In the case of metaphors, they are not literal, but are logical (else they would be nonsensical, though I suppose idioms provide ample examples of that.) In general though, verbal language is often less precise than math, one big way its symbols are usually better suited to its tasks than words are. That said, I think that advantage diminishes the further one gets into set theory, infinitesimals etc.


I am only an armchair mathematician who cannot answer that absolutely. The armchair philosopher in me thinks so, however, and notes that philosophers do not get division by zero errors.


Which is the primary way math is usually better suited to its task than verbal language. Verbal language is more versatile but less precise, so math is usually more precisely and clearly understood in its own language (assuming one knows that language,) though verbal language can convey it. Conversely, many valid concepts verbal language can express are completely inexpressable via math.

I feel obliged to note in passing that several of your examples are less about the flexibility of verbal language than the human capacity to comprehend meaning even when the logical rules of verbal language are ignored. If I write, "Eye lyk peetsa" you know exactly what I mean because of your own grasp of logic, DESPITE my butchered language.


Well, I conceded that at the outset; "the symbolism of each is better suited to some tasks than others." Verbal language CAN do math, but has less of the precision and brevity that facilitate clarity, so mathematical language does it better. Likewise, there are many places mathematical language cannot but verbal language can go, notwithstanding (sometimes, as you say, because of) its imprecision. Heaven knows I have written enough sonnets where I deliberately relied on the possibility of understanding the same phrase multiple ways because I wanted it uncertain and/or meant both.