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Monday, February 09, 2015

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Bill,

Thank you for reading (and considering!) my argument. I think your representation is spot on, and much clearer than mine. I find your reasoning sound and I am for the most part swayed that the argument in its current form fails. That said, I will think about improving it. None the less...

Here's how I would try to attack your claim that "[t]he number of different conceptions of the LDM has no bearing on the probability of its existence." I'll try to illustrate with a story. If I number the sides a fair coin 1 and 2, then we have two outcomes:


(A) "The result of the flip is 1."
(B) "The result of the flip is not 1."


In this case they are equally probable at 50%. If we do the same thing but with a fair three-side die (numbered 1,2, and 3) then P(1) = 1/3 and P(B) = 2/3. If I repeat this over and over again, then P(B) shrinks until it's all but vanished. Analogously, as I add more God-positions that are not atheistic, I should be shrinking the probability of atheism being true.

But this is absurd. By this reasoning theists would be best served by inventing religions whenever possible.

I think the trouble comes from reasoning about things that presumably already exist in the same way that one reasons about things that have not yet happened. In the latter form of reasoning, we can think about the ways in which something could possibly happen and comparing that to the set of possible things that can happen. In the former, we try to see if the propositions about it seem reasonable.

But this too is troublesome. How do we draw the distinction between an unknown future outcome and a the truth of a proposition we have yet to encounter. Why should probabilistic reasoning fail?

Something that may be interesting, provide a resolution, and is likely beyond my depth, is applying this to how we think about truthmakers. Consider the following propositions:

(P) "There exists a cat."
(Q) "There exists a cat named 'Ayn Rand.'"

A truthmaker x for (P) is just a cat. A truthmaker for (Q) is a cat named "Ayn Rand." It seems obvious that (P) is much more likely to be true than (Q) because the number of possible truthmakers for (P) is greater than or equal to the number of possible truthmakers for (Q).

And maybe this is how my argument finally get's defeated. If the probability of a propositions truth is related to the number of truthmakers, then theism and atheism, as God-positions, both have one possible truthmaker, which suggests an equal probability.

Thanks again.

Best,
James

Two errors in my prior post:

(1) In the story it should say that "P(A) shrinks it's all but vanished." P(B) should approach 1.

(2) The paragraph "But this too is troublesome. How do we draw the distinction between an unknown future outcome and a the truth of a proposition we have yet to encounter. Why should probabilistic reasoning fail?"

Would be better as: "But this too is troublesome. How do we draw the distinction between an unknown future outcome and the truth of a proposition the subject of which we have yet to encounter? Why should probabilistic reasoning fail?

My reasoning is similar to a paper by van Inwagen which has been criticized for not dealing with measure problems. Kenny Pearce does a good job describing them here.

There appears to me to be a simpler problem with the argument, though I'm likely misunderstanding.

Assuming that the probabilistic inference from (5) to (6) were granted, are there not actually as many atheistic positions as there are theistic positions (contrary to premise 1, I suppose)? What I mean is this:

For some series of theistic positions Pt1, Pt2, Pt3 etc, where each differs in the account offered of God's existence (what his properties are, or what they consist in), could the atheist not actually construct some specific position against each position offered by out putative theist, such that we arrive at a set of opposing positions Pa1, Pa2, Pa3 etc? In this case it seems we actually have equally as many theistic position as atheist positions, and the argument is thereby trivialized.

In other words, if I offer an account of the triune God of Christianity, is the atheist not taking up an account or position denying the existence of this particular account of God, even if his atheism is, as concerns prior belief, general enough to rule out the existence of any conception of God, Christian or otherwise?

However, I think I'm missing something, or that perhaps the above is not relevant in some way.

Good comment.

I thought of something similar as an alternative way of criticizing the argument.

We could put it this way. There are as many theisms as there are concepts of God. And there are the same number of atheisms. Thus Plantinga affirms the instantiation of his concept of God (according to which God is not simple) and the corresponding atheist denies the instantiation of that very same concept. And Thomas affirms the instantiation of his different concept of God (according to which God is simple) while the corresponding atheist denies the instantiation of that very concept.

Plantinga could be called an atheist with respect to Aquinas' concept of God, and Aquinas an atheist with respect to Plantinga's concept.

Surely we cannot possibly assign probabilities to reality on the basis of the probabilities of human conceptions of reality!

On that basis, the probability of "action at a distance" changed from zero to one over the course of Newton's life.

Another thought: what would define the "denominator" for those probability calculations? Would it be the number of God-positions, or the number of instantiations of God-positions (i.e., the number of humans). In any event, the assignment of reality-probability on the basis of position-probability is fallacious.

Doug:

A quick response: the denominator is the number of unique God positions.


“Surely we cannot possibly assign probabilities to reality on the basis of the probabilities of human conceptions of reality!”

I would argue that we all do that every day. Let’s say you and I sit at a table, I show you a coin and ask you what the probability is that it is fair. I then flip it 10 times and only heads come up. If I ask you the same question, you should update your probability based on your new conception of reality and the probability that you assign to your conception of reality corresponding to reality.

If I understand your issue, it’s with equating actual probabilities with subjective probabilities because this leads immediately to absurdity. My conviction that the probability that unicorns exist is 1 should not and does not mean the actual probability that they exist is 1. I agree.

My argument was based in the following line of thinking:

When we reason about probabilities, we often compare the ways things could happen/be true with the totality of things that could happen/be true. I wanted to apply this reasoning to existential claims about God. The confusion, as Bill has pointed out, is calling a “conception” a “way it could be true.” There is only one way “God exists” could be true: God’s existence! Similarly, there is only one way it could be false: God doesn’t exist. Thus they should be equiprobable at 50%.

I may try to see if the thinking in the above paragraph could be used as justifying a fair Bernoulli distribution as the correct prior for evidential Bayesian arguments.


Jared & Bill:

I see your objection, which seems to be with premise (3), and I think it doesn’t work. First of all, I think it’s unlikely that Plantinga would call himself an “atheist with respect to a simple God” but would say “I don’t think God is like that.” I of course don’t mean to put words in his mouth.

Let’s look at their two claims and translate them into almost-symbols:

(P) “God is not simple.”
(T) “God is simple.”

become

(P*) Exists x, x is God, x is not simple.
(T*) Exists, x, x is God, x is simple.

Both share the claim that God exists, and so calling one an “atheism” with respect to the other seems like it loosens the meaning of the word atheism.

My bigger concern is that thinking that way leads to double counting, which leads us to Jared’s conclusion of equinumerous (and thereby equiprobable) atheisms and theisms. As a simple example: if you ask me my beliefs and I say “atheist and not Christian and not Jewish ….” would you not consider that redundant? Similarly doesn’t being Christian entail “not Buddhist” etc.? Why should we count each theism as an atheism if they already are mutually exclusive?

Your reasoning is akin to giving the answer “72” the question “how many possible pairs of outcomes are there from two rolls of a die”? The answer is 36, but you’re doubling it without warrant because I did not ask for ordered pairs.


Let’s define a God-position as a set of answers to the following pair of questions:

1. Do one or more divine beings exist?
2. If so what is its/are their attributes?

Evidently, there’s only one God-position that is atheistic.

We could even then augment premise (1):

“1. There are several actual and many possible unique positions on the nature and existence of God. Call them God-positions.  One who occupies a God-position takes a stand on the existence of God, yes or no.”

I think this answers the objections you two have voiced, but the probabilistic reasoning one stands.

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