Combativeness is the name of the quality: the readiness to fight or argue. Combative is the adjective; combativeness is the noun we use when we talk about that spirit itself — someone’s combativeness, or the combativeness of a debate. The range is the same as the adjective. It can mean a taste for physical fighting, but in real use it is more often a verbal, competitive push: courtrooms, interviews, sport, family rows. It is a formal, slightly heavy word. You can often say fighting spirit or a taste for argument instead, and people will still follow you.