Cactus Language • Preliminaries 2
As a temporary notation, let the relationship between a particular sign and a particular object , namely, the fact that denotes or the fact that is denoted by , be symbolized in one of the following two ways.
Now consider the following paradigm.
In the same vein, if we let the sign “blank” denote the sign “ ” then the string of characters inside the first pair of quotation marks will serve as another name for the string of characters inside the second pair of quotation marks. In other words, “blank” is a higher order sign whose object is the sign “ ” and the string of five characters inside the first pair of quotation marks is a sign at a higher level of signification than the string of one character inside the second pair of quotation marks. The relation in question can be abbreviated in either one of the following two ways.
Using the raised dot “∙” as a sign to mark the articulation of a quoted string into a sequence of possibly shorter quoted strings, and thus to mark the concatenation of a sequence of quoted strings into a possibly larger quoted string, one can write the following equation.
The above usage allows us to refer to the blank as a type of character, and also to refer any blank we choose as a token of this type, referring to either in a distinctive way, but without the use of quotation marks. Since a blank is just what the name “blank” names, it is possible to represent the denotation of the sign “ ” by the name “blank” in the form of an identity between the named objects, as follows.
Given the above identities it is possible to extend the use of the “∙” sign to mark the articulation of either named or quoted strings into both named and quoted strings. For example, we have the following equations.
Resources
cc: Academia.edu • BlueSky • Laws of Form • Mathstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
– In case someone’s interested I’m happy to explain how to set this up. 
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