This makes me think about formalised notation. If you have a mathematical formalised notation, you can express things either more expressively, or with less amb

This makes me think about formalised notation. If you have a mathematical formalised notation, you can express things either more expressively, or with less ambiguity (or both) than without it. One thing that is required by a formal notation is that before you write a statement in your formalised notation, you need to define the terms and symbols and how they interact with one another or the statement makes no sense to the reader. I would say this is true even when you're trying to use words rather than some type of syntax, because what you are trying to do is paint a very specific picture (or concept) in peoples minds, and you need these definitions there or people wouldn't understand them. If you're trying to be concise and to constrain the space of possible interpretations of the words you have written, to only contain the concept that you are trying to explain, and not contain other valid interpretations of the words, that may disagree with the concept you are trying to get the reader to explain, the easiest way to do so is probably with up-front definitions of the terms you are about to use. TL;DR I posit that an up-front definition of terms simplifies explanation of formal notation (or words) which is necessary to constrain the semantic idea-space to only the valid definition trying to be conveyed.