>There is nothing within the definition of coherence which makes it impossible for two entirely different sets of beliefs to be internally coherent. Thus there might be several such sets. But if one supposes—in line with the principle of non-contradiction—that there can only be one complete set of truths, coherentism must provide a way to choose between these competing sets.

Yes and no. This only implies that we cannot know what is ultimately true (in absolute sense). This should be obvious in analogy to the halting problem in computability theory and Gödel's incompleteness theorems of mathematical logic (which again are all proven). The choice between two equally coherent beliefs is arbitrary. However, one theory is in practise always more coherent than others and even if they are on exactly equal footing, their current utility is equal and optimal so no problem exists.

Furthermore, the scale of required coherence expands as our experiences of the world keep growing so the coherence of our best theories converges towards the most coherent theory and theories incoherent with our experiences must be dropped out. The principle of non-contradiction applies, but coherentism has no need to provide a way to choose between two equally strong competing sets as the precise truth is unobtainable, yet coherentism allows an optimal way to approach this truth and provides a way to choose between unevenly matched theories.

https://en.wikipedia.org/wiki/Coherentism

https://en.wikipedia.org/wiki/Halting_problem

https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems

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The question as to why the Universe exists cannot be answered by "god" or "quantum fluctuations" because both of them are at most only parts of the Universe (which encapsulates everything). The explanation for the existence of the Universe must by nature be such that it leaves no references to any unexplained phenomena.