Peter Kirby

Hypothesis: God exists, God does not exist (G, ~G)

By God, I mean an intelligent creator of this universe.

Outcomes: The universe is orderly, the universe is not orderly (O, ~O)

By order, I refer to regularities in nature.

We will assume that there are intelligent beings in all universes in which the existence of God or the existence of order can be contemplated. The existence of intelligent beings will be represented by I, our background information.

Background probabilities:

P( G | I ) = 0.5
P( ~G | I ) = 0.5

In other words, the existence of intelligent beings alone can tell us nothing about the existence of God, because intelligent beings must exist in either case in order for there to be contemplation. The existence of order that allows intelligent beings to exist might tell us something about the existence of God; the background probabilities above say nothing about that. As an aside, it is also good to select equal background probabilities if only for the reason of determining the effect of order on the question of God's existence. It is not excluded that there is other evidence that may affect these background probabilities.

Anything is possible with God, so we shall assign equal probabilities to the two possible outcomes. In other words, God could create a universe in which things happen without naturalistic regularities in which intelligent beings exist just as easily as God could create a universe in which naturalistic regularities and intelligent beings co-exist.

P( O | G, I ) = 0.5
P( ~O | G, I ) = 0.5

Without God, it is quite nearly impossible for intelligent beings to evolve in a disorderly universe. If there are intelligent beings, then the universe is orderly, if there is no God. So we shall assign certainty to the idea that there is order given that there is no God and that there are intelligent beings in the universe.

P( O | ~G, I ) = 1
P( ~O | ~G, I ) = 0

Bayes's theorem says the following:

P( G | O, I ) = P( G | I ) * P( O | G, I ) / P( O | I )

With a substitution for the last term above, we get:

P( G | O, I ) = P( G | I ) * P( O | G, I ) / ( P( O | G, I ) * P( G | I ) + P( O | ~G, I ) * P( ~G | I ) )

Now we can solve:

P( G | O, I ) = 0.5 * 0.5 / ( 0.5 * 0.5 + 1 * 0.5 ) = 0.25 / 0.75 = 0.33333

In other words, all else being equal, the probability that God exists given that there is order in the universe is only half as likely as the probability that God does not exist. But note well that further evidence could easily tip the scales in favor of the existence of God or just as easily make the existence of God even more improbable. This is only one consideration.

best,
Peter Kirby

hinduwoman

In other words, 50-50 chance.
But I don't think this can get settled like that, for science cannot either prove or disprove God.

Peter Kirby

Careful attention to what I wrote would reveal that the non-existence of God is twice as likely as the existence of God with the evidence of order (66-33 chance in favor of non-existence), with the assumption that the existence of God is a 50-50 proposition based on other background information. If the other background information is in any way probative concerning the existence of God, then the probabilities would be changed, either to make the existence of God more or less likely. But the direction to which this argument points is the non-existence of God.

I should note again that, in the context of this argument, "God" is defined as an intelligent creator of this universe. This argument says nothing about the existence of gods defined in a different manner.

Of course, the careful reader would again realize that my argument makes use of philosophy and mathematical theory, not just science. Science can reveal that there is order to the universe, but it takes the disciplines of philosophy and mathematics to complete the argument.

The careful reader would finally realize that this is an argument that does not amount to proof beyond a reasonable doubt. It would need to be combined with other probabilistic arguments to make a total and persuasive case.

best,
Peter Kirby

Silent Dave

Peter, I remember you from alt.atheism. It's nice to see you here.

Let me anticipate a few objections to your argument. First, it only works if you assume that the existence of God is as likely as not given the existence of intelligent beings, and many theists do not grant that assumption for the reason that they believe that the existence of intelligent being NECESSITATES the existence of God (see this or that ontological and/or transcendental argument).

Second, depending on how God is defined, a theist might also say that the existence of God necessitates the existence of an orderly universe, given that the universe reflects the attributes of God, or what have you.

And third, how do you deal with the common arguments against Bayes' Theorem?


Regards,

Dave

Peter Kirby

I've been posting over in Biblical Criticism & Archaeology for a few months, and otherwise I have been sticking to e-mail lists.

Obviously, if God is a necessary being, all bets are off (quite literally). So a prerequisite for any probabilistic case is that there are defeaters for any "a priori" arguments (using "a priori" in the correct sense of knowledge that requires no recourse to sense data). The same holds true for theistic arguments: if the existence of God entails contradictions, all the evidence in the world won't make him come into being (or, at least, not without promptly disappearing in a puff of logic). Myself, I indeed do think that ontological arguments fail.

In the context of this argument, a god is defined as an intelligent creator of the universe. Or, if you prefer, the hypothesis in question is whether the universe was created. When phrased this last way in particular, the spuriousness of any further attributes piled on to the god-concept become apparent. One might as well say that 'god by definition contains a model of this specific universe in all its details in his mind', but that is certainly not the only way to imagine a creator, so such a definition entails that we are not just asking about the existence of a creator. But that does not mean that we can't imagine such a god. But the existence of such a specific god can never be more likely than the existence of a creator in general. So, by such a definition, the theist can only render the existence of the divine more improbable.

I am vaguely aware that there are critics of statistics that build on Bayesian principles, but I am not aware of the details, or whether such arguments apply here, so you will have to supply them. I worked out Bayes's Theorem myself from the axioms/definitions of probability theory when reading through a typical textbook, so I cannot give any credit to an objection that does not make clear which axioms/definitions are not accepted. It would be like an argument against the Pythagorean Theorem that did not first specify that we are dealing with a different geometry than the Euclidean system.

best,
Peter Kirby

The Dark Lord

Well here's my attempt to contribute to an intelligent discussion...

Two points:
1) The universe, as far as we know, is not orderly. We know this because reactions that go from an orderly state, e.g. a solid, to a more entropic state, e.g. a gas, having a positive change in entropy, i.e. an increase in the chaos of the universe, proceed spontaneously.

2) Is the evolution of human beings orderly? And if it is, do we have to assume that an intelligent creator provided the energy to do this? Or could, for instance, there have been some event on the earth giving enough energy to cause the process of evolution.

Then, of course, I could just be really confused.

Silent Dave

Peter--

I think the most germane objection to Bayes' theorem is that it is unable to shed light on evidential relevance. That is, under what circumstances does a piece of evidence confirm a theory, and why does some evidence confirm some parts of a theory but not others? How does Bayes' Theorem answer these questions?

There's also the problem of "old" evidence, -- that is, a piece of evidence is established as fact, or at least accepted as fact. Therefore, for old evidence, P(E) seems to equal 1, and therefore P(E/T) must also equal 1, regardless of what T is. It follows that E cannot confirm T. Therefore, although scientific tradition says that old evidence can in fact confirm a theory, Bayesians seem forced to deny this. How would you deal with these problems?


Dave

Peter Kirby

The Dark Lord, I was using "order" to refer to natural regularities.

Dave, first let me prove Bayes's Theorem from the definition of conditional probability.

P( A | B ) = P( A, B ) / P( B )
[Defintion of conditional probability.]

P( A, B ) = P( A | B ) * P( B )
[Corollary of the definition.]

P( G | O ) = P( G, O ) / P( O )
P( G | O ) = P( O, G ) / P( O )
[From the definition.]

P( O, G ) = P( O | G ) * P( G )
[From the corollary.]

P( G | O ) = P( O | G ) * P ( G ) / P( O )
P( G | O ) = P ( G ) * P( O | G ) / P( O )
[Substitution.]

The P( O ) part is often expanded with something called the law of total probability.

Anyway, unless we define conditional probability in a different way, Bayes's Theorem is proven.

Dave writes: I think the most germane objection to Bayes' theorem is that it is unable to shed light on evidential relevance. That is, under what circumstances does a piece of evidence confirm a theory, and why does some evidence confirm some parts of a theory but not others? How does Bayes' Theorem answer these questions?

I don't understand why one would expect Bayes's Theorem to answer these questions. Bayes's Theorem is just an equation, not a methodology or an epistemology.

If these questions pertain to the original argument in this thread, please explain the way in which they do so.

Dave writes: There's also the problem of "old" evidence, -- that is, a piece of evidence is established as fact, or at least accepted as fact. Therefore, for old evidence, P(E) seems to equal 1, and therefore P(E/T) must also equal 1, regardless of what T is. It follows that E cannot confirm T. Therefore, although scientific tradition says that old evidence can in fact confirm a theory, Bayesians seem forced to deny this. How would you deal with these problems?

Bayes's Theorem says:

P( T | E ) = P ( T ) * P( E | T ) / P( E )

If P( E ) is 1, then the simplification ensues:

P( T | E ) = P( T )

This is undoubtedly correct. So this does nothing to cast doubt on Bayes's Theorem.

best,
Peter Kirby

hinduwoman

But my argument is that no amount of science and maths can actually prove or disprove the Creator. Since he is the creator, he cannot be known by finite human brain --- that is the argument used.
Also, devout Christians argue that though we apparently see disorderliness, it is actually part of a greater design.

Peter Kirby

These are assertions, not arguments. "An argument is a connected series of statements intended to establish a definite proposition."

You must have not been following this thread very closely, because I have assumed that "order" exists in the sense of natural regularities. I have not argued from disorder but from order. See the topic title.

best,
Peter Kirby