between and among: worth Phobosization?

[Timon Gehr]

On 12/18/2013 09:06 PM, "Ola Fosheim Grøstad" 
<ola.fosheim.grostad+dlang at gmail.com>" wrote:
> On Wednesday, 18 December 2013 at 19:47:05 UTC, Andrei Alexandrescu wrote:
>> I don't think so. Algebraic properties have been derived from
>> desirable and useful properties and have long shown good returns.
>
> No, when you change the foundation/definitions some of the theorems will
> break. That always happens. I can't think of a single example where that
> does not happen.
>
> Some theorems are more important to uphold than others, it is a good
> thing to avoid breaking DeMorgans for instance.
> ...

Giving up Eg. ¬(A ∧ B) → ¬A ∨ ¬B is actually a sensible thing to do in 
constructive logic.