Saturday, January 31, 2015

Aron and the transcendental argument (part of the Aron Series)

Please see below for my discussion with Aron about the transcendental argument for God's existence (TAG).  I apologize for the abrupt beginning, but I jumped into the conversation in medias res, as it were.  And unfortunately I have no way of retrieving Aron's earliest points in the argument, including his formal argument points (1-8).

For links to the full series, see here.


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Greg Reeves wrote:
As a scientist/engineer and not a philosopher, I am also not the best qualified, but with that disclaimer... If Ron is right that the possibility of having evidence against God is necessary for the design argument to succeed, then yes indeed the design argument fails. And he would be absolutely right about the first line of argumentation.

But even if we grant him that needing the possibility of having evidence against God is required for successful evidential arguments against God, Argument 1 is a paradox, not a contradiction, because he is leaving out crucial qualifiers in statements (1) and (8).

When he says "the design argument succeeds" he should be saying "were logic possible without God, the design argument succeeds" (a true statement).

At the end, when he says "the design argument fails" it is instead "now that we have proven that God is necessary for logic to be possible, and the design argument rests on the operation of logic, then the design argument fails (in that it cannot not be true)". This last statement does not contradict the previous statement; they are different statements and he is guilty of equivocation in the word "fails".
In other words, the design argument goes through under certain premises, and does not under others. So what? What he has shown is that if TAG is true, the design argument fails, but only because God is proven rather than uncertain; while if TAG is false, then the design argument succeeds and therefore God is a high probability. In other words, he has shown that God is either a certainty or a highly probable being.

What about his second line of argumentation? Equivocation again. If he is granting TAG in the second argument, then not only is (1) true, but the laws of logic would not hold were God to not exist. Therefore, instead of (3) he should be saying "The fine tuning argument is a successful evidential argument for God if logic is possible without God (assumption)." Instead of (4) it would be "Therefore, God would exist even if logic were possible without God." Then (6) would become, "But there could be theoretical evidence against God, given the success of the fine tuning argument, were logic to be possible without God." And (7) would be a near-tautology: "Therefore, there is no being whose nature is the foundation of logic were logic possible without God." Then (8) Therefore, God would not exist were logic possible without God." Finally, (9) "Therefore, logic is impossible without God." Which is where you began anyway since he started by granting TAG.

We should all (myself included) be very careful about his hidden premises/equivocation.

What about his proof that starts out with "If there is a true statement that takes the form 'there is evidence for x', then it confirms theism?" In this proof, I think he is starting with the assumption that TAG is true, meaning the laws of logic depend on God. But this proof clearly has a problem with it...I am probably not getting my terms 100% correct, but I think Ron is conflating epistemic probability (what we think is true based on the evidence) from ontological probability (what actually IS). If we are uncertain that God exists, then based on evidence, we can epistemically put a probability on our belief (crudely). Such and such evidence favors the interpretation that God exists. Other evidence may favor atheism. But in an uncertain world you can truly have evidence that favors a proposition that is untrue. Therefore, having evidence for a proposition does not make that proposition true...all it does is make the statement "there is evidence for this proposition" true.

But if God really does exist, then atheism (here I am using it as the state of affairs in which no God exists) is ontologically untrue. No matter how much evidence you may say there is for atheism, if God does in fact exist that makes atheism untrue. So the way in which he wants "there is evidence for atheism" to mean atheism is true is just a false maneuver. So let's update his actual argument with this in mind:

1. If there is a true statement that takes the form “there is evidence for x”, then it confirms theism (because of TAG).
2. The statement “there is evidence for atheism” is a statement that takes the form “there is evidence for x”.
3. Therefore, if the statement “there is evidence for atheism” is true, then it confirms theism (which has already been proven because TAG was granted).
4. If the statement “there is evidence for atheism” is true, then it, in principle, challenges theism because it means evidence against theism exists.
5. Therefore, if the statement “there is evidence for atheism” is true, then it both confirms (100%) and challenges (makes you wonder about) theism.
6. If the truth of the statement “there is evidence for atheism” both confirms and challenges theism, then the conclusion that one may draw from the evidence for atheism (ie, that atheism is true) statement is necessarily false. In other words, even though there is evidence for atheism, that evidence does not go through.
7. Therefore, the statement “there is evidence for atheism” if true, may lead you to a false conclusion if you don't realize that such a logically true statement confirms theism (100%) under TAG.
8. Therefore, Premise 1 necessarily leads to the conclusion that while there can be evidence for atheism, atheism is still false.

So in summary, atheism can have evidence for it, but *if TAG is granted* then atheism is false, so evidence for atheism is incorrect. But if TAG is not granted, then you can marshal evidence all you want and we'll see which one stacks up better. Ultimately the existence of the laws of logic have a more comfortable fit in a theistic worldview rather than an atheistic one, and the atheist is left with the uncomfortable task of explaining their existence.

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Aron wrote:
Greg, in your first post, what exactly do you mean with this paragraph: "In other wordsthe design argument goes through under certain premises, and does not under others. So what? What he has shown is that if TAG is true, the design argument fails, but only because God is proven rather than uncertain; while if TAG is false, then the design argument succeeds and therefore God is a high probability. In other words, he has shown that God is either a certainty or a highly probable being." My point was to show that, under the assumptions of TAG, the design argument fails, and under the assumptions of the design argument, TAG fails. Are you agreeing with me that the success of one entails the failure of the other?

I'm talking about epistemic probability here.

When I talk about evidence, I mean that some fact makes a hypothesis more epistemically likely than it would have been without it. E is evidence if P(H/E)>P(H). This condition will be met if P(E/H)>P(E/~H).

You're absolutely right that there can be evidence against a true hypothesis (i.e., evidence that lowers it's epistemic probability). For example, if I were framed for murder and the weapon was planted in my sock drawer, this would increase the epistemically probability in the detective's mind that I was guilty. This is despite the fact that, ontologically, the probability that I'm guilty is 0.

So there is no doubt that evidence can pull in different directions epistemically. Some evidence may suggest I'm the killer, and other evidence may suggest I'm innocent. However, no single piece of evidence can simultaneously confirm and challenge a hypothesis. This would mean that for that particular evidence E, P(E/H)>P(E/~H) and P(E/H)
P(H/E) and P(H)

So imagine some fact F raises the epistemic probability of atheism. This would mean P(F/atheism)>P(F/theism), and therefore P(atheism/F)>P(atheism). But, if we think that logic presupposes theism, then we should think every fact about the world increases the epistemic probability of theism to 100% (this is bc in order for there to be facts, laws like the law of identity and non contradiction must apply). This would mean that while F raises the epistemic probability of atheism, it must do the same for theism. Contradiction.

Thus, while it is true that we can have evidence against a true hypothesis, this is only true when that hypothesis is not the foundation of logic itself. If you want to admit the possibility of evidence against theism, you need to drop the premise that logic depends on God.


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Greg Reeves wrote:
Aron, sorry that I did not know you had responded to me.  I guess I didn't get any update saying so.  Like I said originally, I am a scientist and engineer, so you have to take what I say with a grain of salt about these matters.

What I meant in the first paragraph is that under some conditions, TAG goes through, and under others DAG (design) goes through.  Meaning, if you accept TAG, and you condition your DAG argument on TAG, then you end up with an inescapable 100% probability for God, because you have already conditioned your DAG argument on the background that God exists.  So, yes I do agree with you that the success of TAG entails the failure of DAG *only if you are correct that* and *only in the sense that* you must have the possibility of some evidence contrary to an argument to make the argument successful.  But I did say up front that I do not necessarily accept that. But again, even if I did, then DAG would only fail in that sense, but would not fail in the sense that God has been proven to not exist.  It seems to be only a technicality.

But I definitely could be wrong about that, so let's explore your suggestion about probabilities.  Let me make sure I am understanding you correctly.  You are concerned that if you have a piece of evidence that increases your epistemic probability for atheism, then under TAG it also simultaneously decreases the evidence for atheism (because any logical construct, if it exists, on TAG, proves theism).  You are then worried that if you accept TAG then you get a logical contradiction.  Therefore, TAG cannot be true.

Problem is, since we are dealing with epistemic probability, you have to be *very careful* because epistemic probability can be very tricky.  You can end up sneaking all sorts of stuff in the back door.  Here is where I think you are going wrong.  I will try to parse my answer in the context of your previous paragraph that started with "So imaging some fact F...":

So imagine some fact F raises the epistemic probability of atheism if you do not accept TAG. This would mean P(F/atheism)>P(F/theism), and therefore P(atheism/F)>P(atheism). But, if we think that logic presupposes theism, in other words, if we then condition our probabilities on TAG, then we should think every fact about the world increases the epistemic probability of theism to 100% (this is bc in order for there to be facts, laws like the law of identity and non contradiction must apply). This would mean P(atheism/F & TAG)

Remember, formally the law of non-contradiction says both A and ~A cannot hold at the same time, in the same way, and *under the same circumstances*.  Conditioning on TAG completely changes your circumstances.  So we are back to what I said in my original post.  It depends on your premises.  You change your premises and then of course your conclusions can change.  If logic were possible without God (ie, you don't condition on TAG), then you could use logic to try to prove atheism.  If indeed TAG is true, and you condition on it, then any piece of evidence that you previously used in support of atheism when you did not condition on TAG is no longer in support of atheism.  If you wish, I could write out a full Bayesian analysis on this, but I get the feeling that most readers of this forum would not benefit from it.


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Aron wrote:
I don't think we disagree about anything. Once you have come to accept TAG and incorporated it into your background knowledge, then any probability assessments you make will be conditioned on TAG. And you agree that if we condition on TAG, there could never be evidence against theism. But if this is the case, then there could never be evidence for theism either, so the design argument won't work. You seem to agree with this, but think it's "trivial." The reason I don't think it is trivial is that it forces people to make a choice. If you think TAG is true, then you can't think that biological complexity makes theism more likely than it would otherwise be. And if you think biological complexity lends support to theism - i.e. Pr(theism/biology)>Pr(theism) - then you can't have TAG in your background knowledge. I have seen people make cumulative cases that include both arguments, and I don't think this is an option. You can't simultaneously believe that both arguments are sound.

Greg, I wouldn't mind seeing your Bayesian analysis of Dawkins.


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Greg Reeves wrote:
Aron, I am glad we aren't disagreeing then, but I do want to take you to task a little bit because I was primarily responding to how you said these things were *contradictions*.  It is not a formal contradiction because you are either conditioning on TAG or not, and that changes your outcome.

But I like how you want to be very precise about it.  If I were to be building such a cumulative case, I probably wouldn't have caught that, but now that you point it out, I'll be careful.  But I think you can still do it...let me unpack what I mean by that.

First, if one is being as precise as you are, I still argue it is "trivial", because in that case, Pr(theism | biology) >= Pr(theism) --- note here the greater than or equal to rather than the strict greater than --- if you include TAG in your background.  That is because TAG means Pr(theism) = 1.  So Pr(theism | biology) = 1.  So it is a trivial result as to whether you "add" the argument from biological design to your background knowledge.  In either case, Pr(theism) = 1.

So how in the world would you build a cumulative case with TAG included?  Well, since we're talking about epistemic probability here (which is a measure of belief rather than frequency), then you could say "Let 'A' be the event that someone believes TAG is true with a 60% probability".  Could you not then condition on "A"?  Would then TAG not be part of a cumulative case?  I think it could be.

In that case, TAG is just another part of your toolbox in the cumulative case for God.  This is where I fall because I think it's a powerful argument, but no one will be 100% convinced on the basis of this argument alone.  On a frequentist approach, either TAG is true, or not; just like either God actually does exist or not.  But in terms of epistemic/Bayesian thinking, the question is rather, how convinced are you that this argument goes through? If you are 90% certain of TAG, then both Pr(theism | A & B) >= Pr(theism | B) and Pr(theism | A) > 90%, where A = TAG is 90% probable and B = background knowledge.

If you argue for some reason it cannot be part of a cumulative case, then we are faced with two possible choices: either you accept TAG and then arguing further about the existence of God is trivial since you accept the proof from TAG, or you reject TAG and then we go on with the rest of the cumulative case.  Either way, any other evidence/argument I mount in favor of theism is at least neutral: in the former case it's irrelevant and in the latter it strengthens the case for God.

Which camp do you fall under?  Do you accept TAG and therefore need no further convincing on the strength of that argument alone?  Or do you reject TAG and therefore are open to discussing the strength of the other myriad arguments for God's existence?

Again, if you are like me, then TAG is a powerful argument and if correct then God's existence is 100% certain.  But we don't know for sure it's correct, meaning that, in terms of epistemic probabilities, God's existence is not 100% certain. Therefore, we marshall other arguments.

Regarding the Bayesian analysis of Dawkins's statements, it is specifically about the case for the fine tuning of the universe.  The general Bayesian analysis goes like this:

Pr(G | FT) = P(FT | G)*P(G)/P(FT)

where G = God exists and FT = the fine tuning of the universe is instantiated.  As usual, we can split the denominator into two terms:

P(FT) = P(FT | G)*P(G) + P(FT | ~G)*(1 - P(G))

Now, the fine tuning argument says that P(FT | ~G) = epsilon (ie, small).  Usually numbers like 10^-120 or 10^-10^123 are thrown around, but the exact number is not important, just that it's small.

For the sake of simplicity, let me just say that P(FT | G) = 1 (ie, God would indeed make a universe in which advanced life is possible, and of course by necessity such a universe would be finely tuned as we observe).  We can keep this term around for precision but I think it's easier to discuss over facebook if I make this assumption.  The results are essentially the same either way unless you want to argue P(FT | G) = epsilon also, which I think would be hard to justify.

Anyway, this leaves us with:

P(G | FT) = P(G) / (P(G) + epsilon*(1 - P(G))

So the only thing left here "unknown" is our prior probability of the existence of God.  Now, you can see right away that if the fine tuning argument is correct in that epsilon is small, then only if you have an absurdly low prior for God existing can you escape the conclusion that P(G | FT) is close to 1.  Well, that's exactly what Dawkins does.  He says, "It doesn't matter how improbable our universe is; the probability that God exists is smaller."  That's a sneaky statement, but what it means is that P(G) = 0.  The only number that could be a probability that is smaller than *any other number* that is also a probability is zero.  By definition.

Mathematically, Dawkins's statement is: for every epsilon > 0, 0 <= P(G) < epsilon.  This is *mathematically identical* to saying P(G) = 0.  But if someone's prior for God is zero, then there is no reason to have any discussion.  Dawkins is essentially saying, "I don't care what the scientific evidence for fine tuning says, I will choose to believe that God does not exist."  That is not reason or rationality, that is blind belief.  Belief, as it were, in spite of the evidence.  :-P

But let's instead say that your prior is also super-small.  Let's say it's much smaller than epsilon even.  Then you are left with:

P(G | FT) = P(G)/epsilon

In other words, the most hardened skeptic, unless he is exhibiting blind faith that God does not exist (and thus P(G) = 0 for him), would objectively increase his epistemic belief that God exists by orders of magnitude once the evidence for the fine tuning of the universe were examined.  And if you have a set prior for God's existence (and not a moving target so that as more evidence comes in, you "conveniently" make your P(G) smaller), all you have to do is wait a while.  As we discover more about the universe, I predict that epsilon will get smaller and smaller.  If I am right, then eventually, epsilon will either shrink past your set P(G), or you will have to find some other reason to reject this argument.  Or else you are fooling yourself.

Now, don't get me wrong, you can attack what I've said in a number of places.  I did gloss over what one might think P(FT | G) is.  Also, you can argue that the universe is not in fact finely-tuned.  However, in the first case, as I've said, unless you unjustifiably put P(FT | G) ~ epsilon or less, then it doesn't really matter what P(FT | G) is.  In the second case, you would be going against hard scientific data, and thus must object out of a precommitment to a non-theistic philosophy rather than objectively examining the evidence.  I think that in either case you are in a weaker position than the theist.

I can go through a similar Bayesian argument for the resurrection.  I like that one too.