Dialetheism in reality
Dialetheism is a manifestation of logic, and, perhaps, language. Some have asked whether it is possible to have a real object that's a dialethia.
At first sight, and probably second and more sights, this is a category mistake. You can't ask if the word 'apple' and an apple are both 'real' objects - they occupy different realms.
However, interestingly, there's a recent discovery of something very like a dialethism in the real world.
It's a fermion that's both a particle and an anti-particle - it is its own anti-particle.
If you take the property 'is a particle' as your 'p' and 'as an anti-particle' as your '~p', then this fermion demonstrates that it is both p and ~p. A dialethism in the real world.
It's OK if you continue to insist that this as a category mistake, it is. It's also interesting and fun.