Minimax Feature Merge: The Featural Linguistic Turing Machine

In Minimalist syntax, linguistic expressions are typically modelled as being ‘projected’ from a set of lexical items, themselves composed of three independent kinds of ‘features’ (phonological, syntactic and semantic/pragmatic). The nature of syntactic features has perpetually been confused, as noted by Adger & Svenonius (2010) among others, and yet they remain the foundation of much of syntactic theory. I contest that an alternative architecture may be preferable in terms of explanatory power within the purview of mathematical biolinguistics, as described by Watumull (2012, 2013, 2015). This view combines insights from a range of theories, some of which that on the surface seem incompatible but which crucially overlap; in particular, these are Boeckx’s (2014) ‘elementary syntactic structures’, Distributed Morphology (DM; Marantz, 1997), Nanosyntax (Baunaz et al, 2018), Scheer’s (2020) interface theory, and Watumull’s (2015) linguistic Turing machine. Namely, I contest that, rather than being the driving force behind syntax, the lexicon is instead distributed amongst the interfaces in the form of non-generative lookup tables, taking Scheer’s view to the logical conclusion, in parallel to DM. Syntax combines syntactic primitives I call ‘features’ freely except as constrained by the interfaces, eliminating what Boeckx calls ‘lexicocentrism’. I define ‘features’ explicitly, as atomic, arbitrary (‘substance-free’) computational symbols comprising the set F with cardinality at least one. Following Watumull (2015), language is considered as a mathematical structure, abstracted from its neurological substrate. This structure is isomorphic to the featural linguistic Turing machine, in turn isomorphic to the simplest group-theoretical object, known as the free magma. The central motivation to this proposal is the concept of optimality as captured in the minimax principle, in turn minimising the burden of the innate first factor and maximising the role of the mathematical laws and heuristics that comprise the third factor, adopting Chomsky’s (2005) three-factor model. The ultimate aim is to begin to meet the prerequisites of explanation as defined in biolinguistics – learnability and evolvability – by formalising a theory of syntax and its place in the linguistic architecture from the ground up.

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