[CG] Logic Syllabus • Discussion

Cf: Logic Syllabus • Discussion 1 https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/ Re: Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ ) Re: Laws of Form ( https://groups.io/g/lawsofform/topic/logic_syllabus/99218507 ) ::: John Mingers ( https://groups.io/g/lawsofform/message/2326 ) <QUOTE JM:> In a previous post you mentioned the minimal negation operator. Is there also the converse of this, i.e. an operator which is true when exactly one of its arguments is true? Or is this just XOR? </QUOTE> Yes, the “just one true” operator is a very handy tool. We discussed it earlier under the headings of “genus and species relations” or “radio button logic”. Viewed as a venn diagram it describes a partition of the universe of discourse into mutually exclusive and exhaustive regions. Reading (x₁, ..., xₘ) to mean just one of x₁, ..., xₘ is false, the form ((x₁), ..., (xₘ)) means just one of x₁, ..., xₘ is true. For two logical variables, though, the cases “condense” or “degenerate” and saying “just one true” is the same thing as saying “just one false”. • ((x₁), (x₂)) = (x₁, x₂) = x₁ + x₂ = XOR(x₁, x₂). There's more information on the following pages. Minimal Negation Operators • https://oeis.org/wiki/Minimal_negation_operator Related Truth Tables • https://oeis.org/wiki/Minimal_negation_operator#Truth_tables Genus, Species, Pie Charts, Radio Buttons • https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-bu… Related Discussions • https://inquiryintoinquiry.com/?s=Radio+Buttons Regards, Jon