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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