On the mathematical foundations of crash-proof grammars
This paper looks at how the particular computational mechanism of Crash-Proof Syntax (CPS) (Frampton & Gutmann 1999, 2002) as an instantiation of the Minimalist Program (Chomsky 1995) can be understood from the point of view of mathematical foundation that captured the spotlight among mathematicians during the nineteenth century. I claim that CPS can be analyzed as an analogy with Classical Peano’s Axioms that generate the theory of natural numbers. Instead of its computational efficiency, CPS is driven by the economization of axioms of formal systems. Further comparisons between syntax and natural numbers reveal that the central tenets of CPS can be defined mathematically on one hand, and highlight the significance of the ‘third factor’ as the design feature of language (Chomsky 2005) on the other hand.