Re: Peano's Axioms are Inconsistent

In article
<671e72b0-218b-43c2-b6d1-d781183d0a46@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
RussellE <reasterly@xxxxxxxxx> wrote:


What the end result means is that, although every cell is written to,
there exists no time at which all cells have been written to--you need
to actually pass infinity to be able to do that.

We agree there is no step when the
set of blank positions is empty.

Then you say BNTM writes to every position.

That is precisely what we do NOT say because it is ambiguous, and
ambiguity is ruinous in mathematics.


You can't have it both ways.


It is only you who tries to have it "both ways" by insisting on stating
things ambiguously.

You are saying there is a step when the set
of blank positions is empty.

No we aren't.

If the set of blank positions is empty, I can
prove there is a step it becomes empty.

Why bother when your premise is wrong?

Time has nothing to do with it.

Does your notion of the TM operation come to an end?
If so, when?


You have to prove there exists a step for every
position.

We have done that by numbering both with the naturals


And the only way you can do that
is by proving the set of blank positions is empty.

On the contrary we have another way of doing it and deny that you way
works.

By proving BNTM writes to every position,
you are proving there are no more positions
to write to.

Another ambiguous statement.

One of the elements of X has no successor.

I'm n o loner sure what X is, but if there is such a member of X, which
member of X is it?

.

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