On Wed, Nov 19, 2014 at 5:12 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:

>
> On 19 Nov 2014, at 05:18, meekerdb wrote:
>
>  On 11/18/2014 4:57 PM, LizR wrote:
>
>  On 19 November 2014 06:45, meekerdb <meeke...@verizon.net> wrote:
>
>>  On 11/18/2014 5:00 AM, Bruno Marchal wrote:
>>
>>
>>  On 17 Nov 2014, at 21:13, meekerdb wrote:
>>
>>  On 11/17/2014 2:55 AM, Bruno Marchal wrote:
>>
>> The bible explains better (if we assume it is correct)
>>
>>
>> And if it isn't correct it doesn't explain anything.  Which is why
>> science seeks to test correctness prior to explanatory power.
>>
>>
>>  Ideally, or FAPP, perhaps.
>>
>>  But fundamentally, science cannot test correctness, not even define it
>> properly.
>>
>>
>>  Are you saying that a theory cannot be tested an found incorrect??
>>
>>
> I would think the obvious way to parse what Bruno has said here is
> "science cannot show that something is correct".
>
>
> Is that right, Bruno?
>
>
> Yes.
>
>
>
> Of course empirical tests are better at showing a theory is wrong than
> showing it's right, which is Popper's observation.
>
>
> Indeed.
>
>
>
> I'm curious as to how you define correctness properly?
>
>
> I can't do it for myself, nor can any machine do it for herself. But a
> "sufficiently strong" machine can do it for a lesser strong machine. You
> can define arithmetical truth and PA's correctness in the set theory ZF for
> example. In that case "correctness" is defined in the manner of Tarski: p
> is correct if it is the case that p is satisfied by this or that
> mathematical structure, (for RA and PA, you can use the usual (N,+, *)
> structure, and with computationalism, that arithmetical truth (not
> definable in arithmetic) is enough).
>
>
This sounds like a description of which mathematical theories suggest the
existence of higher more-correct selves.
Richard



> Bruno
>
>
>
>
>
>
> Brent
>
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