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Now you're starting to understand, except you think it can be solved by simply allowing t=0 to stretch back indefinitely.Well then how do you define time? If there was a point from which there wasn't past, then time was created at a point, and it didn't exist earlier. But it was created at the point...In time again. Because if we say:
We again use the word "earlier" and with the word before we mean before in time. So if we look at the new time we've got it has to have a beggining too,a point at which it had not existed earlier. And then we go in never ending loops, which again point to some kind of infinity.
So let me ask a related question: even if it were infinite, what caused this infinite sequence of time to exist? Why does something exist instead of nothing? Clearly there can't be a cause that something exists instead of nothing, because a cause is something, and that would be a circular reference to something existing.
You can push causes back, but you can never push them back far enough. There must be at least one uncaused thing, and that thing would by definition be truly unpredictable, and therefore at least one truly random event exists.