Re: Peano's Axioms are Inconsistent

On Aug 8, 7:02 pm, Ben Bacarisse <ben.use...@xxxxxxxxx> wrote:
RussellE <reaste...@xxxxxxxxx> writes:
On Aug 8, 6:44 pm, Joshua Cranmer <Pidgeo...@xxxxxxxxxxxxxxx> wrote:
RussellE wrote:

So, PA plus Axiom of Commutation is inconsistent?

Apparently.

It took me 10 years to figure this out.
It takes a while to get use to.

You do realise that Joshua's "Axiom of Commutation" was a joke?  It's
not always clear if you are on the same page.

He was joking about binary operations being commutative?
http://en.wikipedia.org/wiki/Commutativity
I thought he was using the Axiom of Ambiguity.

You still haven't answered my question.

Is the following statement true in whatever formal system
you want to use? I have never actually seen anyone
prove something in a formal system, so this could
be a first.

1) AxEy T(y)(x) ='1' => ExAy T(y)(x) = '1'

After you are done with that I have another.
Prove the following statement is false:

2) EyAx T(y)(x) = '1' OR ExAy T(y)(x) =/= '1'

I can show, using strictly finite means, statement (2)
is true for BNTM at any step on any tape.


Russell
- 2 many 2 count
.

Relevant Pages

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