Re: Implementable Set Theory and Consistency of ZFC

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

In my patient response to Moeblee, I've argued that my model is in fact
"every model". It's essentially independent of the suggested
bitmapping.

If it is essentially every model, then you are being far too modest.
After all, ~Infinity is true in your model, yes? And hence, if your
model is essentially every model, then ~Infinity is a theorem of
(1)-(4).
Do you believe that?

You act as if Infinity is a no nonsense statement, which it is not.
This does not answer my question.
Do (1)-(4) also suffice to prove ~Infinity?

No.

Why not?

Your proof of Foundation proceeds by showing that Foundation is true
in your model. You claim that this shows (1)-(4) entail Foundation.

But ~Infinity is also true in your model, so why not claim (1)-(4)
also entail ~Infinity?

What is the difference between the two arguments?

--
"So how do you go on? [...] How will you keep moving for the next few
weeks or months until you are known for what you are, the story
becomes huge all over the world, and you have reporters at your
schools asking you, why?" -- Another JSH mystery
.

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