Cf: Animated Logical Graphs • 68 http://inquiryintoinquiry.com/2021/03/29/animated-logical-graphs-68/
Re: Ontolog Forum https://groups.google.com/g/ontolog-forum/c/ru_NmgntJq0 ::: Mauro Bertani https://groups.google.com/g/ontolog-forum/c/ru_NmgntJq0/m/RIwyFDXoBgAJ Dear Mauro, Let's take a another look at the Table we reached at the end of Episode 21. ( https://inquiryintoinquiry.com/2019/07/12/animated-logical-graphs-21/ ) . Table 1. Formal Operation Table (a, b) https://inquiryintoinquiry.files.wordpress.com/2021/03/formal-operation-table-a-b.png I call it a Formal Operation Table — rather than, say, a Truth Table — because it describes the operation of mathematical forms preceding the stage of logical interpretation. I know the word “formal” tends to get overworked past the point of semantic fatigue but I can still hope to revive it a little. We'll use other labels for Table entries at other times but I tried this time to mitigate interpretive bias by choosing a mix of senses from both Peirce and Spencer Brown. Entering the stage of logical interpretation, we arrive at the following two options. The entitative interpretation of (a, b) produces the truth table for “logical equality”. Table 2. En (a, b) https://inquiryintoinquiry.files.wordpress.com/2021/03/truth-table-en-a-b.png The existential interpretation of (a, b) produces the truth table for “logical inequality”, also known as “exclusive disjunction”. Table 3. Ex (a, b) https://inquiryintoinquiry.files.wordpress.com/2021/03/truth-table-ex-a-b.png Resources ========= Futures Of Logical Graphs https://oeis.org/wiki/Futures_Of_Logical_Graphs Themes and Variations https://oeis.org/wiki/Futures_Of_Logical_Graphs#Themes_and_variations Regards, Jon
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