Re: The shocking truth about the naturals

On Sep 7, 1:33 pm, Boris Borcic <bbor...@xxxxxxxxx> wrote:
I am not sure I understand where
you locate the dissymmetry,

Well, I was about to say where, but then, *you* say,
because I don't understand (yet) how the restriction
to "prove in classical finitary 1st-order logic" creates a(n artifical) symmetry
(what you appear to be saying).

I had hoped to appear to be saying the opposite.
I am saying that that restriction creates the Asymmetry, or
breaks the symmetry, alleged by "the other side", by the people
who want to say that the upward theorem should cast a symmetric shadow
of
doubt on denumerability.

Instinctively it appears clear that the downward
theorem impacts on interpreting the upward theorem in a way that has no converse
(but, well, instincts...).

But I had the *same* instinct.
In trying to come up with something more theoretical to found it on,
I am trying the definition of a 1st-order language.
The point being that the cardinality-floor of the downward version IS
the cardinality OF THE (underlying/formal/theoretical) LANGUAGE.
The first-order languages underlying this whole proof-paradigm are
denumerable
because their definition says they are.



.

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