Apologies for the late post. But I found this argument fascinating and wanted to share my thoughts. Also sorry to see the reception you got on the reddit page. I took a peek at the comments, and they seemed especially dull and mean-spirited. Just a reminder of how much we should cherish philosophical blogs like these I suppose!
Before I get into the meat of your argument, let me make a minor quibble about your points that there is no set of possible observers (the observer reference class is greater than Beth 2):
1. As mentioned already in the comments, not all truths are knowable. So it seems dubious that truths can be put in 1-to-1 correspondence with observers.
2. This assumes that infinite minds count in the set of possible observers. But maybe it doesn't make sense to include such minds in the reference class of possible observers one can be. If so, then (assuming every mind is decomposable into a computational structure with finite parts), we won't be able to construct a diagonal proof showing that there is a mind not in the set of all possible observer-minds, since that mind would have to be describable by a real number (i.e. infinite).
Now into the meat of the argument:
A) It seems to me that there is a lacuna in your argument which has to do with the construction of one's reference class. Endorsing SIA doesn't obviate the need for constructing a reference class, since we still need to define what we think an observer is. Reasonable people can disagree about what constitutes an observer. Particularly, if we accept SIA then we accept that we should reason as if we were sampled from the reference class of all possible observers we could have been. But what constitutes an observer that "we could have been"? Maybe a physicalist might argue that an observer can only be a physical entity which is composed of some finite computational structure (related to point 2 above). It could also be argued that we should only consider ourselves to belong in the reference class of entities which could be physically constructed according to possible natural theories. If so, then hypothetical entities in the Beth 2 realm won't count as observers. And the multiverse counter still goes through.
B) It's not clear to me that atheism is incompatible with Beth 2 worlds. Just because we reject theism doesn't mean we have to accept some common naturalistic alternative (e.g. multiverse theory). Maybe there exists some metaphysical principle (e.g. simpler patterns reproduce into complex repeatable patterns) which governs the construction of worlds, and which entails that there will exist uncountably infinite number of worlds where induction is sound, and little to no worlds where induction is falsified. I don't see why our prior for such a principle must be lower than our prior for theism.
Alternatively, one could simply accept the existence of Beth-2 observers in uncountable number of worlds as a brute fact. One presumably has to endorse a brute fact at some stage (whether God or something else). So the atheist can simply say that they take on a brute fact one step sooner in the explanatory chain. Perhaps this could be retorted with appeals to simplicity (similar to Swinburne's cosmological argument), so that accepting a simpler explanation (i.e. God) as a brute fact is easier. However, I find such arguments really dubious. It's not clear to me that there are metaphysical reasons to favor simplicity. Maybe there are physical reasons to favor simplicity (our universe is constructed such that simpler theories will be more likely to be true), but why should we think that the success of simplicity in the physical world is explained by the existence of a metaphysical rule in favor of simplicity which applies to cases outside our physical universe?
C) I think the reliance on infinite classes is problematic for the argument here. Infinity is especially tricky, as evidenced by cases like the measure problem and Pascal mugging. The problem with infinites in general suggests to me that the real trouble in such cases is that anthropic reasoning in ordinary cases is not equipped to handle infinites, and we need to make modifications like introducing cutoff thresholds (e.g. regularization).
Just as an example. Suppose I told you that I was an interdimensional being who had been in contact with a superintelligence that had discovered a new physical theory which predicted some staggering super-infinite class of observers but also predicted that theism was false. For simplicity, let's just say that this super-infinite class of observers was larger than Beth omega.
Now obviously you aren't going to believe me. But presumably you should assign some vanishingly small, but still finite, prior credence that what I say is true. But now given the insane posterior shift advantage that my theory, if true, would accrue over the theistic theory, it seems that you must endorse my theory.
I think what this reveals is that we simply can't naively reason on infinities in anthropic cases as we would ordinarily do; we need some cutoff value somewhere. But once we introduce a cutoff value, nothing stops the atheist from asserting that the increase in possible observers from aleph-null to Beth-2 goes beyond the cutoff, and thus does not affect the posterior shift in any way. Hence, theism need not be more probable than multiverse theory.
1. This would also seem to support the evil god hypothesis. If there's only a 1% chance that a good god would create everyone, there seems to be an equal chance that anti-nataliss are right and that there's a 1% chace of an evil god creating everyone as well.
2. This argument defeats psychophysical harmony. If God creates infinite minds, then presumably he will create many minds that are not psychophysically harmonious, and many more which cannot tell the difference. What's to say that you and I are not one of those minds? However, if God really does create every possible mind in a way that's harmonious, then it's unclear why an infinite material universe couldn't do the same. If an infinite universe cannot, why can a (logically constrained) God do so? (Actually this latter point also seems convincing. If there is "no set of all truths" in logic, why can God make one. Are you arguing for some sort of divine transcendence of logic?).
3. This argument seems to also defeat induction in the same way that modal realism does. If an infinite number of actually created minds exists, then surely there are an infinite number of minds where induction spontaniously breaks down, and everything around them turns into cantelopes.
4. One atheist account that solves this argument is to deny that there are other minds exist at all. There is only one possible mind, and it is the mind that is currently experiencing. :P
You posted this on Reddit (r/debateanathiest) and it got torn apart and thoroughly debunked. (I'm assuming, based on the fact that you didn't respond to any of the arguments, that you no answer for them)
Maybe you should revisit this terrible argument.
(And don't be so dishonest as to post on a debate forum and avoid debate)
Hi! I stumbled upon this while reading about SIA, and I'm very surprised by your assumption that truths (or sets) and minds can be put in a one-to-one correspondence:
1. There are good reasons to think that not all truths are knowable: see Fitch's paradox (https://plato.stanford.edu/entries/fitch-paradox/). It could be the case than almost all truths are unknowable and don't correspond to any mind.
2. There are numerous results in mathematics about there being only countably many objects one can reasonably think about. For example, there are only countably many computable real numbers, or definable integer sequences. Likewise, there are only countably many propositions we can express in a formal language, because their statements are finite.
Now, you might object that it doesn't mean those undefinable propositions are unthinkable of. But I don't see an argument for why they must be thinkable of either. I myself can only think of reasonably "finite" objects. I can't conceive of a mind thinking about some undefinable proposition or some weird incredibly large set.
3. Even if there are minds capable of thinking about absurdly large infinities, I don't see why there should be a one-to-one correspondence between them and all truths. It seems like you're confusing "a mind that is capable of thinking about T existing" and "a mind being in a state of thinking about T". Maybe there's some supermind that is capable of thinking of any truth, but there's only one such mind. You'd have to postulate something bizarre like possible minds that are only capable of thinking of a single particular truth for a one-to-one correspondence to exist.
Of course, this leaves other arguments about there being at least Beth 2 minds, I haven't investigated those.
If God creates all possible people, does this mean that He also creates Boltzmann Brains and Brains-In-Vats? Or are Boltzmann Brains and Brains-In-Vats only possible people when there is no God?
Consider universal reconciliation: all created people shall be saved. If universal reconciliation is true, then while we have an answer to anti-natalism, what is the answer to the question: why not procreate as much as possible even if we cannot take care of the children? Or if life begins at conception, then why not have as many abortions are possible since all created people will be saved including the aborted?
I think the anthropic argument does answer these questions. Suppose that Jane is an only child and dies a virgin. She dies having no siblings and no children. If God created all possible people, then all of Jane's brothers and sisters and children do exist and will all be saved. So we don't need to procreate as much as possible to ensure that as many souls as possible will enjoy Heaven.
Has anybody suggested the Fermi Paradox as evidence for Theism? On Naturalism, we'd expect the universe to be full of life eons older than us and there to be abundant evidence of extraterrestrials. On Theism, humans are something special and created by God outside the normal material order and we shouldn't be surprised if it's only us.
Thank You, I really enjoyed seeing a strong novel argument for the existence of God!
1. Why can’t you use the same style argument for modal realism, our world is extremely complex and seems arbitrary, if modal realism is true than we should expect a world like ours to exist, if modal realism is false than the probability of our world existing out of all possible worlds is null, so must be modal realism is correct?
2. Dose the argument still work if you use a measure of complexity to assign prior probabilities, more complex people (power set) would have a substantially lower prior probability which should significantly raise the probability of you existing. (Although I have no idea how to model the complexity of elements within an uncountable infinite set)?
God doesn't have to make all possible humans. He just has to make some humans right?
Are you saying that all the possible humans are created in this world? Or are many in a multiverse elsewhere?
Naturalist multiverse models also do the trick right? Many world's interpretation of QM would predict the data that you exist, even more than theism maybe bcz there would be multiple copies of you.
Hi Matthew, interesting flurry of writings here. I have been skimming through them, and don't find myself particularly moved in the theistic direction (I have always been agnostic leaning, but I think your agnosticism is quite different from mine).
A basic question: couldn't several of these arguments (this article and others) work if the word "God" were replaced with "creator"?
An agent can create something for a purpose. So theism doesn't require that every possible thing be created, merely that every thing that is created furthers the overall purpose.
I don't think that all humans have to be constructed. But under theism, there exists one or more agents who could choose for the humans that are constructed to form.
Apologies for the late post. But I found this argument fascinating and wanted to share my thoughts. Also sorry to see the reception you got on the reddit page. I took a peek at the comments, and they seemed especially dull and mean-spirited. Just a reminder of how much we should cherish philosophical blogs like these I suppose!
Before I get into the meat of your argument, let me make a minor quibble about your points that there is no set of possible observers (the observer reference class is greater than Beth 2):
1. As mentioned already in the comments, not all truths are knowable. So it seems dubious that truths can be put in 1-to-1 correspondence with observers.
2. This assumes that infinite minds count in the set of possible observers. But maybe it doesn't make sense to include such minds in the reference class of possible observers one can be. If so, then (assuming every mind is decomposable into a computational structure with finite parts), we won't be able to construct a diagonal proof showing that there is a mind not in the set of all possible observer-minds, since that mind would have to be describable by a real number (i.e. infinite).
Now into the meat of the argument:
A) It seems to me that there is a lacuna in your argument which has to do with the construction of one's reference class. Endorsing SIA doesn't obviate the need for constructing a reference class, since we still need to define what we think an observer is. Reasonable people can disagree about what constitutes an observer. Particularly, if we accept SIA then we accept that we should reason as if we were sampled from the reference class of all possible observers we could have been. But what constitutes an observer that "we could have been"? Maybe a physicalist might argue that an observer can only be a physical entity which is composed of some finite computational structure (related to point 2 above). It could also be argued that we should only consider ourselves to belong in the reference class of entities which could be physically constructed according to possible natural theories. If so, then hypothetical entities in the Beth 2 realm won't count as observers. And the multiverse counter still goes through.
B) It's not clear to me that atheism is incompatible with Beth 2 worlds. Just because we reject theism doesn't mean we have to accept some common naturalistic alternative (e.g. multiverse theory). Maybe there exists some metaphysical principle (e.g. simpler patterns reproduce into complex repeatable patterns) which governs the construction of worlds, and which entails that there will exist uncountably infinite number of worlds where induction is sound, and little to no worlds where induction is falsified. I don't see why our prior for such a principle must be lower than our prior for theism.
Alternatively, one could simply accept the existence of Beth-2 observers in uncountable number of worlds as a brute fact. One presumably has to endorse a brute fact at some stage (whether God or something else). So the atheist can simply say that they take on a brute fact one step sooner in the explanatory chain. Perhaps this could be retorted with appeals to simplicity (similar to Swinburne's cosmological argument), so that accepting a simpler explanation (i.e. God) as a brute fact is easier. However, I find such arguments really dubious. It's not clear to me that there are metaphysical reasons to favor simplicity. Maybe there are physical reasons to favor simplicity (our universe is constructed such that simpler theories will be more likely to be true), but why should we think that the success of simplicity in the physical world is explained by the existence of a metaphysical rule in favor of simplicity which applies to cases outside our physical universe?
C) I think the reliance on infinite classes is problematic for the argument here. Infinity is especially tricky, as evidenced by cases like the measure problem and Pascal mugging. The problem with infinites in general suggests to me that the real trouble in such cases is that anthropic reasoning in ordinary cases is not equipped to handle infinites, and we need to make modifications like introducing cutoff thresholds (e.g. regularization).
Just as an example. Suppose I told you that I was an interdimensional being who had been in contact with a superintelligence that had discovered a new physical theory which predicted some staggering super-infinite class of observers but also predicted that theism was false. For simplicity, let's just say that this super-infinite class of observers was larger than Beth omega.
Now obviously you aren't going to believe me. But presumably you should assign some vanishingly small, but still finite, prior credence that what I say is true. But now given the insane posterior shift advantage that my theory, if true, would accrue over the theistic theory, it seems that you must endorse my theory.
I think what this reveals is that we simply can't naively reason on infinities in anthropic cases as we would ordinarily do; we need some cutoff value somewhere. But once we introduce a cutoff value, nothing stops the atheist from asserting that the increase in possible observers from aleph-null to Beth-2 goes beyond the cutoff, and thus does not affect the posterior shift in any way. Hence, theism need not be more probable than multiverse theory.
1. This would also seem to support the evil god hypothesis. If there's only a 1% chance that a good god would create everyone, there seems to be an equal chance that anti-nataliss are right and that there's a 1% chace of an evil god creating everyone as well.
2. This argument defeats psychophysical harmony. If God creates infinite minds, then presumably he will create many minds that are not psychophysically harmonious, and many more which cannot tell the difference. What's to say that you and I are not one of those minds? However, if God really does create every possible mind in a way that's harmonious, then it's unclear why an infinite material universe couldn't do the same. If an infinite universe cannot, why can a (logically constrained) God do so? (Actually this latter point also seems convincing. If there is "no set of all truths" in logic, why can God make one. Are you arguing for some sort of divine transcendence of logic?).
3. This argument seems to also defeat induction in the same way that modal realism does. If an infinite number of actually created minds exists, then surely there are an infinite number of minds where induction spontaniously breaks down, and everything around them turns into cantelopes.
4. One atheist account that solves this argument is to deny that there are other minds exist at all. There is only one possible mind, and it is the mind that is currently experiencing. :P
You posted this on Reddit (r/debateanathiest) and it got torn apart and thoroughly debunked. (I'm assuming, based on the fact that you didn't respond to any of the arguments, that you no answer for them)
Maybe you should revisit this terrible argument.
(And don't be so dishonest as to post on a debate forum and avoid debate)
Hi! I stumbled upon this while reading about SIA, and I'm very surprised by your assumption that truths (or sets) and minds can be put in a one-to-one correspondence:
1. There are good reasons to think that not all truths are knowable: see Fitch's paradox (https://plato.stanford.edu/entries/fitch-paradox/). It could be the case than almost all truths are unknowable and don't correspond to any mind.
2. There are numerous results in mathematics about there being only countably many objects one can reasonably think about. For example, there are only countably many computable real numbers, or definable integer sequences. Likewise, there are only countably many propositions we can express in a formal language, because their statements are finite.
Now, you might object that it doesn't mean those undefinable propositions are unthinkable of. But I don't see an argument for why they must be thinkable of either. I myself can only think of reasonably "finite" objects. I can't conceive of a mind thinking about some undefinable proposition or some weird incredibly large set.
3. Even if there are minds capable of thinking about absurdly large infinities, I don't see why there should be a one-to-one correspondence between them and all truths. It seems like you're confusing "a mind that is capable of thinking about T existing" and "a mind being in a state of thinking about T". Maybe there's some supermind that is capable of thinking of any truth, but there's only one such mind. You'd have to postulate something bizarre like possible minds that are only capable of thinking of a single particular truth for a one-to-one correspondence to exist.
Of course, this leaves other arguments about there being at least Beth 2 minds, I haven't investigated those.
I need help with this argument.
If God creates all possible people, does this mean that He also creates Boltzmann Brains and Brains-In-Vats? Or are Boltzmann Brains and Brains-In-Vats only possible people when there is no God?
Consider universal reconciliation: all created people shall be saved. If universal reconciliation is true, then while we have an answer to anti-natalism, what is the answer to the question: why not procreate as much as possible even if we cannot take care of the children? Or if life begins at conception, then why not have as many abortions are possible since all created people will be saved including the aborted?
I think the anthropic argument does answer these questions. Suppose that Jane is an only child and dies a virgin. She dies having no siblings and no children. If God created all possible people, then all of Jane's brothers and sisters and children do exist and will all be saved. So we don't need to procreate as much as possible to ensure that as many souls as possible will enjoy Heaven.
Has anybody suggested the Fermi Paradox as evidence for Theism? On Naturalism, we'd expect the universe to be full of life eons older than us and there to be abundant evidence of extraterrestrials. On Theism, humans are something special and created by God outside the normal material order and we shouldn't be surprised if it's only us.
Thank You, I really enjoyed seeing a strong novel argument for the existence of God!
1. Why can’t you use the same style argument for modal realism, our world is extremely complex and seems arbitrary, if modal realism is true than we should expect a world like ours to exist, if modal realism is false than the probability of our world existing out of all possible worlds is null, so must be modal realism is correct?
2. Dose the argument still work if you use a measure of complexity to assign prior probabilities, more complex people (power set) would have a substantially lower prior probability which should significantly raise the probability of you existing. (Although I have no idea how to model the complexity of elements within an uncountable infinite set)?
God doesn't have to make all possible humans. He just has to make some humans right?
Are you saying that all the possible humans are created in this world? Or are many in a multiverse elsewhere?
Naturalist multiverse models also do the trick right? Many world's interpretation of QM would predict the data that you exist, even more than theism maybe bcz there would be multiple copies of you.
Hi Matthew, interesting flurry of writings here. I have been skimming through them, and don't find myself particularly moved in the theistic direction (I have always been agnostic leaning, but I think your agnosticism is quite different from mine).
A basic question: couldn't several of these arguments (this article and others) work if the word "God" were replaced with "creator"?
An agent can create something for a purpose. So theism doesn't require that every possible thing be created, merely that every thing that is created furthers the overall purpose.
I don't think that all humans have to be constructed. But under theism, there exists one or more agents who could choose for the humans that are constructed to form.