value wrote: ↑November 24th, 2022, 9:24 amConsul wrote: ↑November 22nd, 2022, 6:19 pm
If there is no first time

*t*_{0}, then for all times

*t*_{m} there are infinitely many times

*t* <

*t*_{m}; 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 (

*T*_{n}) 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

*T*_{n} 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

*t*_{m} <

*T*_{n} and

*T*_{n} is

*finite*; so there is no time

*t*_{m} in the infinite past from where you cannot "get to"

*T*_{n} in a finite amount of time. You certainly cannot "get from" -∞ to

*T*_{n}, since there is no such time in the past as -∞.

The explanation for the relation between

*t*_{m} and

*T*_{n} is lacking.

I suspect that @Terrapin Station would ask: what about historical

*T*_{n} 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

*T*_{n} 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.