Cactus Language • Pragmatics 12

The concatenation $\mathfrak{L}_1 \cdot \mathfrak{L}_2$ of the formal languages $\mathfrak{L}_1$ and $\mathfrak{L}_2$ is just a cartesian product $\mathfrak{L}_1 \times \mathfrak{L}_2$ of the sets $\mathfrak{L}_1$ and $\mathfrak{L}_2$ but the relation of cartesian products to set‑theoretic intersections and thus to logical conjunctions is not immediately clear. One way of seeing a type of relation is to focus on the information needed to specify each construction and thus to reflect on the signs used to bear the information. As a first approach to the topic of information I introduce the following set of ideas, intended to be taken in a very provisional way.

A stricture is a specification of a certain set in a certain place, relative to a number of other sets yet to be specified. It is assumed one knows enough to tell if two strictures are equivalent as pieces of information but any more determinate indications, for instance, names for the places mentioned in the stricture or bounds on the number of places involved, are regarded as extraneous impositions, outside the proper concern of the definition, no matter how convenient they happen to be for a particular discussion. As a schematic form of illustration, a stricture can be pictured in the following shape.

$``\ldots \times X \times Q \times X \times \ldots"$

A strait is the object specified by a stricture, in other words, a certain set in a certain place of an otherwise yet to be specified relation. Somewhat sketchily, the strait corresponding to the stricture just given can be pictured in the following shape.

$\ldots \times X \times Q \times X \times \ldots$

In that picture $Q$ is a certain set and $X$ is the universe of discourse relevant to a given discussion. As a stricture does not contain a sufficient amount of information to specify the number of sets it intends to set in place, or even to pin down the absolute location of the set it does set in place, it appears to place an unspecified number of unspecified sets in a vague and uncertain state of affairs. Taken out of its interpretive context the residual information a stricture is able to bear makes all of the following potentially equivalent as strictures.

$\begin{array}{ccccccc} ``Q" & , & ``X \times Q \times X" & , & ``X \times X \times Q \times X \times X" & , & \ldots \end{array}$

With respect to what those strictures specify, that leaves all of the following equivalent as straits.

$\begin{array}{ccccccc} Q & = & X \times Q \times X & = & X \times X \times Q \times X \times X & = & \ldots \end{array}$

Resources

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

	Survey of Semiotics,… on Sign Relations • Semiotic Equi…
	Survey of Semiotics,… on Sign Relations • Semiotic Equi…
	Sign Relations • Sem… on Survey of Semiotics, Semiosis,…
	Survey of Semiotics,… on Sign Relations • Semiotic Equi…
	Sign Relations • Sem… on Survey of Semiotics, Semiosis,…
	Sign Relations • Sem… on Survey of Semiotics, Semiosis,…
	Survey of Semiotics,… on Sign Relations • Semiotic Equi…
	Sign Relations • Sem… on Survey of Semiotics, Semiosis,…
	Survey of Semiotics,… on Systems of Interpretation •…
	Survey of Semiotics,… on Sign Relations, Triadic Relati…

M	T	W	T	F	S	S
				1	2	3
4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31