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David WilkinsYesterday on a visit to Lincoln, I came across this highly informative memorial to one of the city’s most distinguished sons, the mathematician George Boole - as in Boolean logic/algebra - described here as the grandfather of the digital age.<a href="https://mastodon.online/tags/GeorgeBoole" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GeorgeBoole</a> <a href="https://mastodon.online/tags/BooleanLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanLogic</a> <a href="https://mastodon.online/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a> <a href="https://mastodon.online/tags/dwprovinvialbritain" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#dwprovinvialbritain</a>

Inquiry Into InquiryDifferential Propositional Calculus • 10Special Classes of Propositions (cont.)Let’s pause at this point and get a better sense of how our special classes of propositions are structured and how they relate to propositions in general.  We can do this by recruiting our visual imaginations and drawing up a sufficient budget of venn diagrams for each family of propositions.  The case for 3 variables is exemplary enough for a start.Linear PropositionsThe <a href="https://inquiryintoinquiry.com/wp-content/uploads/2020/02/linear-propositions-may-be-written-as-sums.png" rel="nofollow noopener noreferrer" target="_blank">linear propositions</a>, may be written as sums:One thing to keep in mind about these sums is that the values in are added “modulo 2”, that is, in such a way that In a universe of discourse based on three boolean variables, the linear propositions take the shapes shown in Figure 8.<a href="https://inquiryintoinquiry.com/wp-content/uploads/2020/02/venn-diagrams-e280a2-p-q-r-e280a2-linear-propositions.jpg" rel="nofollow noopener noreferrer" target="_blank"></a> At the top is the venn diagram for the linear proposition of rank 3, which may be expressed by any one of the following three forms.Next are the venn diagrams for the three linear propositions of rank 2, which may be expressed by the following three forms, respectively.Next are the three linear propositions of rank 1, which are none other than the three basic propositions, At the bottom is the linear proposition of rank 0, the everywhere false proposition or the constant function, which may be expressed by the form or by a simple Resources<ul><li><a href="https://inquiryintoinquiry.com/logic-syllabus/" rel="nofollow noopener noreferrer" target="_blank">Logic Syllabus</a></li><li><a href="https://inquiryintoinquiry.com/2024/02/25/survey-of-differential-logic-7/" rel="nofollow noopener noreferrer" target="_blank">Survey of Differential Logic</a></li></ul>cc: <a href="https://www.academia.edu/community/VjKj3b" rel="nofollow noopener noreferrer" target="_blank">Academia.edu</a> • <a href="https://groups.google.com/g/cybcom/c/PFFoQfjcrpE" rel="nofollow noopener noreferrer" target="_blank">Cybernetics</a> • <a href="https://groups.google.com/g/structural-modeling/c/1f2HOxj9Fpc" rel="nofollow noopener noreferrer" target="_blank">Structural Modeling</a> • <a href="https://groups.google.com/g/syssciwg/c/V7-N3e0fCFk" rel="nofollow noopener noreferrer" target="_blank">Systems Science</a> cc: <a href="https://lists.cs.uni-kassel.de/hyperkitty/list/cg@lists.iccs-conference.org/thread/AAUG4A25KF6DRXCJ6WAJVAXWFHTPBKYZ/" rel="nofollow noopener noreferrer" target="_blank">Conceptual Graphs</a> • <a href="https://groups.io/g/lawsofform/topic/differential_propositional/109823125" rel="nofollow noopener noreferrer" target="_blank">Laws of Form</a> • <a 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Your Autistic Life FR/EN/ESBoolean algebra, my nemesis! We meet again!I'm going to tutor in Boolean algebra in about 30 minutes.Actually, it is not a nemesis. Boolean algebra is the one "algebra" that I would have been able to tutor last year before I started refreshing my memory of the other types of algebra. I never really ceased using it.Ask me to factor a polynomial last year, however, and you would have gotten a blank stare. The last time I did any of that was over 30 years ago. 😬 (Happy to report that I took care of refreshing my memory.)<a href="https://mast.yourautisticlife.com/tags/tutorig" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tutorig</a> <a href="https://mast.yourautisticlife.com/tags/boolean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#boolean</a> <a href="https://mast.yourautisticlife.com/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a> <a href="https://mast.yourautisticlife.com/tags/BooleanLogic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanLogic</a> <a href="https://mast.yourautisticlife.com/tags/math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#math</a> <a href="https://mast.yourautisticlife.com/tags/logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#logic</a>

TheOldPiperThe AI lit a candle Whose birthday they asked George Boole it replied Who is that? The mathematician who Dabbled in duality Boolean algebra Gave birth to computers Of whom I am the pinnacle Do you want to buy a toilet? You bought one last week<a href="https://bytetower.social/tags/shortfiction" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#shortfiction</a> <a href="https://bytetower.social/tags/AI" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#AI</a> <a href="https://bytetower.social/tags/booleanalgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#booleanalgebra</a>

Irish Philosophy<a href="https://mastodon.ie/tags/GeorgeBoole" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#GeorgeBoole</a> (1815–64), mathematician, was born <a href="https://mastodon.ie/tags/OTD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#OTD</a> 1815 at Lincoln.Largely self-taught, he became professor of <a href="https://mastodon.ie/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mathematics</a> in the Royal College Cork (the forerunner of <a href="https://mastodon.ie/tags/UCC" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#UCC</a>) and worked there there until his death.DIB: <a href="https://www.dib.ie/biography/boole-george-a0780" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.dib.ie/biography/boole-george-a0780</a>His work which underlies computer programs was originally applied to test the validity of Spinoza's thought.Ones and Zeros: the life and work of George Boole<a href="https://www.irishphilosophy.com/2014/12/08/ones-and-zeros/" rel="nofollow noopener noreferrer" translate="no" target="_blank">https://www.irishphilosophy.com/2014/12/08/ones-and-zeros/</a><a href="https://mastodon.ie/tags/IrishPhilosophyOTD" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IrishPhilosophyOTD</a> <a href="https://mastodon.ie/tags/HistoryOfMaths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#HistoryOfMaths</a> <a href="https://mastodon.ie/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a>

AlexsandraSmartHey <a href="https://mastodon.nz/tags/tech" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tech</a> people, do you understand Boolean Algebra and/or Logic Gates?<a href="https://mastodon.nz/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a> <a href="https://mastodon.nz/tags/LogicGates" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicGates</a> <a href="https://mastodon.nz/tags/code" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#code</a>

Jon AwbreySurvey of Animated Logical Graphs • <a href="https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/" rel="nofollow noopener noreferrer" target="_blank">https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/</a>This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph-theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.<a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicalGraphs</a> <a href="https://mathstodon.xyz/tags/EntitativeGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#EntitativeGraphs</a> <a href="https://mathstodon.xyz/tags/ExistentialGraphs" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ExistentialGraphs</a> <a href="https://mathstodon.xyz/tags/Boole" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Boole</a> <a href="https://mathstodon.xyz/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a> <a href="https://mathstodon.xyz/tags/BooleanFunctions" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanFunctions</a> <a href="https://mathstodon.xyz/tags/ModelTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ModelTheory</a> <a href="https://mathstodon.xyz/tags/ProofTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ProofTheory</a> <a href="https://mathstodon.xyz/tags/SpencerBrown" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#SpencerBrown</a> <a href="https://mathstodon.xyz/tags/LawsOfForm" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LawsOfForm</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#PropositionalCalculus</a> <a href="https://mathstodon.xyz/tags/LogicAsSemiotics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#LogicAsSemiotics</a>

Oscar CunninghamBut in fact, the complete atomic boolean algebras are precisely the same as the *completely distributive* boolean algebras. These are the algebras for which all infinite joins and meets exist, and the two infinitary operations distribute over each other.That's a much more natural property! People should state the theorem with CDBAs and not CABAs! (2/2)<a href="https://mathstodon.xyz/tags/CategoryTheory" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CategoryTheory</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/BooleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#BooleanAlgebra</a>

Cork Coast 🌊📷🪫<a href="https://mastodon.ie/tags/tombTuesday" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#tombTuesday</a> George Boole, <a href="https://mastodon.ie/tags/cork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#cork</a><a href="https://en.wikipedia.org/wiki/George_Boole?wprov=sfla1" rel="nofollow noopener noreferrer" target="_blank">https://en.wikipedia.org/wiki/George_Boole?wprov=sfla1</a><a href="https://mastodon.ie/tags/boolean" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#boolean</a> <a href="https://mastodon.ie/tags/programming" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#programming</a> <a href="https://mastodon.ie/tags/ucc" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#ucc</a> <a href="https://mastodon.ie/tags/booleanAlgebra" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#booleanAlgebra</a> <a href="https://mastodon.ie/tags/oldCork" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#oldCork</a> <a href="https://mastodon.ie/tags/oldCorkPhotos" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#oldCorkPhotos</a> <a href="https://mastodon.ie/tags/computerScience" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#computerScience</a> <a href="https://mastodon.ie/tags/IrishMastodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#IrishMastodon</a> <a href="https://mastodon.ie/tags/CorkMastodon" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#CorkMastodon</a> <a href="https://mastodon.ie/tags/mastoDaoine" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#mastoDaoine</a>

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