The basic linguistic process is the binding of word forms to structures of meaning. I think that is an irreducibly computational process. Just how that computation works, that’s unknown. I note that the semantic system is richly structured and that much of syntax derives from that.
It is not necessarily the case that all the processes involved are themselves computational. The fact that we can simulate a neural net, at various levels of detail, on a digital computer does not mean that the neural net is itself computational, any more than simulating an atomic explosion implies that such explosions are computational.
Finally, I note that, when David Hays and I wrote “Principles and development of natural intelligence” (abstract below), we asserted that indexing is what transformed apes into humans. It was indexing that gave us language as we now know it.
More later. HERE for example.
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William L. Benzon and David G. Hays. Principles and development of natural intelligence. Journal of Social and Biological Structures 11, 1988, pp. 293-322. https://www.academia.edu/235116/Principles_and_Development_of_Natural_Intelligence
Abstract: The phenomena of natural intelligence can be grouped into five classes, and a specific principle of information processing, implemented in neural tissue, produces each class of phenomena. (1) The modal principle subserves feeling and is implemented in the reticular formation. (2) The diagonalization principle subserves coherence and is the basic principle, implemented in neocortex. (3) Action is subserved by the decision principle, which involves interlinked positive and negative feedback loops, and resides in modally differentiated cortex. (4) The problem of finitization resolves into a figural principle, implemented in secondary cortical areas; figurality resolves the conflict between pro-positional and Gestalt accounts of mental representations. (5) Finally, the phenomena of analysis reflect the action of the indexing principle, which is implemented through the neural mechanisms of language.
These principles have an intrinsic ordering (as given above) such that implementation of each principle presupposes the prior implementation of its predecessor. This ordering is preserved in phylogeny: (1) mode, vertebrates; (2) diagonalization, reptiles; (3) decision, mammals; (4) figural, primates; (5) indexing. Homo sapiens sapiens. The same ordering appears in human ontogeny and corresponds to Piaget's stages of intellectual development, and to stages of language acquisition.