7.5 Diagrams in Linguistics In the final section of Chapter 7, language emerges from the Dicisign doctrine as diagrammatical tool combining “loosely coupled parts” in order to serve as a representing and reasoning organ with potentially “universal” application. Using the premiss that diagrams are responsible for all deductive reasoning, we can then produce an account of how ordinary language possesses 'diagrammaticity' at the very least in its ability to encode logical inferences in the form of syllogisms. But if the difference between language and pictorial representations is a diagrammatical matter of degree (measure of iconicity), not a difference of kind, then the Herculean tasks of reinterpreting the “levels” of natural language into their diagrammatic forms and figuring out how to measure gradations within natural language as well as with other iconic forms of signification appear before us. Later chapters might clarify why Peirce's Existential Graphs remain a valuable instrument for both ostensibly Sisyphean endeavors. But ignoring the Alpha and Beta Graphs for now, many recent cognitive linguists cited by the author seem to agree that the logical connectors of propositional logic, the linguistic quantifiers of first order predicate logic, and other more basic structures of grammar allow for possible topological formalization(s).
Recall that for Peirce, Dicisigns are formed with icon rhemes and their saturation by means of index rhemes. The cognitive linguist would agree that sentences are formed by predicates and their saturation by means of subjects. To wit: “A basic tendency seems to be that the distinction between grammar and morphology on the one hand, and lexical semantics on the other roughly corresponds to diagrams pertaining to formal and material ontologies, respectively” (NP, 196). If iconic structures can be found in the form of conjunctions and sentence structures as well as the the multiplicity of structures of rhemes/predicates themselves, grammatical transformations contain logical content, and more broadly grammar and morphology will generally contain discoverable implicit formal-material ontologies while lexical semantics can fill in regional ontological information with particulars: adjectives, common nouns, verbs and combinations thereof. Based on underlying forms of diagrammatic reasoning, ordinary language does not remain committed to any particular ontology (because diagrammatic reasoning is not committed to any particular topological framework), even if it acquires variable ontological commitments to objects and relational properties of the universe of discourse in which we engage, which Qualities and Existents we recognize, and how we choose to construct our Arguments. Stjernfelt relates the blurring of the grammar/semantics distinction to Husserl's use of the scholastic distinction between *syncategorematica* (closed classes)and *categoramatica* (open classes), and makes the observation that, in all three accounts, formal ontologies are produced that contain subclasses of formal ontologies such as modal logic, temporal logic, higher order logic on the one hand and high-level material ontological concepts from epistemic logic, deontic logic, speech act logic on the other. The linguist might say that high-level material ontologies include modal verbs, tempus morphemes of verbs, in propositional stances verbs, in speech act verbs,” (NP, 199) but regardless of the terminological variation, the “doubleness of isomorphism and independence recognized between logic, language, and ontology” (NP, 202) is a common thread whereby a gluing (interdependence) between the global/local provided by the Dicisign structure overcomes the structuralist account the arbitrarity of language (usually inferred from the relationship between sounds and words), because “conceived from a diagrammatical point of view, language has two levels, one general, formal, vague, formalized in grammar and closed-class categorematica—and another in lexical semantics and open-class syncategorematic,” (NP, 199) which are open to further investigation. Ordinary language remains 'secular'—not committed to any topological or metaphysical viewpoint ahead of time because the genuine interaction between (what I am calling) the relatively autonomous global/local levels allows for language to remain an ecumenical, indefinitely-extended, self-critical means of information processing. The author closes the chapter with a discussion of Hintikka's identification of two strands of 20th century philosophy, one which views language as universal representation and one which sees it as a calculus. According to the Hintikkan geneaology, Frege, Russell, Wittgenstein, Quine, and even Heidegger and Derrida seem to favor the former approach (language as one reference domain to all reality with privileged semiotic access to the world) while Boole, Peirce Schroder, Hilbert, Husserl, and the late Carnap understand that multiple representational systems with differing degrees of generality, granularity, are quite possible if not necessary to productive inquiry as an open-system which does run up against, in Hintikka's words, “prisonhouse of language hypotheses.” I do not disagree with Stjernfelt's claim that for the model-theoretic tradition considers language as closer to a *calculus ratiocinator* than a *mathesis univseralis* but I would contend that Irving Annelis's *paper <http://arxiv.org/pdf/1201.0353.pdf>* ( c.f. pp. 25-28) offers a more nuanced assessment how these Leibnizian themes are re-appropriated by the late Peirce than that of Hintikka, in my humble opinion. For Peirce, representational pluralism does not conflict with a robust realism given his idea of inquiry as a distinctly communal activity, one in which natural language is able to engage by means of presenting various formalizations which “semiotically triangulate the object,” (NP, 200) and one in which individual inquiry itself engages in a sort of game-theoretic semantics. Given one representational system's ability to assess another, we are not left with the ineffability claims but a science of semantics. Indeed, a careful reading of Chapter 7 offers the reader a deeper understanding of how language remains capable of entertaining universes of discourse which lack logical consistency or logical commitment so we have at our disposal a tool capable of examining and experimenting with the ontologically inconsistent, the vague, the general, and the imaginary. Peirce's 'fallibilistic apriorism' (opposed to Kantian apriorism) is better able to account for the various *a priori* structures of different material ontologies. Language from the diagrammatic perspective thus resembles a versatile collaboration between different topological considerations found inside, outside, and between conjunctions, grammar, semantics, and their various instantiations. Along with recent developments in Existential Graphs, the trajectory cognitive semantics exposited by Stjernfelt makes a strong case for CSP's continued relevance to diagrammatological linguistics. I would like to close by asking Professor Stjernfelt if he agrees with Francesco Bellucci that the late Peirce saw diagrammatic reasoning containing its own abductive and inductive phases. I look forward to any questions or comments before we begin Chapter 8. Thankfully, Doug
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