value wrote: ↑November 24th, 2022, 9:24 amConsul wrote: ↑November 22nd, 2022, 6:19 pm
If there is no first time t0, then for all times tm there are infinitely many times t < tm; but there is no (impossible) completing of an actual temporal infinity, because the actual temporal infinity involved has always been complete.
The idea of 'completing' an actual (beginning-less) infinity is absurd in my opinion. Can you please explain how an actual infinity can contain numerable parts (Tn) that allow for mathematical calculation?
Actual infinities aren't completable because they aren't successively constructible. No action or process like adding, counting, or stacking can possibly result in an actual infinity of things.
Let's say that
Tn is the year 2022 and consider the following beginningless series of years: -∞, …, -3, -2, -1, 0, 1,…, 2020, 2021, 2022.
There is no first year, so every year is preceded by infinitely many years; but every year is only
finitely many years away from any other year, so there are always well-defined
finite temporal distances between any pair of years—which can of course be unimaginably large, since there are infinitely many
finite numbers of years.
value wrote: ↑November 24th, 2022, 9:24 amConsul wrote: ↑November 22nd, 2022, 6:19 pmMoreover, the temporal distance (interval) between any time tm < Tn and Tn is finite; so there is no time tm in the infinite past from where you cannot "get to" Tn in a finite amount of time. You certainly cannot "get from" -∞ to Tn, since there is no such time in the past as -∞.
The explanation for the relation between tm and Tn is lacking.
I suspect that @Terrapin Station would ask: what about historical Tn states? If those events cannot be considered facts that obtain whether a mind is looking or not then it would undermine physicalist theory. If those states are to be considered facts independent of mind then historical Tn would be applicable in the form of -∞.
Terrapin Station wrote: ↑February 18th, 2020, 6:57 pmFacts are states of affairs--ways that things happen to be, or (dynamic) arrangements of things in the world. Facts obtain whether people exist or not.
The problem is the "continuing flux of change." There's this state, and then it changes to that state, etc.
To get to any particular state, T, if there's an infinity of previous change states, it's not possible to arrive at T, because an infinity can't be completed to get to T.
So in other words, change state T is the destination. Well, before change state T arrives, change state T-1 has to obtain. But before that can obtain, change state T-2 has to obtain. And before that, change state T-3, etc. If that goes on for infinity, it's not possible for T to arrive, because it's not possible for all of the "T minuses" to pass to get to T.
Even if a beginningless infinite series is defined dynamically in terms of changes of states, we have a well-defined sequence. For although
T is preceded by infinitely many changes, the number of changes between
T and any
T-n prior to
T is always
finite; so there is no problem of "arrival", since
T-n,…,T is always a
finite series of changes.
There is no completion of an infinite series of changes, since this series has always been a complete infinity by virtue of every change in the series being preceded by infinitely many prior changes.
The question
But how do you get from -∞ to T? is simply ill-posed, because there is no such infinite process as
getting from -∞ to T. There are only
infinitely many finite processes of
getting from T-n to T.