Argument 1: If there were an infinite amount of time before today, then today would never have come, because you can’t count backwards from infinity.
Response: The problem here is with treating infinity like a normal number. In particular, this argument seems to have a naive, flawed conception of what an infinite past would be. It does not mean the world had a “beginning infinity days ago”, but rather that it always existed at every time. So, to use the counting analogy, it does not mean you would have counted down “from infinity”, but rather from every natural number. It is worth noting that even the claim that you can’t count down from infinity is only true if you only use the natural numbers and ignore the transfinites, such as the hyperreal ones.
Argument 2: One infinity might seem larger than another and yet they would still be infinity, such as if the solar system had existed from eternity with Jupiter completing 2.5 orbits for every orbit of Saturn, in which case there would be different numbers and yet they would still be infinity.
Response: This argument simply ignores that there are different sizes of infinity such as the different cardinals and hyperreals. So, for instance, Saturn could have completed aleph-null omega orbits while Jupiter would have completed aleph-null 2.5 omega orbits and there would be no contradiction.
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