More thoughts on language

Language and the systems we devise for our understanding present their own kinds of problems. Describing this philosophical dilemma, concerning the language of mathematics, David Foster Wallace writes in his book on infinity, Everything and More, that “the hyperdimensional jump from math as a practical abstraction of real-world properties to math as a Saussurian ‘system of symbols … independent of the objects designated.’[produces] ‘displacements that are incalculable…’; because the abstract math that’s banished superstition and ignorance and unreason and birthed the modern world is also the abstract math that is shot through with unreason and paradox and conundrum and has, as it were, been trying to tie its shoes on the run ever since the beginning of its status as a real language. Re which, again, please keep in mind that a language is both a map of the world and its own world [emphasis mine], with its own shadowlands and crevasses – places where statements that seem to obey all the language’s rules are nevertheless impossible to deal with.”