Cactus Language • Stylistics 5

Before the capacity of a language to describe itself can be evaluated, the missing link to meaning must be supplied for each of its expressions.  That means opening a dimension of semantics to be navigated by means of interpretation, topics to be taken up in the case of \mathfrak{C} (\mathfrak{P}) at a later stage of the present inquiry.

The pressing issue at this point is the distinct placements of formal languages and formal grammars with respect to the question of meaning.  The sentences of a formal language are merely the strings of signs which happen to belong to a certain set.  They do not by themselves make any meaningful statements at all, not without mounting a separate effort of interpretation, but the rules of a formal grammar make meaningful statements about a formal language, to the extent they say what strings belong to it and what strings do not.

A formal grammar, then, a formalism appearing even more skeletal than a formal language, still has bits and pieces of meaning attached to it.  In a sense, the question of meaning is factored into two parts, structure and value, leaving the aspect of value reduced to the simple question of belonging.  Whether that single bit of meaningful value is enough to encompass all the dimensions of meaning we require, and whether it can be compounded to cover the complexity which actually exists in the realm of meaning — those are questions for an extended future inquiry.

Resources

cc: Academia.edu • BlueSky • Laws of FormMathstodonResearch Gate
cc: Conceptual GraphsCyberneticsStructural ModelingSystems Science

This entry was posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

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