[CG] Re: Cactus Language • Preliminaries

Cactus Language • Preliminaries 2 • https://inquiryintoinquiry.com/2025/04/05/cactus-language-preliminaries-2/ As a temporary notation, let the relationship between a particular sign s and a particular object o, namely, the fact that s denotes o or the fact that o is denoted by s, be symbolized in one of the following two ways. 1. s → o 2. o ← s Now consider the following paradigm. Cactus Language Display 1 • https://inquiryintoinquiry.files.wordpress.com/2025/04/cactus-language-disp… 1. If “A” → Ann that is, “A” denotes Ann then A = Ann and Ann = A Thus “Ann” → A that is, “Ann” denotes A 2. If Bob ← “B” that is, Bob is denoted by “B” then Bob = B and B = Bob Thus B ← “Bob” that is, B is denoted by “Bob” 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. “blank” → “ ” “ ” ← “blank” 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. “ ” ← “blank” = “b” ∙ “l” ∙ “a” ∙ “n” ∙ “k” The above tactic lets us refer to the blank as a type of character and refer to any blank we choose as a token of that type, denoting either in a markèd way, but without the use of quotation marks. As a blank is just what the name “blank” names, it is possible to represent the denoting of the sign “ ” by the name “blank” in the form of an identity between the named objects, as follows. “ ” = blank 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. “ ” = “ ” ∙ “ ” = blank ∙ blank “ blank” = “ ” ∙ “blank” = blank ∙ “blank” “blank ” = “blank” ∙ “ ” = “blank” ∙ blank Resources — Cactus Language • Preliminaries • https://oeis.org/wiki/Cactus_Language_%E2%80%A2_Part_1#Cactus_Language_.E2.… Survey of Animated Logical Graphs • https://inquiryintoinquiry.com/2024/03/18/survey-of-animated-logical-graphs… Survey of Theme One Program • https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/ Regards, Jon