[CG] Cactus Language • Preliminaries

Cactus Language • Preliminaries 1 • https://inquiryintoinquiry.com/2025/03/30/cactus-language-preliminaries-1/ ❝Picture two different configurations of such an irregular shape, superimposed on each other in space, like a double exposure photograph. Of the two images, the only part which coincides is the body. The two different sets of quills stick out into very different regions of space. The objective reality we see from within the first position, seemingly so full and spherical, actually agrees with the shifted reality only in the body of common knowledge. In every direction in which we look at all deeply, the realm of discovered scientific truth could be quite different. Yet in each of those two different situations, we would have thought the world complete, firmly known, and rather round in its penetration of the space of possible knowledge.❞ — Herbert J. Bernstein • “Idols of Modern Science” The task before us is to describe the syntax of a family of formal languages intended for use as a sentential calculus, and thus interpreted for the purpose of reasoning about propositions and their logical relations. To carry out our discussion we need a way of referring to signs as if they were objects like any others, in other words, as the sorts of things which can be named, indicated, described, discussed, and renamed if necessary, which can be placed, arranged, and rearranged within a suitable medium of expression — or else manipulated in the mind — which can be articulated and decomposed into their elementary signs, and which can be strung together in sequences to form complex signs. Signs having signs as their objects are known as “higher order signs”, a topic which demands an adequate level of formalization, but in due time. The present discussion needs a quicker way to get into the subject, even if it settles for informal means which cannot be rendered absolutely precise. 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