Belief in God is rational. Everything has a cause. So unless there is a first cause, then you would have an infinite regress. And then nothing could exist. Therefore there must be a first cause. Therefore God, the first cause, exists. QED.
5.2.25
I have noticed that few people pay much attention to the herem of the Gra. [that is the second letter of excommunication that bears the signature of the Gra on the top of the page]. I have thought that the reason is that people do not think it was valid. But the odd thing about this is that whether the person that has a letter of excommunication pronounced on him by a legitimate authority, can claim it is illegitimate without grounds. After all, time has shown that the Gra knew a lot more about this than people thought at the time.
[However, I do feel that Rav Nahman of Breslov was a true Tzadik, and that in strict legal terms would not have been included in the herem] The significance of the herem of the Gra is great. It means that what people think are good deeds are not, because they violate the herem. For example, learning torah is a mitzvah. However, a person in herem is not allowed in this—neither learning nor teaching. Thus the very value of the mitzvah is nullified and instead becomes a wrong.} And I think here i might mention that Rav Nahman himself did not hold with learning science or philosophy, but in this particular instance I think to go with the Gra, Ibn Pakuda (author of the Obligations of the hearts) and Rambam. This is an old argument and I quote a famous statement of the Talmud about arguments between the sages:"These and these are the words of the living God".[And I admit the flaws today-if I had been able to just sit and learn Torah I would have done so happily but somehow the obstacles got to be too great for me to handle. so, I went into Physics for the sake of making a living, but still, I try to learn Torah as much as I can]