[FOM] The unbearable ghastliness of EFQ, and sundry other matters arising from Harvey's last post

[Hendrik Boom]

On Thu, Sep 03, 2015 at 09:29:20PM -0400, Timothy Y. Chow wrote:
> >From: Harvey Friedman <hmflogic at gmail.com>
> Harvey Friedman wrote:
> 
> >The only proof you have offered of this "empty set contained in A"
> >in ordinary mathematical language read virtually identically to
> >the usual proof with explosion (EFQ), and so I still haven't seen
> >any proof of "empty set contained in A" that isn't obviously based
> >on the idea that a contradiction yields everything. I said that if
> >I see such a thing, I will revisit this whole matter.
> 
> I haven't followed all the ins and outs of this particular
> discussion, but the debate seems to be turning on whether the
> following argument---
> 
> Let b be arbitrary. Suppose b in {x|~x=x}. Then ~b=b. But b=b.
>     Contradiction. So, if b in {x|~x=x}, then b in A. QED
> 
> ---employs the idea that "a contradiction yields everything."  I
> don't understand what Core Logic is, and I'm not sure I even
> understand what "a contradiction yields everything" means.  But I
> can give a data point as a mathematician introspecting on what he
> thinks he is doing when reasoning as above.  I think I am making an
> assumption, arriving at a contradiction, and then concluding that my
> assumption must be mistaken.

The assumption in the above deduction was

	Suppose b in {x|~x=x}

> I am not, or at least am not
> consciously, thinking about "a contradiction yields everything."
> Where is that step supposedly coming in?  I guess this is a question
> for Harvey.  Am I supposedly arriving at the contradiction, then
> making a further step that the contradiction yields everything, and
> then balking at accepting everything, and only then backtracking to
> my assumption to reject it?  It's not possible to balk at the
> contradiction itself and backtrack immediately?

So, backtracking, you would have to conclude

	not b in {x|~x=x}

> We have to justify
> balking at the contradiction by appealing to its undesirable
> consequences, or something?

Nowhere does any of this say anything about

	b in A.  

b in A is what's pulled out of the 'everything'.

-- hendrik