Many logical concepts which we take for granted, might not be meaningful in the realm of infinite. For example, something being equal to itself, some statement being true or false (no third state), things having unique identity or location, the concept or possibility of multiple things (and distinguishability), being able to compare one thing with another etc. All these make sense only in finite contexts but not in infinite or infinitesimal contexts.

If we accept infinity as a participant in the mathematical logic, the infinitesimal also deserves a role as a counter-party.