the claim: "for life to be possible, certain of the fundamental constants of physics had to have values falling in a certain narrow range."
what is the empirical motivation for the phrasing of values "falling in a certain narrow range"? do you have any evidence to motivate that values 'fall' into a range from some other, different range, or that there was a prior state of undetermined potential from which certain values spring forth from potentiality into actuality? do you have any empirical evidence that said values are contingent?
if not, i just don't grasp what motivates creating the explanandum, but my credence is high that it's not some idyllic, neutral following "the" evidence wherever it leads.
Physics has ascertained that there are certain "fundamental constants" of the universe like the charge on an electron, the gravitational constant, Planck's Constant, Speed of light in vacuum, etc etc. Various calculations have been done to model the universe with different values of these constants and if you vary any of them significantly you don't get a universe we could live in. Thus their present values are remarkable and this needs explanation. (It doesn't matter whether they CAN vary, or have varied in the past, we still have to explain why they happen to be "just right".)
i don't understand the inference from finding that x numbers are exactly what they are in our current best theories, to "present values are remarkable and this needs explanation". how are you motivating the inference that there is a legitimate explanandum here?
it does too matter whether they can vary or have varied in the past, because if they cannot, then in fact speculation about non-actual universes with different values are moot. why would i care that you can imagine a universe with cows that can hover just 47 cm above the ground for 46 minutes each leap year's final day? that doesn't motivate the conjecture that this is any more or less remarkable as any other configuration of what exists. it seems to me that you're relying on your vibes about what seems 'remarkable' and 'needing explanation'.
The point is that it's a remarkable coincidence that the values are just right for us to be here and remark upon it. If the values were slightly different the universe would be empty, not exist at all, or adopt some other configuration that is so completely unlike this that we couldn't survive in it.
Yes, the assumption is that all configurations are equally likely/unlikely so that the fact we happen to get the one we need is a cosmic stroke of good luck.
If you quote Steven J. Gould: "life will find a way" you're basically saying that life has no prerequisites. There's a glass of water on my desk, it's been there 15 minutes and there are no fish in it, so life clearly does have prerequisites.
"The point is that it's a remarkable coincidence that the values are just right for us to be here and remark upon it"
Thats not a coincidence. I buy a ticket on a plane, I show up to board and hey, theres a seat open for me. Is that a coincidence or is that the reason I showed up in the first place? If i can't get a seat on the plane, i'm no going to show up for boarding now am I?
If various universal constants were of different value such that life could not evolve, we could never be there to observe it. The only universes observable by life are those with constants amenable to life existing. Thats not fine tuning, thats sampling bias
Exactly, that's sampling bias, but "sampling" implies all the other universes exist too (otherwise it would be "it's got to be like this" and there would be no sampling going on). But it's not until we examine the physics that we realise the values are fine-tuned for life, which suggests a multiverse, then sampling bias can operate. (FWIW the fine-tuning is tighter than 1 part in 10 power 100)
Since my original posting I've read Tegmark's "Our mathematical universe : my quest for the ultimate nature of reality" and this explains it all and gives the background in "proper physics".
"but "sampling" implies all the other universes exist too" no it doens't. We can only observe out own universe, a universe in which life evolved so yeah, that universe will in fact be capable of supporting life
"But it's not until we examine the physics that we realize the values are fine-tuned for life, which suggests a multiverse" yeah thats not at all how that works.
"the fine-tuning is tighter than 1 part in 10 power 100" citation needed
that's a hubristic assumption. unless you offer some empirical motivation as to why on earth we'd assume uniform probability distributions, let alone use probability theory at all, all you've done is assert based on vibes that there's some underspecified 'remarkable coincidence' going on.
"the fact we happen to get the one we need is a cosmic stroke of good luck." you're begging the question. what luck are you talking about? let's do a thought experiment. there is a tabby cat. you say that that particular tabby cat could've been black or any other color, and that it is in fact tabby, is a remarkable cosmic stroke of good luck. what evidence are you using to support the conjecture that this particular cat, which is actually a tabby cat, could've been black or any other way?
you only have a sample size of one; reality is the same, insofar as you are claiming that there are more than distinct, separate realities. you referring to speculative/logical/epistemic possibilities based on all the other cats in existence doesn't tell you anything about why, how, or whether this particular tabby cat could in fact have been otherwise. the only datum you have is the actual tabby cat. to say that this tabby cat could've been black is to say that this tabby cat could have been not this tabby cat.
I'll ignore the tabby cat cos that would just be attacking your analogy.
In the absence of any evidence to the contrary we have to assume they are roughly equally probable. If the values that support life are vastly more probable, then that in itself is remarkable and needs explanation.
Either there is only one possible universe and then it's a remarkable coincidence that, of all the possible values that those parameters might theoretically have had, they happen to all be in the range we need,
OR
there are multiple universes with different sets of values and we have arisen in one that can give rise to us. This is much less remarkable.
no, if necessitarianism is true, then it's simply ill-posed/meaningless to say things like 'remarkable coincidence'. what coincided??? that the only possible thing happened is just that. if necessitarianism is true, there is no such thing as "all the possible values that those parameters might theoretically have had". it isn't relevant that you can imagine varying some details of a theoretical model, says nothing whatsoever about metaphysical possibility. the phrasing 'happen to be' in a necessitarian reality is meaningless, because it couldn't have 'happened' to be otherwise. only the actual is possible, there's no 'happening' from virtual potential into actuality or whatever magical unempirical notion.
"In the absence of any evidence to the contrary we have to assume they are roughly equally probable. If the values that support life are vastly more probable, then that in itself is remarkable and needs explanation."
why would we use probability theory here? you've got a sample size of one with reality. it's only entirely unempirical & infinitely variable speculation that there were something like a series of trials or different metaphysical possibilities for x to be otherwise than x actually is. i don't understand how considerations like logical, epistemic possibility and conceivability are relevant in making inferences about what in fact could have been, is, or will be the case.
It's made more complicated by the fact that we don't know if the current fundamental constants, really are fundamental, or whether there are dependencies between them that only a more comprehensive theory can uncover.
Perhaps the universe is fine tuned by being based on a four dimensional manifold with one dimension of an opposite sign. Symmetries within this form are the physical conservation laws (Noether). Quantum physics falls out of de Broglie's original analysis. We would expect that such a geometrical form would host conscious observers which is why it is the universe we inhabit.
Of course this gets sticky if we move beyond Special Relativity but its an approximation.
If consciousness or conscious entities "produce the mathematical structures of physics" (Goff 2023 127), then one would expect that such entities (us, for example) necessarily would see in the "constants" of physics mathematics that at a minimum made such entities possible. This is not a point of crass "anthropic" bootstrapping (cf. id. 31, 36-37) or support the equally crass "inverse anthropic principle." "Fine-tuning's" a wash. An ad hominem addendum: Someone noted, possibly Goff himself, that fine-tuning actually gave Hitchens, one of the four "horsemen" of "new atheism," pause (or possibly hooves). (I always thought that the better name for that group would have the "three horseman and one horse's ass," as a nod to Harris.)
The vast majority of time and space is inhospitable to living things. Even when life takes hold, most organisms struggle for mere survival or die before even maturing to adulthood. Life is fragile and weak while the universe is brutal and unconcerned with living things. I think if the universe were "Fine-Tuned" for life then life would survive well and most of time & space would be filled with life. I think most versions of the fine tuning arguments are based on a religious perspective trying to justify how a "fine-tuner" must exist when the universe evidence indicates that the majority of time and space have nothing at all to do with living things. The real science denial comes from people arguing that consciousness preceeded the big bang and the evolution of life. That's real science denial.
But chance is likely to create more universes that aren't quite perfect for life. Way down the probabilty scale there would be a universe which was itself a single intelligent entity you might call it God. So if all possible universes exist, so does God, but if only a huge number exist, there probably isn't. And of course if one god exists so do an infinite number.
Even if you do accept that only a very narrow range of the constants can allow for our type of Life, we still have no idea what other universes might give rise to. It may be the very different types of Life can exist and be even more prevalent for different values of these constants.
The idea takes one's own existence as a single random sample. By the Copernican Principle (Doctrine of Mediocrity) we would expect our sample to be banal.
This means you're a fairly ordinary example of an intelligence inhabiting an intelligence-supporting universe. You're more likely to be a member of a populous species, more likely to be in a universe that supports more intelligences, more likely to be in a universe that itself is more likely.
Depending on the shape of the distribution of abundance of intelligence across all the universes (something we can neither estimate nor measure), it may be that most intelligences find themselves in universes where intelligence is abundant, or it may be that most intelligences are in universes with many fewer intelligences. It may even be that intelligence is so unusual that you find yourself in a universe that needed the ramifications of the quantum multiverse to produce intelligence.
So yes, there may be other universes where intelligence is more abundant, but if it's vastly more abundant then that universe is probably more unlikely, otherwise you have to explain why you find yourself in this universe and not that one.
Hey Philip, I couldn't put this on Twitter because of message limitations. This is definitely more of a Substack conversation.
What is the relationship between Shannon information theory and Bayes Theorem? Both of them deal with updates in beliefs given new information. I ran this through Claude 3 and got an interesting answer:
The relationship between Bayes Theorem and Shannon Information Theory is non-monotonic. To demonstrate the non-monotonic relationship between Bayes' Theorem and Shannon entropy and how it poses a problem for Goff's argument, let's consider a simplified version of the fine-tuning problem.
Suppose we have two hypotheses:
H₁: The universe is fine-tuned for life by a creator or teleological laws.
H₂: The universe is not fine-tuned, and life emerged by chance.
Let's assign prior probabilities P(H₁) = p and P(H₂) = 1 - p, where p is a small value, reflecting the initial skepticism towards fine-tuning.
Now, consider the evidence E: The universe appears to be fine-tuned for life.
We'll assign conditional probabilities:
P(E|H₁) = q₁ (high, as fine-tuning is expected under H₁)
P(E|H₂) = q₂ (low, as fine-tuning is unlikely under H₂)
Using Bayes' Theorem, we can calculate the posterior probabilities:
P(H₁|E) = (P(E|H₁) × P(H₁)) / P(E)
P(H₂|E) = (P(E|H₂) × P(H₂)) / P(E)
where P(E) = P(E|H₁) × P(H₁) + P(E|H₂) × P(H₂).
Now, let's calculate the Shannon entropy of the prior distribution H(H) and the posterior distribution H(H|E) for different values of p:
For p = 0.001, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.0114
H(H|E) ≈ 0.0808
For p = 0.01, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.0808
H(H|E) ≈ 0.2048
For p = 0.1, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.4690
H(H|E) ≈ 0.2048
Analyzing these results:
As the prior probability p increases, the prior entropy H(H) increases, reflecting more initial uncertainty about the hypotheses.
The posterior entropy H(H|E) is lower than the prior entropy for small values of p, indicating that the evidence reduces uncertainty when the prior probability of fine-tuning is low.
However, as p increases, the posterior entropy H(H|E) does not always decrease monotonically. In this example, it increases from p = 0.001 to p = 0.01 and then decreases for p = 0.1.
This non-monotonic relationship between the prior probability and the posterior entropy highlights the complexity of the interplay between Bayes' Theorem and Shannon entropy. It shows that the reduction in uncertainty due to evidence depends on the initial prior probabilities in a non-trivial way.
In the context of Goff's argument, this non-monotonic relationship suggests that the strength of the fine-tuning evidence in reducing uncertainty about the existence of a creator or teleological laws may not be as straightforward as claimed. The impact of the evidence on the posterior probabilities and the resulting reduction in uncertainty can vary depending on the initial prior probabilities assigned to the hypotheses.
This analysis demonstrates that the relationship between Bayes' Theorem and Shannon entropy is complex and non-monotonic, which poses challenges for arguments that rely on straightforward applications of Bayesian reasoning to support conclusions about fine-tuning and the existence of a creator or teleological laws.
Basically, if God is a viable solution, then there never was a fine tuning problem in first place.
It's not surprising that the physical structures in our universe allow for the existance of complex mental life because complex mental life doesn't require any physical structure.
God, angels, souls etc. are all non-physical minds that have complex mental life. So if these things are possible, matter is not necessary for us to have the kind of experience we have.
Why is not about non-physical minds tuning the laws of physics, so it escapes this argument. But I guess fine tuning, as described in Why, can still fall prey to the 'electrons in love' argument, also in the article, that posits that, for all that we know about the psychophysical laws in this specific world, it's still possible for electrons to have complex mental lives.
Eternal life for any god who is all-knowing gets old very quickly. And if he's also "good" he has no choice but always to do the best. So he'd be looking for a way out. Why not create matter-based life forms that have finite lives where they are not in complete control and never know what to expect, and then inhabit their brains?
What I'm saying is that we can't know a god's motivations. (Tho I can't understand why it would even have motivations)
Could the constants just be a brute fact, such that they are derived from observations that are in the only possible one reality?
For example if the constant pi in geometry could have different values there would be universes with different geometric realities. Perhaps not the best analogy but the ratio of diameter to circumference seems a brute fact in a similar way.
I’m probably hopelessly confused and can’t possibly be right in the face of such giants of the physics.
If the constants happen to be absolute fact you're still left with the unbelievable coincidence that their values all happen to be the ones that support life.
re pi: my personal view is that there may well be universes where pi has other values but the geometry in those universes is corrupted so causality never arises from quantum mechanics, if they even get that far.
Don't forget pi isn't just circumference/diameter there are also mathematical formulae.
no no, conjecturing that it's just a brute fact is far more plausible than speculating that it's somehow linked to 'cosmic purpose', stance-independent values and vibes like that. philip presents no evidence motivating the suggestion that any constant's value is contingent.
physics experts can agree all they want in terms of the conclusions of their counterfactual speculation, eg. were certain values of constants different, x, y, z microstates wouldn't occur. but this doesn't even remotely motivate problematizing the values the way philip does.
the claim: "for life to be possible, certain of the fundamental constants of physics had to have values falling in a certain narrow range."
what is the empirical motivation for the phrasing of values "falling in a certain narrow range"? do you have any evidence to motivate that values 'fall' into a range from some other, different range, or that there was a prior state of undetermined potential from which certain values spring forth from potentiality into actuality? do you have any empirical evidence that said values are contingent?
if not, i just don't grasp what motivates creating the explanandum, but my credence is high that it's not some idyllic, neutral following "the" evidence wherever it leads.
Physics has ascertained that there are certain "fundamental constants" of the universe like the charge on an electron, the gravitational constant, Planck's Constant, Speed of light in vacuum, etc etc. Various calculations have been done to model the universe with different values of these constants and if you vary any of them significantly you don't get a universe we could live in. Thus their present values are remarkable and this needs explanation. (It doesn't matter whether they CAN vary, or have varied in the past, we still have to explain why they happen to be "just right".)
i don't understand the inference from finding that x numbers are exactly what they are in our current best theories, to "present values are remarkable and this needs explanation". how are you motivating the inference that there is a legitimate explanandum here?
it does too matter whether they can vary or have varied in the past, because if they cannot, then in fact speculation about non-actual universes with different values are moot. why would i care that you can imagine a universe with cows that can hover just 47 cm above the ground for 46 minutes each leap year's final day? that doesn't motivate the conjecture that this is any more or less remarkable as any other configuration of what exists. it seems to me that you're relying on your vibes about what seems 'remarkable' and 'needing explanation'.
The point is that it's a remarkable coincidence that the values are just right for us to be here and remark upon it. If the values were slightly different the universe would be empty, not exist at all, or adopt some other configuration that is so completely unlike this that we couldn't survive in it.
Yes, the assumption is that all configurations are equally likely/unlikely so that the fact we happen to get the one we need is a cosmic stroke of good luck.
If you quote Steven J. Gould: "life will find a way" you're basically saying that life has no prerequisites. There's a glass of water on my desk, it's been there 15 minutes and there are no fish in it, so life clearly does have prerequisites.
"The point is that it's a remarkable coincidence that the values are just right for us to be here and remark upon it"
Thats not a coincidence. I buy a ticket on a plane, I show up to board and hey, theres a seat open for me. Is that a coincidence or is that the reason I showed up in the first place? If i can't get a seat on the plane, i'm no going to show up for boarding now am I?
If various universal constants were of different value such that life could not evolve, we could never be there to observe it. The only universes observable by life are those with constants amenable to life existing. Thats not fine tuning, thats sampling bias
Exactly, that's sampling bias, but "sampling" implies all the other universes exist too (otherwise it would be "it's got to be like this" and there would be no sampling going on). But it's not until we examine the physics that we realise the values are fine-tuned for life, which suggests a multiverse, then sampling bias can operate. (FWIW the fine-tuning is tighter than 1 part in 10 power 100)
Since my original posting I've read Tegmark's "Our mathematical universe : my quest for the ultimate nature of reality" and this explains it all and gives the background in "proper physics".
"but "sampling" implies all the other universes exist too" no it doens't. We can only observe out own universe, a universe in which life evolved so yeah, that universe will in fact be capable of supporting life
"But it's not until we examine the physics that we realize the values are fine-tuned for life, which suggests a multiverse" yeah thats not at all how that works.
"the fine-tuning is tighter than 1 part in 10 power 100" citation needed
that's a hubristic assumption. unless you offer some empirical motivation as to why on earth we'd assume uniform probability distributions, let alone use probability theory at all, all you've done is assert based on vibes that there's some underspecified 'remarkable coincidence' going on.
"the fact we happen to get the one we need is a cosmic stroke of good luck." you're begging the question. what luck are you talking about? let's do a thought experiment. there is a tabby cat. you say that that particular tabby cat could've been black or any other color, and that it is in fact tabby, is a remarkable cosmic stroke of good luck. what evidence are you using to support the conjecture that this particular cat, which is actually a tabby cat, could've been black or any other way?
you only have a sample size of one; reality is the same, insofar as you are claiming that there are more than distinct, separate realities. you referring to speculative/logical/epistemic possibilities based on all the other cats in existence doesn't tell you anything about why, how, or whether this particular tabby cat could in fact have been otherwise. the only datum you have is the actual tabby cat. to say that this tabby cat could've been black is to say that this tabby cat could have been not this tabby cat.
I'll ignore the tabby cat cos that would just be attacking your analogy.
In the absence of any evidence to the contrary we have to assume they are roughly equally probable. If the values that support life are vastly more probable, then that in itself is remarkable and needs explanation.
Either there is only one possible universe and then it's a remarkable coincidence that, of all the possible values that those parameters might theoretically have had, they happen to all be in the range we need,
OR
there are multiple universes with different sets of values and we have arisen in one that can give rise to us. This is much less remarkable.
no, if necessitarianism is true, then it's simply ill-posed/meaningless to say things like 'remarkable coincidence'. what coincided??? that the only possible thing happened is just that. if necessitarianism is true, there is no such thing as "all the possible values that those parameters might theoretically have had". it isn't relevant that you can imagine varying some details of a theoretical model, says nothing whatsoever about metaphysical possibility. the phrasing 'happen to be' in a necessitarian reality is meaningless, because it couldn't have 'happened' to be otherwise. only the actual is possible, there's no 'happening' from virtual potential into actuality or whatever magical unempirical notion.
"In the absence of any evidence to the contrary we have to assume they are roughly equally probable. If the values that support life are vastly more probable, then that in itself is remarkable and needs explanation."
why would we use probability theory here? you've got a sample size of one with reality. it's only entirely unempirical & infinitely variable speculation that there were something like a series of trials or different metaphysical possibilities for x to be otherwise than x actually is. i don't understand how considerations like logical, epistemic possibility and conceivability are relevant in making inferences about what in fact could have been, is, or will be the case.
It's made more complicated by the fact that we don't know if the current fundamental constants, really are fundamental, or whether there are dependencies between them that only a more comprehensive theory can uncover.
That doesn't change the argument that the values they have adopted are suspiciously convenient for us. You're just kicking the can down the road.
Perhaps the universe is fine tuned by being based on a four dimensional manifold with one dimension of an opposite sign. Symmetries within this form are the physical conservation laws (Noether). Quantum physics falls out of de Broglie's original analysis. We would expect that such a geometrical form would host conscious observers which is why it is the universe we inhabit.
Of course this gets sticky if we move beyond Special Relativity but its an approximation.
If consciousness or conscious entities "produce the mathematical structures of physics" (Goff 2023 127), then one would expect that such entities (us, for example) necessarily would see in the "constants" of physics mathematics that at a minimum made such entities possible. This is not a point of crass "anthropic" bootstrapping (cf. id. 31, 36-37) or support the equally crass "inverse anthropic principle." "Fine-tuning's" a wash. An ad hominem addendum: Someone noted, possibly Goff himself, that fine-tuning actually gave Hitchens, one of the four "horsemen" of "new atheism," pause (or possibly hooves). (I always thought that the better name for that group would have the "three horseman and one horse's ass," as a nod to Harris.)
The vast majority of time and space is inhospitable to living things. Even when life takes hold, most organisms struggle for mere survival or die before even maturing to adulthood. Life is fragile and weak while the universe is brutal and unconcerned with living things. I think if the universe were "Fine-Tuned" for life then life would survive well and most of time & space would be filled with life. I think most versions of the fine tuning arguments are based on a religious perspective trying to justify how a "fine-tuner" must exist when the universe evidence indicates that the majority of time and space have nothing at all to do with living things. The real science denial comes from people arguing that consciousness preceeded the big bang and the evolution of life. That's real science denial.
https://philosophicalrebellion.substack.com/p/the-universe-is-not-fine-tuned-for
But chance is likely to create more universes that aren't quite perfect for life. Way down the probabilty scale there would be a universe which was itself a single intelligent entity you might call it God. So if all possible universes exist, so does God, but if only a huge number exist, there probably isn't. And of course if one god exists so do an infinite number.
Even if you do accept that only a very narrow range of the constants can allow for our type of Life, we still have no idea what other universes might give rise to. It may be the very different types of Life can exist and be even more prevalent for different values of these constants.
The idea takes one's own existence as a single random sample. By the Copernican Principle (Doctrine of Mediocrity) we would expect our sample to be banal.
This means you're a fairly ordinary example of an intelligence inhabiting an intelligence-supporting universe. You're more likely to be a member of a populous species, more likely to be in a universe that supports more intelligences, more likely to be in a universe that itself is more likely.
Depending on the shape of the distribution of abundance of intelligence across all the universes (something we can neither estimate nor measure), it may be that most intelligences find themselves in universes where intelligence is abundant, or it may be that most intelligences are in universes with many fewer intelligences. It may even be that intelligence is so unusual that you find yourself in a universe that needed the ramifications of the quantum multiverse to produce intelligence.
So yes, there may be other universes where intelligence is more abundant, but if it's vastly more abundant then that universe is probably more unlikely, otherwise you have to explain why you find yourself in this universe and not that one.
Hey Philip, I couldn't put this on Twitter because of message limitations. This is definitely more of a Substack conversation.
What is the relationship between Shannon information theory and Bayes Theorem? Both of them deal with updates in beliefs given new information. I ran this through Claude 3 and got an interesting answer:
The relationship between Bayes Theorem and Shannon Information Theory is non-monotonic. To demonstrate the non-monotonic relationship between Bayes' Theorem and Shannon entropy and how it poses a problem for Goff's argument, let's consider a simplified version of the fine-tuning problem.
Suppose we have two hypotheses:
H₁: The universe is fine-tuned for life by a creator or teleological laws.
H₂: The universe is not fine-tuned, and life emerged by chance.
Let's assign prior probabilities P(H₁) = p and P(H₂) = 1 - p, where p is a small value, reflecting the initial skepticism towards fine-tuning.
Now, consider the evidence E: The universe appears to be fine-tuned for life.
We'll assign conditional probabilities:
P(E|H₁) = q₁ (high, as fine-tuning is expected under H₁)
P(E|H₂) = q₂ (low, as fine-tuning is unlikely under H₂)
Using Bayes' Theorem, we can calculate the posterior probabilities:
P(H₁|E) = (P(E|H₁) × P(H₁)) / P(E)
P(H₂|E) = (P(E|H₂) × P(H₂)) / P(E)
where P(E) = P(E|H₁) × P(H₁) + P(E|H₂) × P(H₂).
Now, let's calculate the Shannon entropy of the prior distribution H(H) and the posterior distribution H(H|E) for different values of p:
For p = 0.001, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.0114
H(H|E) ≈ 0.0808
For p = 0.01, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.0808
H(H|E) ≈ 0.2048
For p = 0.1, q₁ = 0.99, q₂ = 0.01:
H(H) ≈ 0.4690
H(H|E) ≈ 0.2048
Analyzing these results:
As the prior probability p increases, the prior entropy H(H) increases, reflecting more initial uncertainty about the hypotheses.
The posterior entropy H(H|E) is lower than the prior entropy for small values of p, indicating that the evidence reduces uncertainty when the prior probability of fine-tuning is low.
However, as p increases, the posterior entropy H(H|E) does not always decrease monotonically. In this example, it increases from p = 0.001 to p = 0.01 and then decreases for p = 0.1.
This non-monotonic relationship between the prior probability and the posterior entropy highlights the complexity of the interplay between Bayes' Theorem and Shannon entropy. It shows that the reduction in uncertainty due to evidence depends on the initial prior probabilities in a non-trivial way.
In the context of Goff's argument, this non-monotonic relationship suggests that the strength of the fine-tuning evidence in reducing uncertainty about the existence of a creator or teleological laws may not be as straightforward as claimed. The impact of the evidence on the posterior probabilities and the resulting reduction in uncertainty can vary depending on the initial prior probabilities assigned to the hypotheses.
This analysis demonstrates that the relationship between Bayes' Theorem and Shannon entropy is complex and non-monotonic, which poses challenges for arguments that rely on straightforward applications of Bayesian reasoning to support conclusions about fine-tuning and the existence of a creator or teleological laws.
It may be non-monotonic, but it certainly is monotonous.
I read Why. Cool book.
Neil Sinhababu has a great refutation for God as a solution to the Fine Tuning Argument: https://philpapers.org/archive/SINFAP.pdf
Basically, if God is a viable solution, then there never was a fine tuning problem in first place.
It's not surprising that the physical structures in our universe allow for the existance of complex mental life because complex mental life doesn't require any physical structure.
God, angels, souls etc. are all non-physical minds that have complex mental life. So if these things are possible, matter is not necessary for us to have the kind of experience we have.
Why is not about non-physical minds tuning the laws of physics, so it escapes this argument. But I guess fine tuning, as described in Why, can still fall prey to the 'electrons in love' argument, also in the article, that posits that, for all that we know about the psychophysical laws in this specific world, it's still possible for electrons to have complex mental lives.
But, of course, there is evidence for fine tuning!
Just not conclusive evidence. But still persuasive evidence.
Eternal life for any god who is all-knowing gets old very quickly. And if he's also "good" he has no choice but always to do the best. So he'd be looking for a way out. Why not create matter-based life forms that have finite lives where they are not in complete control and never know what to expect, and then inhabit their brains?
What I'm saying is that we can't know a god's motivations. (Tho I can't understand why it would even have motivations)
I notice he starts off with God but by the second page He's become "a good God".
Could the constants just be a brute fact, such that they are derived from observations that are in the only possible one reality?
For example if the constant pi in geometry could have different values there would be universes with different geometric realities. Perhaps not the best analogy but the ratio of diameter to circumference seems a brute fact in a similar way.
I’m probably hopelessly confused and can’t possibly be right in the face of such giants of the physics.
Loving the book though.
If the constants happen to be absolute fact you're still left with the unbelievable coincidence that their values all happen to be the ones that support life.
re pi: my personal view is that there may well be universes where pi has other values but the geometry in those universes is corrupted so causality never arises from quantum mechanics, if they even get that far.
Don't forget pi isn't just circumference/diameter there are also mathematical formulae.
no no, conjecturing that it's just a brute fact is far more plausible than speculating that it's somehow linked to 'cosmic purpose', stance-independent values and vibes like that. philip presents no evidence motivating the suggestion that any constant's value is contingent.
physics experts can agree all they want in terms of the conclusions of their counterfactual speculation, eg. were certain values of constants different, x, y, z microstates wouldn't occur. but this doesn't even remotely motivate problematizing the values the way philip does.