing as truly objective probability: Things are either true or false. You will either get cancer or you won't. You either will be dealt a royal flush or you won't. Or, to be even more rigorous, it is impossible to distinguish between epistemic probability and objective probability."




This is a gross oversimplification of the physical world, and a mis-characterization of probability.

Error detection and recovery in digital systems, as well as the science of cryptology is entirely objective, based purely on measured data and objective probabilities that do not rely on bimodal distributions.

For example, in the English language the probability of occurrence of the letter "E" is 0.12705 and the probability of occurrence of the letter "Q" is 0.00121. Probabilities of letter instance for the most common eight letters are E T A O I N S R, in that sequence from most probable to least. Probabilities of all 26 symbols must add to 1.0. Valid probability values are a non-discrete continuum ranging from 0.12705 ("E") to 0.00121 ("Q").

The same may be said (using BBs example) for poker hands: the total number of poker hands is 52!/(5!×47!) = 2,598,960. With this number of combinations, the OBJECTIVE probability that a royal flush will occur is 1.53908E-06 (4/2,598,960).

The Barefoot Bum said...

Philosophy is the art of gross oversimplification. :D

I'm a computer programmer, pretty well versed in probability and statistics as well as cryptography. I'm also a strong poker player. I understand and I have no problem with probabilistic language in general. But it's language, and I try not to infer too much about the real world from our use of language—especially language that exists to quantify our ignorance.

Let's take that poker hand. Suppose I shuffle the deck and deal you five cards... don't look at them, though. Now that hand has one singular content: It either actually is or actually is not a royal flush. Period. Any probability is not a property about the cards themselves, but essentially a property of what you know—or don't know about the cards.

However, it's very very cumbersome to actually express this epistemic language in purely epistemic terms: It's much more convenient, and yields the correct answer, to talk about the probabilities as if they were properties of the hand itself.

The Barefoot Bum said...

...it's very very cumbersome to actually express this epistemic property in purely epistemic terms...

steve said...

Stephen Law said ...

"The idea, I take it, is that the fact that God is supposed to be a conscious, knowing, intelligent designing subject means he is himself very far from being “simple”. He must be terrifically sophisticated and complex, in fact."




"Complexity" is a misunderstood term. In an effort to shorten this, lets talk about a sequence. Say, the sequence of a given genetic code.

In the case of such a sequence, its complexity is the Shannon entropy of the shortest algorithm needed to compute (describe) a given sequence in that code.

The sequence that has the highest Shannon entropy and is MOST COMPLEX is a RANDOM one.

Nature, and natural processes are fundamentally random (or pseudo-random).

Using the logic that Dawkins proposes would make random/pseudo random processes most complex, and therefore NATURE would be more complex than God.

(Unless God has higher Shannon entropy than nature)

But God as described in monotheistic religions is characterized by order.

Referring back to the discussion of a sequence, those sequences which have lowest Shannon entropy are those that are most ordered: they would be least complex: i.e., SIMPLE.

Such an entity would then be most SIMPLE, NOT COMPLEX.

Perhaps "complexity" isn't what Dawkins is discussing. This conclusion is purely speculative, because Dawkins never provides an operational definition of "complexity."

The Barefoot Bum said...

"Complexity" is a misunderstood term.

No, the word "complexity" is, like everything else in natural language, ambiguous. The complexity of organisms (or God) from the Design argument that Dawkins talks about is clearly not Shannon entropy. We are supposed to use context to resolve the ambiguity.

Using the logic that Dawkins proposes would make random/pseudo random processes most complex...

No, using the logic that you propose would make random processes most complex. AFAIK, Dawkins does not talk about Shannon entropy in the arguments that Law references.

steve said...

The Barefoot Bum said...

No, the word "complexity" is, like everything else in natural language, ambiguous. The complexity of organisms (or God) from the Design argument that Dawkins talks about is clearly not Shannon entropy. We are supposed to use context to resolve the ambiguity.


The complexity of an organism's CODE is a measure of that organism's complexity. The only means you have to objectively MEASURE that complexity is in terms of its Shannon entropy. THAT is the context. If THAT isn't the context, you have nothing measurable.




The Barefoot Bum also said...

No, using the logic that you propose would make random processes most complex. AFAIK, Dawkins does not talk about Shannon entropy in the arguments that Law references.


Then what is Dawkins operational definition of "complexity", and how will one objectively quantify it?

steve said...

The Barefoot Bum said...

"Let's take that poker hand. Suppose I shuffle the deck and deal you five cards... don't look at them, though. Now that hand has one singular content: It either actually is or actually is not a royal flush. Period. Any probability is not a property about the cards themselves, but essentially a property of what you know—or don't know about the cards."


This is nonsense. The reason the royal flush is valuable is because it has a low probability of occurrence. There is an objective value associated with it. That number is sufficiently low as to provide the royal flush high value.

If it had a low or medium probability of occurrence, it would receive value in parity with that probability.

Jeremy said...

Stephen:

If I am understanding him right, Mellor thinks the universe neither probable nor improbable since it lacked initial conditions or a prior state, which are needed in order to make an assessment of objective probability. I agree that he would then have to say the same for God.

But could you not try something along these lines:
If we cannot put an objective probability on the universe turning out one way or another, then ANY way is equally improbable or probable (or more correctly, neither improbable nor improbable).

Therefore, in the complete absence of any (objective) probability to sway me one way or another, any INDIVIDUAL way is actually rendered improbable, since it is swamped by other potentially possible ways, each of which we have agreed to call neither probable nor improbable.

Thus, this particular universe's existence is objectively improbable, although it is obviously epistemically very probable. This is why physicists are justified in asking questions like, "Why this universe?" (Even if they can't get an answer.)

Again, I agree will Mellor that we can't put an objective probability on one of the universe's fundamental laws like, for argument's sake, the electron's mass being [whatever]. But I'm not so sure that I'm prevented from legitimately asking why the electron mass didn't turn out do have some different value. In fact this may be PRECISELY BECAUSE I'm unable to put a high objective probability on it being [whatever].

In a similar vein, the existence of a being who (to paraphrase Dawkins) answers prayers, condemns sinners, brings down plagues and transubstantiates wine if you're Catholic would be rendered improbable. Again, if he lacked a prior state and therefore prior objective probability, there would be equal odds of him being a ball of slime, nothing, the Eifel tower or the editor of "Think". ;)

BTW, I don't mean this as a defence of Dawkin's argument, as I think this is a little different.

Not sure if it holds water, though. I feel slightly queasy even reading it! Ideas anyone?

Jeremy said...

P.S. Stephen, would it be possible to get a copy of Mellor's paper? Is it available electronically?

Many thanks!
Jeremy

Paul Power said...

1)
(I am not sure this is disagreeing with what Stephen wrote; if so I apologize in advance for wasting people's time.)

Surely epistemic probability rests on objective probability ?

We can assign an epistemic probability in some instance only because we have seen the same sort of thing happenalready. Consider a basic situation: if it rains during the night, in the morning the land around my house will be wet. In the morning I find the land wet in a way consistent with rainfall (and not recent flooding as in suffering England). So the epistemic probability of overnight rainfall is high but I cannot be ceetain because perhaps someone hosed my garden. I can speak meaningfully about the epistemic probability because I know how things get wet.
Now apply this to the universe itself. Because we cannot get at its objective probability, we therefore cannot talk of its epistemic probability either.



2) Regarding the definition of epistemic probability: "The epistemic probability of a claim etc. is the probability of its being true, given the evidence". This seems to me to be a definition of Bayesian conditional probability (see e.g. http://en.wikipedia.org/wiki/Bayes'_theorem).

Timmo said...

Mellor's paper supplied on request.

I am interested to read Mellor's paper. At what e-mail do you prefer to be contacted? Or, if the paper is published, you can give me the citation -- being at a university, I have access to the university library! :-P

Nutcasenightmare said...

When Dawkins mentioned replacing the improbability of fine-tuning with the improbability of God...

...I think he meant replacing the epistemic probability of any theory on fine-tuning with the epistemic probability of God.

So, it boils down to epimestic probability only. Mellor's views on the objective probability of the universe are therefore, irrelevant.

Alrightythen. =D
~Nutcasenightmare

P.S: I can't find 'epistemic' in my dictionary. After all this talk about the semantics on probability, what does epistemic really mean? X_x

Nutcasenightmare said...

Mellor assumes that for something to have an objective probability, it must have some precursor.

Once upon a time there was an Evil Internet Connection, which, for literally no reason at all, sometimes turns itself off when I try to send an email. When it's in a good mood it just sends me spam.

I want to know just how unlucky I was with the Evil Internet Connection, and decided to run some tests by typing up emails and seeing how often it turns off.

Email 1: Okay.
Email 2: My rebuttal to an anti-evolution site got lost.
Email 3: Fine.
Email 4: My opinions of religious homophobia became roadkill on the Superinformation Highway.
Email 5: Good.

...and so on.

I soon figure out that the objective probability of the Evil Internet Connection betraying me is 50-50.

Now, the point is that the Evil Internet Connection fails for LITERALLY NO REASON. The email failures have no precursor, yet I can still determine their objective probabilities.

Therefore, Mellor's argument is invalid. I think.

Let's keep our fingers crossed as I submit this comment, and that the Evil Internet Connection'll only send me XXX product-endorsing death threat chain letters.

~Nutcasenightmare

Paul Crowley said...

Who knew that my expertise in cryptography would serve me in a philosophical argument?

First, I agree that Dawkins's "Ultimate 747 argument" won't fly, for reasons roughly in the region Mellor indicates - there's no sensible way to assign an a priori probability to God.

But going into more detail in the way the argument is presented, it looks to me like what you call "objective probability" would be better termed "model probability" - what probability would our current predictive model assign to such an event? So when we say "I've been dealt a royal straight flush, what are the chances of that?" our epistemic probability is one, but our objective probability is based on a model in which the initial state of the deck was drawn fairly from the set of all possible shuffles. Actually, real shuffles are often astonishingly poor, leaving easily-detectable biases in the permutation they induce on the deck of cards.

We can see that in the way you discuss information about smoking changing the objective probability. Nothing has changed in the world, but our model has been updated.

We see this even more strongly in the case of error correction and cryptography, where by and large study wildly idealized channels and sources of randomness. We need a model sufficient to get the job done, not one that is a perfect match with the world.

God is far, far too incoherent a concept for us to have a model which would assign a probability to him arising with sufficient complexity to make the Universe, so the Ultimate 747 argument founders on the same incoherence.

online poker site said...

so does dawkins suggest the outcome of a hand of poker is determined by God!

If so, praise the lord for online poker!!

Brian said...

Hi Stephen, I just discovered your blog via butterflies and wheels. Is it still possible to find a copy of the paper you're referencing?

Thanks,
Brian.

Stephen Law said...

email me direct brian and I'll send you an electronic copy (if I can find it...)

Brian said...

Hi Stephen, I tried emailing you direct but it doesn't seem to work. You can send it to me, when you find it, at baeng72 'at' hotmail 'dot' com

Cheers.

Anonymous said...

Hi,Edmund Spenser here,

Well, of course Dawkins would say a God is improbable---from a physicalist scientific presumptions and perspective
--his only perspective---it is correct.

But from the perspective of somone who presumes that God is pure being/consciousness which is
the substrate giving rise to
what is commonly called the physical and mental worlds,God is not only probable but patently
and continuously present.
The same consciousness/being
(call it a Pan-consciousness)
gives rise to thought as well as sense. God, inthis conception, is
the foundational isness itself, and therefore to doubt that there is God, would be absurd--like a fish denying water.
The foundational scientific
presumptions of Dawkins (which same underlie his calculation of God's probable existence)
preclude him from coming to any other conclusion.
Foundational presumptions--e.g.,
there being no deeper level of reality from which physicality arises---are just that,presumptions, not subject in principle to scientific proof or denial, yet used to derive and limit the scope of all subsequent conclusions.
Ultimately, Dawkins wants us to
abandon our investigations and submit our analytical imaginations
to the narrow limits of scientific physicalism. He seeks a taboo against other presumptions.
Such a taboo is not an anwer to the question and mystery
of life--it is merely
an assertion that such questions,
outside a narrow scientific perspective, are not legitimate.
The philosopher can and I think must assert the independence of his analytical imagination in the face of such a taboo and get on with investigation--by which he has much to contribute--this I assert! Go to it people!

Anonymous said...

Murcheson Fahls here,
That an explanation can tell you the ultimate reason for something
is a myth. If may find an answer
to the question--what will stop or start the process, event, happening or what have you.
This does not tell you why there
should be such a thing as the event and something that stops or starts it.
And if you posit an overarching reason for it--say GOd's providence or some such----it can simply be asked why that should in turn be the case. And so on with any explanation. There is no end to this.
When you ask of an ultimate why you are always thrown back onto the is of things---the very raw fact of existence.
And probability? Gimme a break.
Probability is specifically how many times an x has shown up in so many instances of event y. Or given a fixed number of things how often something will show up in some random process or other.
SO, apparently Dawkins is thinking something like --"how many times out of millions that tornados have spawned in Kansas--has god shown up to claim responsibility?" or "how many times
has a god contacted me to tell me I am being a bad boy?"
Well, none of course. So how could there be a God?
But this depends upon a self serving assumption about what God would do and what God's nature is. But there are other conceptions of God's nature that would not serve Dawkin's agenda.
And why should probability --in this statistical sense----be relevant at all? Dawkins' assumptions --these premises--- are
, as with all premises without argument, eminently dismissable.
And finally, it seems to me that Dawkins simply dismisses any intuition of God or deity or what have you that confirms GOd to a person. If Dawkins is saying something like --"from the scientific point of view intuitions
cannot be the basis for conclusion"
that's one thing. But another if he is going farther and saying any intuition in any context is illegitimate. Well, that's a friggin' assumption.
And that there is an easy line between intuition and logic or scientific thinking is another of Dawkins's apparent assumptions.
And in my view silly. The only reason that A follows (or doesn't) from B is that an intuition arises in us which confirms that it does or doesn't. And this applies to mathematics also.
As I maintain, no one knows ultimately why anything is the way it is--why anything shows up as it does. Dawkins science blindness
makes him think that the limits of scientific inquiry are the limits of questioning. That is a friggin' assumption.
Also, Science can fail miserably. The current hunt for "dark energy" and "dark matter" is an attempt to
salvage a theory of gravitation which failed miserably to predict accurately. If science can be wrong about this fundamental---it, in the guise of Dawkins, should not be so smug about God.
Also, part of that smugness comes from the old nominalist vs realist split. Dawkins may see physics quantum fluctuations as perfectly real existing entities---though no one has seen any such thing directly (not to mention electrons or particles and so on)
but God is, at best a name a notion. This is all assumption.
I am not a fan of organized religion and condemn as Dawkins does the terrible cruelty inflicted upon humanity by organized religion over the centuries. I am no dogmatist. And this is why I think Dawkins is a bonehead.
He does not have the intellectual wherewithal nor the initiative to present cogent arguments to counter
theists directly--he simply takes the stance that anything that is not conventional science is illegitimate. That is dogma and
such laziness.