I think I arrived to this principle when I still considered myself a Christian: if you think that the existence of a God solves any philosophical problems - your are missing the point of these philosophical problems.
Back in these days I could not articulate it like that, but now I can say that using God as an explanation for anything, simply passess the buck of improbability one level further. If we think that the existence of finetuned universe is extremely unlikely, then simply saying "God created universe this way and this is why its finetuned" takes all the improbability from finetunning and passes it to the existence of the kind of God who creates finetuned universe. On its own we are simply supposed to believe that the existence of God who creates a finetuned universe is at least as unlikely as the existence of finetuned universe.
We need to have some separate evidence about the space of all-possible-Gods, to priviledge the God hypothesis. Just like we need to already have knowledge about humans tending to carve things on stones to be confident that a stonecarving is more likley to be human made than otherwise. You seem to simply accept the premise that obviously a God would be more than 1/googol likely to make a finely tuned universe, but why? Why do you think you know that?
Likewise, you say that God is perfect and unlimitedly good. Why do you think that you know that? What kind of evidence allows you to priviledge specifically this type of God from the space of all possible Gods? If finetuned unverses are very unlikely and for some reason perfectly good Gods create finetuned universes, maybe it's that such Gods are extremely unlikely? I don't see where you adress such possibility.
The problem doesn't get passed up a level because God doesn't have any manipulable parameters. He has a single simple property--perfection. Now, maybe you think the prior probability of such a God is ~zero, but then that's a different argument. Fine-tuning is still major evidence for a perfect God, but you think the odds of that are near zero (compare--your argument for lab leak is bunk because I assign a prior of basically zero to it).
I'm dubious that you should think God has a prior of near zero because:
1) contingency arguments and Godelian ontological arguments might work. If they have a 1% chance of work, then there's a 1% chance that God exists necessarily and so his prior should be around 1%.
2) Theism is very simple: it posits just one property--perfection.
3) theism is ontologically unique, being the only worldview that posits something fundamental truly without limits, and is the simplest personal explanation of reality.
4) Theism lacks arbitrary limits which inhibit the probability of a theory.
So that's why I posit a perfect God--it's simpler, more provable, lacks arbitrary limits, and ontologically unique, giving it a higher prior.
> God doesn't have any manipulable parameters. He has a single simple property--perfection.
That's a very specific kind of creator you are talking about. We started from universe is finetuned -> someone created it this way. But now you are jumping to a conclusion that this "someone" is a perfect being. And I don't see why.
When I think about all possible creators of this universe most of them are not perfectly good. There are creators who would create only finetuned universes, or creators who create only variants of this universe in particular. These should be our first candidates. Perfect creator is not even in top 10%. It's possible to come up with some clever reasoning why a perfectly good God would create this universe https://www.lesswrong.com/posts/Lt8Rn4rkYwqiTXGPy/answer-to-job but they get complexity penalties, and, I suppose, under SIA you would still expect to be in the universe fully saturated by bliss. Also you can use exactly the same type of reasoning to explain why absolutely evil creator would make this universe as well. Maybe there are multiple gods with their different utility functions and this universe is a compromise between them. As soon as you stop thinking in "either atheism or theism and God is perfection" terms it becomes clear that there are a lot of different adjustable parameters to the demiurge hypothesis. And so just picking one specific type of creator for no apparent reason out of the space of all possible creators should indeed give us prior to near zero for such creator to be the one who made our universe. Maybe even literally zero - there seems to be infinite degrees of freedom - lacking limits cuts both ways.
The question whether perfection is a simple property is a bit tangental here, but I don't see much reasons to believe in it, too. I understand why one can come up with such hypothesis based on some semantic argument, but this seems to be just that - a confusing over semantics. In practise we do not encounter perfection in our universe, trying to be closer to perfection is very hard and consists of multiple changes to multiple parameters and omnisient beings seem to be incredibly complex from the perspective of Solomonoff induction.
Well if perfection is simple then perfect being theism is simple which makes it more likely than the other gerrymandered perfect beings with arbitrary sets of powers and desires. I gave other reasons why a perfect being has a decent prior. You say the prior might be zero, but to think that you have to think the odds that something like the Godelian ontological argument works is literally zero. I don't know why you'd think the prior was so low--it's much simpler than naturalism.
> Well if perfection is simple then perfect being theism is simple which makes it more likely than the other gerrymandered perfect beings with arbitrary sets of powers and desires.
On priors - yes, but not after updating on the nature of the universe that we live in. And, once again - a pretty huge "if" it is, as our current best generalisations of Occams Razor treat it as infinitely complex instead of most simple.
> you have to think the odds that something like the Godelian ontological argument works is literally zero.
I'm not sure what you mean by "works" here.
Godelian ontological argument, as far as I can see, doesn't talks specifically about a perfectly good God. Even if we accept all the axioms, they seem to be describing at least absolutely wicked God as well and probably all manner of other "gerrymandered gods", because the definition of "positive property" is extremely vague. And, I suppose, it can be the case that existence is the only positive property so then this argument is about basically anything at all.
> Well as I've argued, lots of features of the world are well-explained by a good God.
As you mention in the post about multiverse, a perfectly good God would still create a multiverse, and you consider multiverse to be a satisfying explaination of finetuning. This means that the addition of perfect good God is just an extra entity with no explanationary power.
What other "features of the world" do you consider well-explained by a good God?
> The Godelian ontological argument points towards a perfect God--possessing all positive properties.
Only if you are confused by the way Godel named his variables. If you look at what the math actually *means* then you'll notice that the notion of "positive property" dosn't have much to do with our human intuitions of what "positive" is.
All that Godel means by "positive property" is that:
1. If A is a positive property then !A is not a positive property
2. If A is positive property and it necessary implies, B then B is also positive property
3. If A is positive property then it's necessary positive property
4. Existence is a positive property
And then he defines Godlikeness as possessing all of positive properties and being itself a positive property.
As you may see there is a trivial case where Existence is the only positive property there is. Or where "being evil" is a positive property and "being good" is not positive property and therefore the argument equally applies to the Most Wicked God as to The Omnibenevolent One. And so on and so forth.
In the end the argument boils down to "If I define X as necessary possessing all properties from some set of properties which may or may not include only existing then X exists!" Which, I think is completely fair to say, gives us exactly zero bit of evidence whether or not any particular type of God exists.
I think a good reason to not assign it an absurdly low prior probability is how common belief in God and belief in religious experiences are - unless you assume that people's experiences are so unreliable that people's testimonies about anything can't ever be trusted, which would be absurd as most of your knowledge comes from information from other people.
I will say yours is the strongest argument for the existence of God I have seen (for the record I’m an agnostic thisclose to atheist).
Given that you assert that God is perfection, how do you answer the question of why there is so much cruelty and suffering in the world, including the torturing of innocents, decapitation of babies, etc.? Be clear that I ain’t asking about “ordinary” levels of suffering, which are easily enough explainable.
I’m at most an advanced beginner on this topic, and haven’t thought deeply about it in many years, so apologies for what I know is a pretty basic question.
Ok, I read em. Your basic answer is that you have a bunch of semi plausible possibilities, but in the end you rely on “we can’t know, and certainly don’t know”. So in other words, faith.
But for this reasoner, at least, that requirement of faith - I.e. that “perfection” involves the existence of massive abject, unnecessary cruelty (and one more time, I ain’t talking slavery, or suffering, I’m talking things like torture of obvious innocents and baby decapitations) makes your argument enormously weaker.
Because of course if God is *anything* other than literal perfection, any of your arguments for evil would be perfectly valid. But I don’t see how you can have it both ways.
I don't think faith is the answer. It's based on evidence. We have evidence that God exists and various explanations of why he might allow evil, so we should regard those as the most likely scenario. I agree evil is powerful evidence against God, but it's potentially outweighed by the powerful evidence for God.
“ but it's potentially outweighed by the powerful evidence for God.”
This statement is fair enough. The key word being “potentially”. And it’s why I’m in the end an agnostic.
But your “powerful evidence for perfection-God” isn’t imo as powerful as you claim it is in your arguments. That said, again, just advanced beginner here. And thanks much for your thoughtful replies.
You say you posit only one thing - a perfect God - but you then suggest that in terms of evidence/proof that theism is more likely there are actually two things: that a perfect God wants an “indifferent” universe.
Don’t both the Old Testament and the New Testament (again, not a scholar) show many examples of a God that is not perfection? Is your answer to this roughly “well, the Bible was written down by imperfect humans who got stuff lost in translation”, that “well, the Judeo-Christians have got key things about God fundamentally wrong”, or something else? Or are we back to faith?
And at least once you mention salvation and one’s relationship to God as an explanation of evil; ain’t that about faith? In fact of the 4 of your 5 explanations listed (I didn’t click to try to understand 3, which you claim is “a bit complicated”), each one either comes down to faith or one’s relationship with God (which again to this mere advanced beginner seems also to be about faith, no?).
Only Michael Huemer has influenced me more than Bryan Caplan, but this is on my shortlist of things he's really wrong about. Include veganism and mental illness on that list.
Among his economic ideas, though, he's almost always right. He's almost always right about philosophy though (aside from the above ideas) because he agrees with Huemer on most things.
Don't get how you're calculating these probabilities. Take any existing constant you consider finely tuned, add a few 0s to the last decimal point number, then add an infinite amount of other numbers after those 0s. Sufficient padding of 0s will ensure that there will be no physically detectable effect of the numbers after the 0s, and you can add numbers after the 0s indefinitely. Ergo we have an infinite number of ways to fine tune the universe under physicalism just by using the existing physical constants as a basis for our fine tuning.
This brings up another problem - the odds we'd see this value of the physical constant are 1/infinity. But then so are the odds God would choose this fine tuning over the infinite other fine tunings. So we in fact have 0 probability to expect either hypothesis, which is incoherent without some further explanation on how to resolve dividing by infinity.
So there will be some values after the decimal point that don't matter. But then there will be some values before the decimal point that have to be finely tuned to an incredible degree of precision.
//This brings up another problem - the odds we'd see this value of the physical constant are 1/infinity.//
It may be true that there are certain probability events on both theories. But there's one feature of the world that's much more strongly predicted on theism which is evidence for theism.
>But then there will be some values before the decimal point that have to be finely tuned to an incredible degree of precision
...Because we're using the current physical constants as a basis for a universe supporting life. Not sure how you could rule out the infinite other sets of possible laws that could also result in a universe supporting life (or whatever it's supposed to be fine tuned for). Or why we should think these possibilia are finite rather than infinite (presumably God could fine tune the universe in an infinite number of ways).
> But there's one feature of the world that's much more strongly predicted on theism which is evidence for theism.
It's not predicted more under theism, because there's no way to resolve whether life is more or less guaranteed under naturalism. Whether you're sampling from the universes with fine tuning or the ones that lack it, your sampling odds are 1/infinity for both. There's no way to calculate which is more likely because classical probability theory doesn't make use of infinity (i.e. it isn't 50/50 you would get a universe that was/wasn't fine tuned).
I don't see how Matthew's calculations require dividing two infinites.
If, for example, Matthew was using the Principle of Indifference, he could derive this equation:
Pr(universe is finely-tuned | universe is naturalist (aka everything is natural)) = # of possible finely-tuned naturalist universes / # of possible naturalist universes
Then, yes, he'd have the problem you pointed out.
The # of possible finely-tuned naturalist universes is infinite, and the # of possible naturalist universes is infinite. So we get an incoherent conditional probability.
But, I haven't seen Matthew use the above equation. Additionally, it's not so clear the Principle of Indifference applies here - we may be reason to prefer one outcome over another. The distribution of constants is skewed in favour of fine-tuned constants if the distribution is normal (as opposed to a uniform distribution, the distribution you get when applying the princple of indifference). And there's some reason to think the distribution of constants is normal. (I won't go into that more here, but for more, see the blog "A note on fine tuning argument" by "knownandstrangethings".)
So it's not clear your claim "there's no way to resolve whether life is more or less guaranteed under naturalism" is true.
That claim was indexed to this context. Obviously if you introduce a context with finite probabilities, that statement is falsified. And knownandstrangethings commits the same error. Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions and 2) that "more likely" is a coherent notion in this context (infinite probabilities have still not been ruled out)?
Honestly, I'm not sure what you're saying. I don't see how your questions connect to or relevant to what I said. Can you give the expanded version of your points?
For example, "Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions" - I don't know what you're asking.
Your questions here just look like you're asking justification for assumptions that were not made. I don't think you fully appreciated the underlying stats or math behind knownandstrangethings blog. It's fine to ask questions about it before jumping the gun.
"2) that "more likely" is a coherent notion in this context (infinite probabilities have still not been ruled out)?"
Not quite sure what you're saying here. If Pr(P|Q)=Undefined, then Pr(P|Q) being greater than some other probability doesn't make sense. That's correct.
"Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions"
Okay, after second thought. I may understand this question.
So important to note, all that matters is the distribution of possible values the fundamental constants may take is not uniform. It may be another distribution besides normal.
If it's not uniform, then the Principle of Indifference doesn't apply. If the PoI doesn't apply, then there's no reason to set Pr(fine-tuning | naturalism) = # of possible finely-tuned naturalist universes / # of possible naturalist universes. If there's no reason to set Pr(fine-tuning | naturalism) like that, then there's no reason to think the conditional probability is incoherent.
So here's the reasoning why the distribution is non-uniform:
Given an observation X=x, our posterior for X should be skewed towards x. This is because the Distributions which make X=x most probable are the ones which see the largest proportional increases in their priors, skewing the posterior marginal distribution for X towards x. If the posterior marginal distributions for X are skewed towards x, then those distributions aren't uniform.
The observation we have is the fundamental constants taking the value that we observed they actually have. So our posterior distribution should be skewed towards the constants having the values they actually have, rather than other values. This means the distribution is non-uniform.
I think I arrived to this principle when I still considered myself a Christian: if you think that the existence of a God solves any philosophical problems - your are missing the point of these philosophical problems.
Back in these days I could not articulate it like that, but now I can say that using God as an explanation for anything, simply passess the buck of improbability one level further. If we think that the existence of finetuned universe is extremely unlikely, then simply saying "God created universe this way and this is why its finetuned" takes all the improbability from finetunning and passes it to the existence of the kind of God who creates finetuned universe. On its own we are simply supposed to believe that the existence of God who creates a finetuned universe is at least as unlikely as the existence of finetuned universe.
We need to have some separate evidence about the space of all-possible-Gods, to priviledge the God hypothesis. Just like we need to already have knowledge about humans tending to carve things on stones to be confident that a stonecarving is more likley to be human made than otherwise. You seem to simply accept the premise that obviously a God would be more than 1/googol likely to make a finely tuned universe, but why? Why do you think you know that?
Likewise, you say that God is perfect and unlimitedly good. Why do you think that you know that? What kind of evidence allows you to priviledge specifically this type of God from the space of all possible Gods? If finetuned unverses are very unlikely and for some reason perfectly good Gods create finetuned universes, maybe it's that such Gods are extremely unlikely? I don't see where you adress such possibility.
The problem doesn't get passed up a level because God doesn't have any manipulable parameters. He has a single simple property--perfection. Now, maybe you think the prior probability of such a God is ~zero, but then that's a different argument. Fine-tuning is still major evidence for a perfect God, but you think the odds of that are near zero (compare--your argument for lab leak is bunk because I assign a prior of basically zero to it).
I'm dubious that you should think God has a prior of near zero because:
1) contingency arguments and Godelian ontological arguments might work. If they have a 1% chance of work, then there's a 1% chance that God exists necessarily and so his prior should be around 1%.
2) Theism is very simple: it posits just one property--perfection.
3) theism is ontologically unique, being the only worldview that posits something fundamental truly without limits, and is the simplest personal explanation of reality.
4) Theism lacks arbitrary limits which inhibit the probability of a theory.
So that's why I posit a perfect God--it's simpler, more provable, lacks arbitrary limits, and ontologically unique, giving it a higher prior.
> God doesn't have any manipulable parameters. He has a single simple property--perfection.
That's a very specific kind of creator you are talking about. We started from universe is finetuned -> someone created it this way. But now you are jumping to a conclusion that this "someone" is a perfect being. And I don't see why.
When I think about all possible creators of this universe most of them are not perfectly good. There are creators who would create only finetuned universes, or creators who create only variants of this universe in particular. These should be our first candidates. Perfect creator is not even in top 10%. It's possible to come up with some clever reasoning why a perfectly good God would create this universe https://www.lesswrong.com/posts/Lt8Rn4rkYwqiTXGPy/answer-to-job but they get complexity penalties, and, I suppose, under SIA you would still expect to be in the universe fully saturated by bliss. Also you can use exactly the same type of reasoning to explain why absolutely evil creator would make this universe as well. Maybe there are multiple gods with their different utility functions and this universe is a compromise between them. As soon as you stop thinking in "either atheism or theism and God is perfection" terms it becomes clear that there are a lot of different adjustable parameters to the demiurge hypothesis. And so just picking one specific type of creator for no apparent reason out of the space of all possible creators should indeed give us prior to near zero for such creator to be the one who made our universe. Maybe even literally zero - there seems to be infinite degrees of freedom - lacking limits cuts both ways.
The question whether perfection is a simple property is a bit tangental here, but I don't see much reasons to believe in it, too. I understand why one can come up with such hypothesis based on some semantic argument, but this seems to be just that - a confusing over semantics. In practise we do not encounter perfection in our universe, trying to be closer to perfection is very hard and consists of multiple changes to multiple parameters and omnisient beings seem to be incredibly complex from the perspective of Solomonoff induction.
Well if perfection is simple then perfect being theism is simple which makes it more likely than the other gerrymandered perfect beings with arbitrary sets of powers and desires. I gave other reasons why a perfect being has a decent prior. You say the prior might be zero, but to think that you have to think the odds that something like the Godelian ontological argument works is literally zero. I don't know why you'd think the prior was so low--it's much simpler than naturalism.
> Well if perfection is simple then perfect being theism is simple which makes it more likely than the other gerrymandered perfect beings with arbitrary sets of powers and desires.
On priors - yes, but not after updating on the nature of the universe that we live in. And, once again - a pretty huge "if" it is, as our current best generalisations of Occams Razor treat it as infinitely complex instead of most simple.
> you have to think the odds that something like the Godelian ontological argument works is literally zero.
I'm not sure what you mean by "works" here.
Godelian ontological argument, as far as I can see, doesn't talks specifically about a perfectly good God. Even if we accept all the axioms, they seem to be describing at least absolutely wicked God as well and probably all manner of other "gerrymandered gods", because the definition of "positive property" is extremely vague. And, I suppose, it can be the case that existence is the only positive property so then this argument is about basically anything at all.
Well as I've argued, lots of features of the world are well-explained by a good God.
The Godelian ontological argument points towards a perfect God--possessing all positive properties.
> Well as I've argued, lots of features of the world are well-explained by a good God.
As you mention in the post about multiverse, a perfectly good God would still create a multiverse, and you consider multiverse to be a satisfying explaination of finetuning. This means that the addition of perfect good God is just an extra entity with no explanationary power.
What other "features of the world" do you consider well-explained by a good God?
> The Godelian ontological argument points towards a perfect God--possessing all positive properties.
Only if you are confused by the way Godel named his variables. If you look at what the math actually *means* then you'll notice that the notion of "positive property" dosn't have much to do with our human intuitions of what "positive" is.
All that Godel means by "positive property" is that:
1. If A is a positive property then !A is not a positive property
2. If A is positive property and it necessary implies, B then B is also positive property
3. If A is positive property then it's necessary positive property
4. Existence is a positive property
And then he defines Godlikeness as possessing all of positive properties and being itself a positive property.
As you may see there is a trivial case where Existence is the only positive property there is. Or where "being evil" is a positive property and "being good" is not positive property and therefore the argument equally applies to the Most Wicked God as to The Omnibenevolent One. And so on and so forth.
In the end the argument boils down to "If I define X as necessary possessing all properties from some set of properties which may or may not include only existing then X exists!" Which, I think is completely fair to say, gives us exactly zero bit of evidence whether or not any particular type of God exists.
I think a good reason to not assign it an absurdly low prior probability is how common belief in God and belief in religious experiences are - unless you assume that people's experiences are so unreliable that people's testimonies about anything can't ever be trusted, which would be absurd as most of your knowledge comes from information from other people.
Agreed
I will say yours is the strongest argument for the existence of God I have seen (for the record I’m an agnostic thisclose to atheist).
Given that you assert that God is perfection, how do you answer the question of why there is so much cruelty and suffering in the world, including the torturing of innocents, decapitation of babies, etc.? Be clear that I ain’t asking about “ordinary” levels of suffering, which are easily enough explainable.
I’m at most an advanced beginner on this topic, and haven’t thought deeply about it in many years, so apologies for what I know is a pretty basic question.
I address this here https://benthams.substack.com/p/a-theistic-theory-of-everything
Ok, I read em. Your basic answer is that you have a bunch of semi plausible possibilities, but in the end you rely on “we can’t know, and certainly don’t know”. So in other words, faith.
But for this reasoner, at least, that requirement of faith - I.e. that “perfection” involves the existence of massive abject, unnecessary cruelty (and one more time, I ain’t talking slavery, or suffering, I’m talking things like torture of obvious innocents and baby decapitations) makes your argument enormously weaker.
Because of course if God is *anything* other than literal perfection, any of your arguments for evil would be perfectly valid. But I don’t see how you can have it both ways.
I don't think faith is the answer. It's based on evidence. We have evidence that God exists and various explanations of why he might allow evil, so we should regard those as the most likely scenario. I agree evil is powerful evidence against God, but it's potentially outweighed by the powerful evidence for God.
“ but it's potentially outweighed by the powerful evidence for God.”
This statement is fair enough. The key word being “potentially”. And it’s why I’m in the end an agnostic.
But your “powerful evidence for perfection-God” isn’t imo as powerful as you claim it is in your arguments. That said, again, just advanced beginner here. And thanks much for your thoughtful replies.
You say you posit only one thing - a perfect God - but you then suggest that in terms of evidence/proof that theism is more likely there are actually two things: that a perfect God wants an “indifferent” universe.
Don’t both the Old Testament and the New Testament (again, not a scholar) show many examples of a God that is not perfection? Is your answer to this roughly “well, the Bible was written down by imperfect humans who got stuff lost in translation”, that “well, the Judeo-Christians have got key things about God fundamentally wrong”, or something else? Or are we back to faith?
And at least once you mention salvation and one’s relationship to God as an explanation of evil; ain’t that about faith? In fact of the 4 of your 5 explanations listed (I didn’t click to try to understand 3, which you claim is “a bit complicated”), each one either comes down to faith or one’s relationship with God (which again to this mere advanced beginner seems also to be about faith, no?).
Only Michael Huemer has influenced me more than Bryan Caplan, but this is on my shortlist of things he's really wrong about. Include veganism and mental illness on that list.
Among his economic ideas, though, he's almost always right. He's almost always right about philosophy though (aside from the above ideas) because he agrees with Huemer on most things.
That's basically my view of Caplan.
Don't get how you're calculating these probabilities. Take any existing constant you consider finely tuned, add a few 0s to the last decimal point number, then add an infinite amount of other numbers after those 0s. Sufficient padding of 0s will ensure that there will be no physically detectable effect of the numbers after the 0s, and you can add numbers after the 0s indefinitely. Ergo we have an infinite number of ways to fine tune the universe under physicalism just by using the existing physical constants as a basis for our fine tuning.
This brings up another problem - the odds we'd see this value of the physical constant are 1/infinity. But then so are the odds God would choose this fine tuning over the infinite other fine tunings. So we in fact have 0 probability to expect either hypothesis, which is incoherent without some further explanation on how to resolve dividing by infinity.
So there will be some values after the decimal point that don't matter. But then there will be some values before the decimal point that have to be finely tuned to an incredible degree of precision.
//This brings up another problem - the odds we'd see this value of the physical constant are 1/infinity.//
It may be true that there are certain probability events on both theories. But there's one feature of the world that's much more strongly predicted on theism which is evidence for theism.
>But then there will be some values before the decimal point that have to be finely tuned to an incredible degree of precision
...Because we're using the current physical constants as a basis for a universe supporting life. Not sure how you could rule out the infinite other sets of possible laws that could also result in a universe supporting life (or whatever it's supposed to be fine tuned for). Or why we should think these possibilia are finite rather than infinite (presumably God could fine tune the universe in an infinite number of ways).
> But there's one feature of the world that's much more strongly predicted on theism which is evidence for theism.
It's not predicted more under theism, because there's no way to resolve whether life is more or less guaranteed under naturalism. Whether you're sampling from the universes with fine tuning or the ones that lack it, your sampling odds are 1/infinity for both. There's no way to calculate which is more likely because classical probability theory doesn't make use of infinity (i.e. it isn't 50/50 you would get a universe that was/wasn't fine tuned).
I don't see how Matthew's calculations require dividing two infinites.
If, for example, Matthew was using the Principle of Indifference, he could derive this equation:
Pr(universe is finely-tuned | universe is naturalist (aka everything is natural)) = # of possible finely-tuned naturalist universes / # of possible naturalist universes
Then, yes, he'd have the problem you pointed out.
The # of possible finely-tuned naturalist universes is infinite, and the # of possible naturalist universes is infinite. So we get an incoherent conditional probability.
But, I haven't seen Matthew use the above equation. Additionally, it's not so clear the Principle of Indifference applies here - we may be reason to prefer one outcome over another. The distribution of constants is skewed in favour of fine-tuned constants if the distribution is normal (as opposed to a uniform distribution, the distribution you get when applying the princple of indifference). And there's some reason to think the distribution of constants is normal. (I won't go into that more here, but for more, see the blog "A note on fine tuning argument" by "knownandstrangethings".)
So it's not clear your claim "there's no way to resolve whether life is more or less guaranteed under naturalism" is true.
That claim was indexed to this context. Obviously if you introduce a context with finite probabilities, that statement is falsified. And knownandstrangethings commits the same error. Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions and 2) that "more likely" is a coherent notion in this context (infinite probabilities have still not been ruled out)?
Honestly, I'm not sure what you're saying. I don't see how your questions connect to or relevant to what I said. Can you give the expanded version of your points?
For example, "Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions" - I don't know what you're asking.
Your questions here just look like you're asking justification for assumptions that were not made. I don't think you fully appreciated the underlying stats or math behind knownandstrangethings blog. It's fine to ask questions about it before jumping the gun.
"2) that "more likely" is a coherent notion in this context (infinite probabilities have still not been ruled out)?"
Not quite sure what you're saying here. If Pr(P|Q)=Undefined, then Pr(P|Q) being greater than some other probability doesn't make sense. That's correct.
"Why think of the set of metaphysically possible laws that they're 1) more likely to yield measurable parameters that form normal distributions"
Okay, after second thought. I may understand this question.
So important to note, all that matters is the distribution of possible values the fundamental constants may take is not uniform. It may be another distribution besides normal.
If it's not uniform, then the Principle of Indifference doesn't apply. If the PoI doesn't apply, then there's no reason to set Pr(fine-tuning | naturalism) = # of possible finely-tuned naturalist universes / # of possible naturalist universes. If there's no reason to set Pr(fine-tuning | naturalism) like that, then there's no reason to think the conditional probability is incoherent.
So here's the reasoning why the distribution is non-uniform:
Given an observation X=x, our posterior for X should be skewed towards x. This is because the Distributions which make X=x most probable are the ones which see the largest proportional increases in their priors, skewing the posterior marginal distribution for X towards x. If the posterior marginal distributions for X are skewed towards x, then those distributions aren't uniform.
The observation we have is the fundamental constants taking the value that we observed they actually have. So our posterior distribution should be skewed towards the constants having the values they actually have, rather than other values. This means the distribution is non-uniform.
Will there be video of the debate, or any way to watch?
Yep