[FOM] Potential and Actual Infinity

[Mario Carneiro]

On Wed, Mar 11, 2015 at 7:31 PM, John Bell <jbell at uwo.ca> wrote:

>  In the internal logic of *E, K *fails be finite in that it  is not
> equipollent with any natural number. On the other hand  K is not
> transfinite in that the set of natural numbers cannot be injected into it.
>

It seems that this notion of "not finite" as not equipollent with a natural
number is quite weak in E, seeing as it would also label the set

W = {0} -> {0,1} -> {0} -> {0,1} -> ...

as "infinite" in this sense, even though W is also a subset of {0,1}.
(Assuming I have correctly captured the "internal logic of E"...)

Mario Carneiro
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