JohnScott
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Jarle said:"Assume time has no beginning, but that it has existed for an infinitely long time back.
Then it would have taken an infinite amount of time until this moment.
As an infinite amount of time will never end, this moment could never have occurred,
and hence time cannot be infinite - it must have a beginning." (This is not quoted from anywhere)
I believe this argument is flawed, because there exist no point on the time line such that there is a period of infinite length between that and this moment. Hence the second sentence of the argument uses a period of time that measures the time between this moment, and a moment that does not exist. And that is my reason why I believe the argument is wrong. However, I am not saying I am absolutely sure about the error I have found.
I agree with you that the argument is flawed, and for the reason that you said.
Sentence 1 says that time has no beginning. One conclusion that we could draw from sentence 1 is if we had a time machine and could travel backwards in time and we start from "now" (present time) we could never reach a "beginning" because there IS no beginning. (Time extends forever into the past.)
But sentence two (restated) says that if time had started at the "beginning" and proceeded forward then time could never reach now because the time from the beginning until now is infinite. However we already said that there IS no beginning. Sentence two implies/assumes a beginning and therefore contradicts sentence one.