Confusing Infinite and/or Innate

 The first three chapters of Carnie’s book shed light not only on how grammar and syntax work, but also on how we as humans come to grasp language.  Carnie starts by laying out the foundations of grammar and then introduces the scientific method as a way of understanding and interpreting syntactic rules of language.

            On page 15, Carnie offers a Universal Grammar hypothesis and postulates that humans have a certain innate understanding of language.  The premises upon which the Universal Grammar hypothesis is founded is that “Syntax is a productive, recursive and infinite system” and “Rule governed infinite systems are unlearnable.”  From this, it apparently follows that since we do possess syntax, we have an innate understand of at least parts of Syntax.  The first sentence of Chapter 3 reads; “Syntax is about the study of sentence structure.”  In Chapter 1, Carnie demonstrates that there are an infinite number of sentences that are structured correctly, but he does not show that there are an infinite number of structures that are correct.    In fact, the rest of the reading elaborates on many (yet finite) rules of syntax we as humans use to determine what constitutes properly and/or ill formed sentences.  This leaves me confused about what Carnie, or rather Chomsky, means by “innate”.

            If we consider mathematics, I could easily contend that mathematics also constitute “a productive, recursive and infinite system.”  In fact, I would contend that even the most basic subsystems of mathematics constitute productive, recursive and infinite systems.  For example, the number of operations one can perform with addition are infinite and recursive.  I could create an infinite and recursive system as follows.  1+1 = 2, (1 + 1) + 1 = 3, ((1+1) + 1) + 1 = 4, etc.  However, there is a single basic rule which we can follow to complete any statement consisting entirely of addition operations.  Does this mean we innately understand addition?  I would contend that addition is something that can be shown to and taught to any rational being.  Furthermore, a computer can be programmed to compute any such operation without a database of all possible operations that follow the rule.  Computers are even becoming advanced enough to process and produce natural speech.  To me, it seems odd to say that a computer innately understands anything.