fom
Posts:
1,677
Registered:
12/4/12
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Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Posted:
Feb 11, 2013 3:05 PM
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On 2/11/2013 1:07 PM, Charlie-Boo wrote:
> On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote:
>>
>> Mathematics is different from logic. So, for example, one
>
> If you want to know what Logic is, try being a programmer of medical
> systems and then explain what is special about the set { inpatient ,
> outpatient }.
>
> 1. It is a finite set.
> 2. We don't really decide it but we enumerate it.
> a. In Logic we decide it and "This is false." is not in it.
> 3. We have a primitive name for each element.
> 4. Axioms use the names of the elements.
> a. E.g. if inpatient then list on inpatient report.
>
> Now change that to { TRUE , FALSE }.
>
> The lesson of the Halting Problem for programmers is that specs may be
> inconsistent but only after a bit of logic is applied!
Nice story.
That should be the lesson for mathematicians
as well.
Correctness is important, though. There is
a great anecdote in economics because of an
economist who ignored the mathematics of
local minima to place tangent concave up
curves along an enveloping concave up curve
so that the minima corresponded with the
tangents. John Maynard Keynes remarked that
he had no great respect for his fellow
economist, but a true respect for his
colleague's mathematicians.
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