Date: Feb 1, 2013 7:13 PM
Author: Virgil
Subject: Re: Matheology � 203

In article 
<074f072a-1efa-4f75-8164-d3eda2eea41d@x18g2000yqo.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> potentially infinite list does not contain every whatever in the
> sense of all. Because a list that in contains all whatevers is actual
> with respect to these whatevers.


Potential infiniteness does not occur in the world of TERTIUM NON DATUR.

In such a world, a set either does or does not have an injection to a
proper subset. as in such TERTIUM NON DATUR worlds as ZF,
>
> But of course the list contains every sequence that is a line between
> 1 and n (including the limits) and therefore contains all these
> sequences.


In SF and similarly "saner than WMytheology" set theories
>
> These two meanings have to be distuingusihed carefully. Example: A
> potentially infinite set of natural numbers does not contain all
> natural numbers.


Then it is not a set at all, at least unless one can tell which naturals
are members and which are not.


> Otherwise it would be an actually infinite set, named |N.


The name |N can refer to an actual set because the membership is
determinate rather than indeterminate.
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