You can find descriptions of associativity as intuitively meaning that the order of operations performed does not matter, e. g. such as that of Wikipedia. However, if you write what associativity means in terms of a formula in either prefix notation, that is that for some binary operation X, XXxyz=XxXyz, or suffix notation xyzXX=xyXzX, the intuitive description of associativity loses sense. So, what does associativity mean intuitively in a prefix or suffix scheme? I suppose one might say that in prefix and suffix notation, associativity means that one can push the second instance of the operation in as far as we can, or as far out as we can and still have an equivalent expression. But, this does not seem to fit with an intuitive description of associativity in an infix notation.
So, what does associativity mean across all notational schemes? Can we meaningfully talk about associativity across all notational schemes, or do intuitive descriptions only work as local to a particular notational scheme?
Addendum: I'm not quite sure if this belongs here or on Philosophy Stack Exchange. I would like it imported there, if it seems more fitting there.