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- Given fine-tuning and our existence, can we make the hypothesis plausible that there are more universes?

Dear all,

I'm reading up on Bayesian inference, and recently read some papers about the fine-tuning argument (FTA) again. I'm not that interested in the details of this fine-tuning, or details of the multiverse. My question concerns Bayesian inference. I'll make an analogy about habitable planets. The scenario is the following.

Say, you are a Middle-Aged monk with revolutionary ideas (say, Giordano Bruno), and you understand that in order to get life as we know it on earth the conditions must be very special. Of all the imaginable planets which could form, it is a priori quite improbable that a life-sustaining planet like Earth will form. Our existence does surprise you. But you haven't observed other planetary systems yet.

The first naive answer would be: yes, because given more planets the expectation value of number of habitable planets increases.

At a second thought, you think about the inverse gamber's fallacy (https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy): if you see an improbable event like 5 dices which are thrown, given you 5 sixes, you cannot statistically infer that there have been many throwns before your arrival. This can be easily shown by Bayes' formula.

At a third thought, you realize that there is no way you could observe a planet which is not habitable. This condition "selects observers", and is also known as the anthropic principle. How does this influence the probability? Shouldn't we make a distinction between the events ''there is a habitable planet'' and '' there is a habitable planet and I happen to live on it?''

So what do you think? Can our hypothetical Bruno make the inference? If so, why and under which conditions? If not, why not?

For those who are interested, here are some papers:

https://arxiv.org/abs/1505.05359?context=physics

http://philsci-archive.pitt.edu/16785/

https://philpapers.org/rec/WHIFAM

I'm reading up on Bayesian inference, and recently read some papers about the fine-tuning argument (FTA) again. I'm not that interested in the details of this fine-tuning, or details of the multiverse. My question concerns Bayesian inference. I'll make an analogy about habitable planets. The scenario is the following.

Say, you are a Middle-Aged monk with revolutionary ideas (say, Giordano Bruno), and you understand that in order to get life as we know it on earth the conditions must be very special. Of all the imaginable planets which could form, it is a priori quite improbable that a life-sustaining planet like Earth will form. Our existence does surprise you. But you haven't observed other planetary systems yet.

**Given that you exist, and given the fine tuning, can you infer that there probably are a lot more planets outside our solar system such that the existence of Earth becomes more probable?**The first naive answer would be: yes, because given more planets the expectation value of number of habitable planets increases.

At a second thought, you think about the inverse gamber's fallacy (https://en.wikipedia.org/wiki/Inverse_gambler's_fallacy): if you see an improbable event like 5 dices which are thrown, given you 5 sixes, you cannot statistically infer that there have been many throwns before your arrival. This can be easily shown by Bayes' formula.

At a third thought, you realize that there is no way you could observe a planet which is not habitable. This condition "selects observers", and is also known as the anthropic principle. How does this influence the probability? Shouldn't we make a distinction between the events ''there is a habitable planet'' and '' there is a habitable planet and I happen to live on it?''

So what do you think? Can our hypothetical Bruno make the inference? If so, why and under which conditions? If not, why not?

For those who are interested, here are some papers:

https://arxiv.org/abs/1505.05359?context=physics

http://philsci-archive.pitt.edu/16785/

https://philpapers.org/rec/WHIFAM