The Metaformal System: Completing the Theory of Language

#1
Ostronomos Offline
The standard theory of languages has two levels, one centering on the study, teaching, and application of natural languages, and the other on formal languages and formal systems as applied throughout the mathematical and empirical sciences, in analytic philosophy, and for computer programming, software engineering, artificial intelligence, and related technologies. On both of these levels, standard language theory is dualistic, defining languages in isolation from their domains of discourse and treating attributes in isolation from their objective instances while omitting important properties and functions ordinarily provided or executed by language users, automata, or physical systems on which they appear to supervene. This decoupling of languages from their universes, and from necessary linguistic functions such as display, processing, interpretation, and communication, has profound epistemological bearing, limiting scientific knowledge by precluding the linguistic formulation of any verifiable comprehensive description of reality. This paper proposes that in addition to the two existing levels of standard language theory involving natural and formal languages and systems, the theory of language be recognized to possess a third "metaformal" level on which languages and their universes are "wrapped" in a uniquely structured, totally self-contained  metalanguage, the Metaformal System, which restores missing linguistic functionality while using a supertautological intelligibility criterion to generically couple languages with their universes on a fundamental level of shared structure and dynamics, thereby restoring the potential for a verifiable comprehensive and fully connected understanding of the reality we share.

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From a technical standpoint, one of the most important features of language is that its study is necessarily self-referential. That is, any attempt to define, describe, analyze, or construct language uses language itself to do so. Self-referentiality is a powerful and underexplored feature of language, one which has puzzled and fascinated mankind for centuries. But at the juncture where language meets cognition, it is also a source of logical and epistemological complications. Due in part to these complications, language has met with many apparent failures, ranging from piles of self-contradictory and seemingly unproductive philosophical verbiage to the undefinability and undecidability problems of formal language-systems. There are many who seem to bel


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Where the deceptive dualistic isolation of language from universe obscures their true relationship and precludes certainty, conclusive identification is impossible. But as physical reality can in fact be clearly identified through direct observation and logical deduction, without which neither science nor human experience could exist, and as deductive logic is a formal language inherent in cognition, this assumed linguistic incapacity is unfounded and illusory. Hence, the third level of language theory herein proposed already has an irrefutable basis. Let us more closely examine these levels of linguistic theorization.

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If we regard natural and formal languages as the first two levels of modern language theory, it is possible to identify a third. Whereas the first two levels are dualistic, taking languages in isolation from their universes, the third is monic and self-dual, structurally fusing language and universe into a single coherent identity on the highest possible level of discourse. Featuring an intrinsic definition of language which is analogous to intrinsic geometry in its self-containment and external independence, it consists entirely of identities, or coherent self-dual language-universe couplings, and the operators and operations which generate and act on them.

https://www.cosmosandhistory.org/index.p...e/740/1214

Recall that this is strikingly similar to my thread in the Philosophy section on sciforums called "Reality is Reduced to Axioms". I believe Langan based his idea for this paper on that.
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#2
Ostronomos Offline
The Metaformal System is an “extended formal system” which is perfectly self-contained, i.e., which has all of the properties and carries all of the ingredients required for its existence and functionality, including those just mentioned (read, write, reference, interpretation, production, processing, display, communication, potentiation, determination, and so on). In short, all of these functions are executed by objects of M (syntactors, telors) using the grammar of M.
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