Proof: Humans are innovative

A loose argument I created about humans being innovative. I'm looking for any obvious flaws in the reasoning.

Axioms:
1. If humans are innovative in one activity, they are innovative.
2. A given person's use of a language they know will not change noticeably during their lifetime (e.g. it is impossible for Shakespeare to start speaking modern English, even if it were to happen gradually throughout his life).

Claim: Humans are innovative in language, from which (axiom 1) the result will follow.
Proof: Suppose for the sake of contradiction that they were not. Then consider a person who can live for 500 years. By axiom 2, the way this person speaks any language they know will not change. In particular, if this person was born during Shakespeare's time, they would still be speaking Shakespearean English today. But this means that the reason language changes is because there is no continuity in the use of language. In other words, breaks between people's lives (because they are short) renders language open to shaping by the new generations, and so they can change the previous generation's language slightly. In other words, they are innovative by nature. This so because language has always evolved, so we may assume, by induction, that it will always evolve, and thus humans are innovative in language. QED

Axiom 3: Hark, lol