We accept logic, geometry, number theory, and other structures as something given, part of the external (though non-material) world that is a basic framework of thought. Why then do the followers of Noam Chomsky think that language structures (grammar, syntax, semantics) have to be innate in human brains in the form of a genetically determined “universal grammar” module? Why should we think of verbal language structures as internal, while mathematical and logical structures are seen as external, only to be discovered by us, and then seen as self-evident?

True, some of the universally present rules of grammar, common to all languages, are not immediately obvious; they could have been otherwise. But geometry, too, could be Riemannian and not Euclidean; logic can be “fuzzy” as well as classical; and numbers can be imaginary or complex as well as real. Yet we do not think of any of these primary structures (Euclidian geometry, classical logic, real numbers) as innate in the brain. Why should generally observed grammatical rules be so considered? It is good to remember that mathematics, too, is a form of language.

Abstract structures, linguistic or mathematical, are in a class by themselves: not material objects in the external world, and not neurological brain states or phenomena (whether innate or not). Abstract structures stem from classification and generalization; for example, Russell and Whitehead’s definition of number as a class of classes of n objects. A noun, a verb, an adjective, an adverb (or subject-predicate-object) are similarly a class of classes of particular names of things, of activities, and of qualities. Abstract thinking is a part of symbolic thinking, which is indeed (probably — but how do we know?) peculiar to humans. Abstract structures are close to Platonic ideas, out there beyond the shadows of the cave, in a cognitive mental heaven (universal mind). We PERCEIVE them through brain mechanisms, but they are not brain mechanisms themselves. They just ARE.