Thank you for your reply. I have try to find out, and I think problem can be solved.
First, calculations of God and multiverse is based on principles which author has covered in chapter 2.
For example, if hypothesis has large number of ad-hoc assumptions, it decrease prior probability of hypothesis because of probability of each assumptions and so on. Author has covered such principles and why should it should followed given in details.
How do we know that we should choose a simple theory rather than a complicated theory? In view of the criteria above, a theory is simple if it is based on a few assumptions, a few kinds of entities and a few properties of entities. Therefore, theory T1 is simpler than T2 if the assumptions needed in T2 is more than that in T1 or the theory T1 involves less entities or properties of entities than that of T2. Keeping other factors constant, a simpler theory means a higher prior probability of the theory because each assumption in the theory would reduce the probability. For example, a theory T has N independent assumptions A1, A2, …, AN. Then prior probability that the theory T is true is P(T|A1, A2, … , AN), which is
P(T|A1,A2, … , AN) = P(T) × ∏iP(Ai)
where P(Ai) is the probability that the ith assumption is true. A multiplication of these probabilities further decreases the prior probability P(T). Therefore, fewer assumptions make a theory more probable
Likewise author has given reasons for why other principles should applied and why it makes theory less probable or more.
Other is prior distribution of probability.
But for it, author has given why is it reasonable to assume principle of indifference in prior distribution:
This principle can be applied in cosmology to determine some relations between different fundamental constants. These relations indicate that the probabilities of getting these fundamental constants are dependent on each other. Therefore, if it is true, the Principle of Indifference may not be a good approximation to the problem. However, we still do not have enough knowledge to determine the exact probabilistic density distribution f and many of the derived distributions are highly model-dependent.115 Holder states that the measures derived from Jaynes’s principle are not unique. There is an inherent ambiguity.116
Therefore, the Principle of Indifference is the most intuitive and basic one that is based on our prior knowledge. For example, we often assign a uniform probability for a die that looks perfectly normal (even if it is loaded).117 Similarly, it is always possible that the “cosmological dice” may be loaded. However, according to our general beliefs that our universe is isotropic and homogeneous, it is reasonable for us to assume that the Principle of Indifference applies.
And if we find some new physics by which we find there is some “Super-laws” which fixes constants and values, there is also problems and it can’t solve, like of string theory which author explains:
Therefore, it has been suggested that if we can obtain the M-theory, we might be able to derive the observed fundamental constants from this “super-law” (M-theory). In other words, the values of the fundamental constants might not be contingent, but “decided” by natural laws.
However, based on the current scientific evidence, the string theory is not yet confirmed by experiment. Even for its supporting theory, the supersymmetry theory, is not favored by Large Hadron Collider experiments.262 In fact, the string theory is still developing. We do not have any idea how the fundamental constants can be derived from the string theory. According to the DN-model in scientific explanation, since the string theory does not have any empirical content to explain the observed fundamental constants,
it should not be qualified to become an explanation.
Furthermore, even if string theory is true and it really explains the fine-tuning phenomena, we still need to ask why we have such a super-law such that many physical constants are fine-tuned. It is because the super-law must involve some particular content (in specific mathematical forms) so that the physical
constants must be those observed values. In other words, the super-law should also be fine-tuned in such a way that we can get all those fine-tuned constants. Therefore, invoking super-law to explain the fine-tuning phenomena is just moving the need for explanation to an upper level. In view of this, Flew points out that “the important point is not merely that there are regularities in nature, but that these regularities are mathematically precise, universal, and tied together… The question we should ask is how nature came packaged in this fashion.”263 Also, Davis thinks that a threefold-question should be asked: “Where do the laws of physics come from? Why is that we have these laws instead of some other set? How is that we have a set of laws that drives featureless gases to life,
consciousness and intelligence?”264 It means that the existence of any precise laws definitely requires an explanation, unless we accept that the existence of the super-law is a brute fact. At least, the existence of a supernatural being might be able to provide an explanation to the existence of natural laws. We should not simply accept that the existence of the super-law is a brute fact.Besides, the initial conditions should be independent of the super-law. Therefore, the super-law cannot “control” the initial conditions such that it is fine-tuned for life. As mentioned in previous chapters, many initial conditions are fine-tuned for the existence of life. Lewis had already pointed out that natural laws are more or less like the rule of addition.265 Natural laws tell you that if you save $1,000 a month, you will
have $3,000 after three months. Natural laws cannot guarantee you have $3,000 in the bank if you did not deposit any money. The actions (put money into the bank) together with the laws (addition rule) enableyour money to accumulate correctly.266 Similarly, initial conditions together with natural laws enable our universe to be created.267 All the natural laws require initial conditions such as specifying the initial entropy, the initial (primordial) quantum fluctuations, and the initial inflation field. Natural laws, including the string theory, cannot generate these conditions. Therefore, the explanation of the fine-tuned constants and conditions cannot be addressed by natural super-law itself. Science can only push this problem to a more fundamental level, but can never fully address this issue. In fact, it is quite easy for us to confuse the terms “cause” and “agency”. Natural laws can tell you the cause of an event, given that all initial conditions are known. However, natural laws will not tell you who or what makes the laws (the agency).268 For example, natural laws can tell you how a steam engine works, but not who makes the steam engine.269 Similarly, natural laws can only tell you “how” but not “who” or “why”.270 Therefore, it is hopeless to invoke natural laws to explain the fine-tuned fundamental constants and conditions.
And statement author has given for which he also gives reason which seems reasonable for why it should be:
However, the massive meteorite impact that makes dinosaurs extinct occurred at a right time with a right amount of power. If it is somewhat larger in power, all organisms in the Earth might be dead. If the power is much smaller, the extinction would not be occurred and human beings would not be able to appear. In fact, statistics show that the frequency of meteorite impact is dependent on the size (power) of the meteorite.
And if inflation doesn’t solve problem, fine tuning and other remains, which won’t affect conclusion of author:
To conclude, the existence of stars and anthropic elements are highly dependent on the 5 fine-tuned values N, ε, Ω, λ and Q (and also the dimension D). If one of the parameters change slightly, says, 10 times larger, no life would exist.