There is indeed a boundary and border between what might be said or defined and what might eventually be understood or known as reality, information, the physical facts that (or as they) exist beyond our descriptions of them. I am sympathetic with any philosophical position that seeks to build and inhabit the difference and distance here but feel that, just as the compelling vacuum as excluded middle and mezzanine between a signifier and its signified remains eminently and yet usefully unbridgeable, the disconnect and discontinuity you identify is global, irreducible as a kernel fact of ontology, metaphysics, and epistemology.
That mischievously complex and unknowable logical and physical depth “beyond” the mathematical description of it appears to encapsulate, infuse and quite positively propel the whole system of information and intelligence that asymptotically approximates towards it. Uncertainty, undecidability, expansive combinatorial dimensionality, incompleteness, non-linearly self-propagating recursive dynamical complexity – they are all the same thing. The holes and hollows in logic and mathematics precisely are the enigmas of mind and matter and only a new, evolving and essentially neuroplastic model of subjectivity and res extensa can ever hope to successfully negotiate the void that they share.
Daedelus Kite 