Desrtopa comments on Configurations and Amplitude - Less Wrong
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Scientists did define their terms way back then. They never introduced the idea of a wave/particle duality without knowing exactly what they meant.
The reason I keep diverting from the topic is that it takes more than just defining one's terms to communicate complex ideas without a shared body of information. Try and explain evolution to a person who's been brought up in a fundamentalist household, for instance, and while you might pat yourself on the back afterwards for an explanation well delivered, they're probably not going to come away understanding it, unless you take the time to bridge the entire gap of uncomprehension.
I seriously suggest reading the Mysterious Answers to Mysterious Questions sequence, which I linked to before, because some of the points you're expressing are misconceptions that it was written for the specific purpose of addressing. Eliezer wrote the sequence in order to bring people up to the point of being able to meaningfully discuss the ideas we work with here without talking past each other. He put a lot of work into them, and I'd rather not replicate it all when it's already there for exactly that reason. There is a reason that Mysterious Answers to Mysterious Questions is the first in the suggested reading order of the sequences, and the quantum physics sequence is the fifth.
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I agree that key terms need a definition. They have apparently all been defined before, but no one here has yet shown an interest in giving those (or any) precise definitions right now. I'm not sure why, especially given that this is LessWrong. I'd help you out on that, but I honestly don't know the precise definition that QM theorists use for wave. Surely someone must know?