The argument for God takes the prior probability of God and considers the posterior probability in light of new 'evidence'. There isn't any evidence being presented for aliens. I made up something similar to serve as evidence - i.e. the great red spot on Jupiter - but it seems pretty clear from the subsequent discussion that you didn't take the idea seriously, nor did you come up with any real observations that have been taken as evidence of aliens (coming up with something or other about giraffes, instead, which I'm pretty sure was made up (at least, a google image search for "giraffe" and "jupiter" didn't come up with anything)). So the one argument claims there is 'evidence' for God and the other makes no claims for evidence of aliens.
The fine-tuning argument claims that evidence of fine-tuning is evidence of a god. The argument based on Drake's equation claims that evidence of the number of stars, estimates of the average numbers of planets for each star, etc. is evidence of the existence of aliens.
Both claim evidence to support the conclusion, but the problem with both is that some needed evidence is missing -- values that are simply guessed at without much if any supporting evidence. In the argument for a god, one of those values is the prior probability of a god, which I think is the one you're objecting to. It's given at 1 in a million, but could be higher or could be lower. One important point is that the fine-tuning argument makes the prior probability of a god low on purpose, because even if you consider the prior probability low, the posterior probability may still be high consider fine-tuning. Even so, saying that the value is a pure guess is a valid objection to the premise of the argument, similar to objecting that any of the values of Drake's equation are pure guesses.
I can't tell if you're objecting to the use of Bayes analysis in general (the fact that Bayes analysis requires a prior probability that in this case is just a guess). While it's true that if you guess at the prior probability, that the conclusion is also a guess, the same is true of Drake's equation -- if you guess at any value, the conclusion is also a guess.
So it isn't that I didn't take your analogy of the spot on Jupiter seriously. Maybe I'm missing the point of the example, but it simply wouldn't conclude that aliens are probable in a Bayesian analysis unless the spot on Jupiter were something that would be unlikely to occur without aliens (such as a building on Jupiter). So if you were meaning for it to be similar to the argument for god, it would fall short. That doesn't mean that Bayesian analysis couldn't be used with the situation you described, but if you did use it the posterior probability of aliens on Jupiter would be very close to the prior probability, as you would expect because the probability of the spot occurring with or without aliens would be about the same. However, if you used Bayesian analysis with the example of a building on Jupiter, you would get a high probability of aliens having been on Jupiter
even if you assume a very low prior probability, as you would expect because there is a higher probability of the building having been there because of aliens than by other means.
Drake's equation serves as an estimate for p(H). At least, it's a better attempt than "a million to one" or an "agnostic p=0.5".
The problem is that an argument based on Drake's equation is
not a better attempt because many of the values you would put in are just as much guesses as the prior probability of a god used in the fine-tuning argument.
The fine-tuning argument claims that God's existence is more likely based on the presentation of 'evidence'. If there was reference to some observation (like the great red spot), then the alien argument would be that the existence of aliens is more likely based on the presentation of that 'evidence'.
The evidence in the fine-tuning argument concerns the probability of fine-tuning. Other values are simply guesses.
Drake's equation isn't a Bayesian argument, but like I said you can form a Bayesian argument for aliens based on the red spot or based on a hypothetical building. The hypothetical building would be closer to the argument for a god in that it is assumed that there would be a much higher probability of the building's existence if there were aliens on Jupiter than if there were no aliens on Jupiter. Even though we don't know the precise prior probability of aliens on Jupiter without considering the new evidence, even if you gave a low probability of aliens on Jupiter as a prior probability, you would still get a high posterior probability considering the building. That's why evidence of a building on Jupiter would indeed be evidence of aliens.
No one has yet proposed a prior based on scientific inquiry for God (references to fine-tuning don't count (I apologize for feeling compelled to say something so trivially obvious)).
I understand what you're saying, and you're right. The prior probability is a guess (it is not based on evidence). But your objection is no different than an objection to guesses (also not based on evidence) for values for Drake's equation.
The next step is to turn to the evidence. Does the presence of the great red spot serve as evidence for aliens?
Nope.
Would the presence of something giraffe-like or building-like in appearance serve as evidence for aliens?
Yes, absolutely.
If and when anyone seriously presents some observation as evidence for aliens, then it would be reasonable for us to discuss it. Until then, it should be obvious that our prior probability remains unchanged.
Correct. But we do have evidence of fine-tuning.
Does fine-tuning serve as evidence for God?
Yes, it would if you accept the other premises of the argument.
So on the one hand we have an estimation of a prior based on scientific inquiry, and a search for evidence. And on the other hand we have a claim based on a prior pulled from someone's ass and suspect 'evidence'. I have no difficulty seeing a difference between the two on the basis of what sorts of claims are made and the extent to which they are supported.
The problem is that there is no valid probability of aliens without the missing pieces of the puzzle (which must also be pulled from someone's ass or based on suspect "evidence"). It's the same objection you have to the fine-tuning argument.
-Bri