By that standard, if f is a function of x and y, then writing f(1,2) is syntactically bad because the argument slots don’t have a meaningful order. One could s

By that standard, if f is a function of x and y, then writing f(1,2) is syntactically bad because the argument slots don’t have a meaningful order. One could surely invent a valid mathematical formalism with exclusively named argument slots, but this isn’t how math is generally done. (I admit it might be a lot easier to avoid losing track of which thing is a row and which is a column in a gnarly linear algebra expression if all dimensions were explicitly named, and this would come with a tradeoff of verbosity. Also, the interpretation of a matrix as a linear function from vectors to vectors would need some clarification as to which dimension is input and which is output, so maybe it would look a bit like Einstein notation with superscript dimensions and subscript dimensions?)