On 2 Mrz., 23:18, Virgil <vir...@ligriv.com> wrote:
> So that in WM's world there is a largest natural number whose value is > variable and dependent on many factors, so that it may sometimes be > increasing and sometimes decreasing. > The alternaive is a completed infinity that allows for a union of subsets that contains more than all its proper subsets. That is obviously a contradiction with mathematics. It is as wrong as the claim that the list 1 1, 2 1, 2, 3 ... contains all natural numbers in the first line, not so obvious a contradiction though for people who lack logical capabilities.
> In the world of the majority, it is your potential infiniteness, not our > actual infiniteness, that is self contradictory.
In the world of people who lack logical capabilities many amazing things can happen. > > In our world every natural is required to have a successor, whereas in > WM's world there must always be a natural not having any successor, > though no one can say which one it is. > > > But there are all FIS of d, which must be in infinitely many different > > lines of the complete list. > > if there are all of them,
There cannot be all. > > > > And we have a contradiction with analysis. Compare "The Paradox of > > Tristram Shandy", PlanetMathOrg (2012) > > Only fools like WM ever expect Tristam to finish recording his whole > life.
The same fools expect by the same argument that all rational numbers can be enumerated. > > > > > Two proofs against actual infinity. In addition there is the Binary > > Tree which has not more than infinitely (aleph_0) paths that can be > > distinguished even by infinite strings (with aleph_0 bits each). > > > But the set of all such paths has uncountably many paths that one will > never be able to list.
Since infinite paths do not exist other than by finite command.
