Re: Fw: [ROSEN] Mathematical logic, computability, and "rigor"

[Torkel Franzen <***>]

>Here are the latest clarifications from Dr. Aloisius Louie:

>Isn't this what Rosen did in LI Ch.10?  For a mechanism,
>ultimately some efficient cause has to be entailed from the outside;
>but for an organism, all the efficient causes are entailed within.
>For example, in a mechanism a "repair the repair" iteration will
>ultimately lead to the environment, whereas in an organism, the
>"repair the repair" iterative loop is closed.

  I don't see how this gives any example of a "why question" answered
within PA or ZFC and a "why question" not answered within PA or ZFC.
PA and ZFC are not mechanisms, but formal systems, and statements in
these theories say nothing about causes.

>This is "naive set theory" in the sense of Paul Halmos.
>It is the standard mathematical usage.

  Actually the title of Halmos's book is quite eccentric, and it is
not standard usage to speak of axiomatic set theory as "naive
set theory". But this, of course, is a very peripheral point.