Specialization-generalization(mathematical logic)

[RockyMarciano]

Specialization as defined in Wikipedia:
"Concept B is a specialisation of concept A if and only if:

• every instance of concept B is also an instance of concept A; and
• there are instances of concept A which are not instances of concept B"

We then call B as special case of A, it seems evident from the definition that in no case, given this definition, can A be simultaneously a special case of B, because it would be in contradiction and that conceptual system would be inconsistent.

Should scientific theories(mathematically founded) follow this logic or can you think of any example that wouldn't necessarily? In other words is this a requirement for consistent scientific theories?

 

[BvU]

yes

 

[RockyMarciano]

yes

Thanks, I supposed so but I wanted to confirm it, people would be surprised by certain established theories that don't fulfill this consistency check.

 

[RockyMarciano]

Thanks, I supposed so but I wanted to confirm it, people would be surprised by certain established theories that don't fulfill this consistency check.

Perhaps the issue is not so clear when the special cases happen to be also degenerate cases, but then I can see that in itself as a symptom of possible inconsistency.