fom
Posts:
1,969
Registered:
12/4/12


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


On 2/11/2013 1:07 PM, CharlieBoo 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.

