Cf: Animated Logical Graphs • 73 https://inquiryintoinquiry.com/2021/04/24/animated-logical-graphs-73/
Re: Animated Logical Graphs https://inquiryintoinquiry.com/2021/04/22/animated-logical-graphs-72/ All, Last time we took up the four singleton orbits in the action of T on X and saw each consists of a single logical graph which T fixes, preserves, or transforms into itself. On that account these 4 logical graphs are said to be “self-dual” or “T-invariant”. In general terms, it is useful to think of the entitative and existential interpretations as two formal languages which happen to use the same set of signs, each in its own way, to denote the same set of formal objects. Then T defines the translation between languages and the self-dual logical graphs are the points where the languages coincide, where the same signs denote the same objects in both. Such constellations of “fixed stars” are indispensable to navigation between languages, as every argot-naut discovers in time. Returning to the case at hand, where T acts on a selection of 16 logical graphs for the 16 boolean functions on two variables, the following Table shows the values of the denoted boolean function f : B × B → B for each of the self-dual logical graphs. Table 1. Self-Dual Logical Graphs https://inquiryintoinquiry.files.wordpress.com/2021/04/self-dual-logical-graphs.png The functions indexed here as f₁₂ and f₁₀ are known as the “coordinate projections” (x, y) ↦ x and (x, y) ↦ y on the first and second coordinates, respectively, and the functions indexed as f₃ and f₅ are the negations (x, y) ↦ ¬x and (x, y) ↦ ¬y of those projections, respectively. Resources ========= Logic Syllabus https://oeis.org/wiki/Logic_Syllabus Truth Tables https://oeis.org/wiki/Truth_table Zeroth Order Logic https://oeis.org/wiki/Zeroth_order_logic Survey of Animated Logical Graphs https://inquiryintoinquiry.com/2020/08/23/survey-of-animated-logical-graphs-3/ Survey of Semiotics, Semiosis, Sign Relations https://inquiryintoinquiry.com/2019/10/29/survey-of-semiotics-semiosis-sign-relations-1/
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