On 16 Mrz., 23:12, William Hughes <wpihug...@gmail.com> wrote: > On Mar 16, 7:38 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 16 Mrz., 19:26, William Hughes <wpihug...@gmail.com> wrote: > > > > On Mar 16, 7:10 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 16 Mrz., 18:10, William Hughes <wpihug...@gmail.com> wrote: > > > > > > > Ok, I understand. Anyhow, if the number of lines is not empty, then > > > > > > there must remain at least one line as a necessary line. > > > > > > Not a particular line. This is similar to > > > > > the case where any set of lines with an unfindable > > > > > last line has at least one "necessary" findable line. > > > > > This line has a line number in the original > > > > > list but we can choose the "necessary" > > > > > findable line to have any line number we want. > > > > > No, it is always the last line. We call it unfindable or unfixable > > > > because as soon as we have found it, it is no longer the last line. > > > > Note, that I am not talking about the unfindable line, > > > but the "necessary" findable line. We can choose this > > > line to have any line number we want > > > In potential infinity there is no necessary line except the last one. > > We know that with certainty from induction. Every found and fixed line > > n cannot be necessary, because the next line contains it. > > And yet you agree that for a set > of lines to contain an unfindable line it is necessary > that it contain at least two findable lines.
Please do not intermingle the facts. If we go through the list of FISONs 1 1,2 1,2,3 ... then we can drop every FISON. We maintain all naturals "that are in the list" if only the last line is maintained. This is like time. If you only preserve the last second, then you have access to everything (including memories) that existed in this last second.
Contrary to this natural although unfamiliar opinon, there are defenders of actual infinity. They have to claim that all natural numbers that ever can exist, already exist in the list. This implies closure, i.e., it is impossible to have a natural outside of the list. The list is complete. But they deny that the list has a last line. And there comes the inconsistency: Completeness requires and end-signal, at least in a scientific theory that should be falsifyable or verifyable.
However, in fact nobody claims a last line. The only alternative, in actual infinity, is that all naturals are there, but not in one line but in two or more lines (unless you want to claim that they are in any empty line). And this claim is contradicted by the construction principle of the list.