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Jon AwbreyFunctional Logic • Inquiry and Analogy • Preliminaries • <a href="https://inquiryintoinquiry.com/2023/06/20/functional-logic-inquiry-and-analogy-preliminaries-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/06/20/functional-logic-inquiry-and-analogy-preliminaries-2/</a>Functional Logic • Inquiry and Analogy • <a href="https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Functional_Logic_%E2%80%A2_Inquiry_and_Analogy</a>This report discusses C.S. Peirce's treatment of analogy, placing it in relation to his overall theory of inquiry. We begin by introducing three basic types of reasoning Peirce adopted from classical logic. In Peirce's analysis both inquiry and analogy are complex programs of logical inference which develop through stages of these three types, though normally in different orders.Note on notation. The discussion to follow uses logical conjunctions, expressed in the form of concatenated tuples \(e_1 \ldots e_k,\) and minimal negation operations, expressed in the form of bracketed tuples \(\texttt{(} e_1 \texttt{,} \ldots \texttt{,} e_k \texttt{)},\) as the principal expression-forming operations of a calculus for boolean-valued functions, that is, for propositions. The expressions of this calculus parse into data structures whose underlying graphs are called “cacti” by graph theorists. Hence the name “cactus language” for this dialect of propositional calculus.Resources —Logic Syllabus • <a href="https://oeis.org/wiki/Logic_Syllabus" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Logic_Syllabus</a>Boolean Function • <a href="https://oeis.org/wiki/Boolean_function" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Boolean_function</a>Boolean-Valued Function • <a href="https://oeis.org/wiki/Boolean-valued_function" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Boolean-valued_function</a>Logical Conjunction • <a href="https://oeis.org/wiki/Logical_conjunction" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Logical_conjunction</a>Minimal Negation Operator • <a href="https://oeis.org/wiki/Minimal_negation_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Minimal_negation_operator</a><a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/Abduction" class="mention hashtag" rel="tag">#Abduction</a> <a href="https://mathstodon.xyz/tags/Deduction" class="mention hashtag" rel="tag">#Deduction</a> <a href="https://mathstodon.xyz/tags/Induction" class="mention hashtag" rel="tag">#Induction</a> <a href="https://mathstodon.xyz/tags/Analogy" class="mention hashtag" rel="tag">#Analogy</a> <a href="https://mathstodon.xyz/tags/Inquiry" class="mention hashtag" rel="tag">#Inquiry</a> <a href="https://mathstodon.xyz/tags/BooleanFunction" class="mention hashtag" rel="tag">#BooleanFunction</a> <a href="https://mathstodon.xyz/tags/LogicalConjunction" class="mention hashtag" rel="tag">#LogicalConjunction</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperator" class="mention hashtag" rel="tag">#MinimalNegationOperator</a> <a href="https://mathstodon.xyz/tags/LogicalGraph" class="mention hashtag" rel="tag">#LogicalGraph</a> <a href="https://mathstodon.xyz/tags/CactusLanguage" class="mention hashtag" rel="tag">#CactusLanguage</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#PropositionalCalculus</a>

Jon AwbreyLogic Syllabus • Discussion 1 • <a href="https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2023/06/02/logic-syllabus-discussion-1/</a>Re: Logic Syllabus ( <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/logic-syllabus/</a> ) Re: Laws of Form ( <a href="https://groups.io/g/lawsofform/topic/logic_syllabus/99218507" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://groups.io/g/lawsofform/topic/logic_syllabus/99218507</a> ) Re: John Mingers ( <a href="https://groups.io/g/lawsofform/message/2326" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://groups.io/g/lawsofform/message/2326</a> )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?❞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 in the form of a venn diagram it describes a partition of the universe of discourse into mutually exclusive and exhaustive regions.Reading \(\texttt{(} x_1 \texttt{,} \ldots \texttt{,} x_m \texttt{)}\) to mean just one of \(x_1, \ldots, x_m\) is false, the form \(\texttt{((} x_1 \texttt{),} \ldots \texttt{,(} x_m \texttt{))}\) means just one of \(x_1, \ldots, x_m\) 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”.\[\texttt{((} x_1 \texttt{),(} x_2 \texttt{))} = \texttt{(} x_1 \texttt{,} x_2 \texttt{)} = x_1 + x_2 = \mathrm{xor} (x_1, x_2).\]There's more information on the following pages.Minimal Negation Operators • <a href="https://oeis.org/wiki/Minimal_negation_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Minimal_negation_operator</a>Related Truth Tables • <a href="https://oeis.org/wiki/Minimal_negation_operator#Truth_tables" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Minimal_negation_operator#Truth_tables</a>Genus, Species, Pie Charts, Radio Buttons • <a href="https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-buttons-1/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2021/11/10/genus-species-pie-charts-radio-buttons-1/</a>Related Discussions • <a href="https://inquiryintoinquiry.com/?s=Radio+Buttons" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/?s=Radio+Buttons</a><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicSyllabus" class="mention hashtag" rel="tag">#LogicSyllabus</a> <a href="https://mathstodon.xyz/tags/BooleanDomain" class="mention hashtag" rel="tag">#BooleanDomain</a> <a href="https://mathstodon.xyz/tags/BooleanFunction" class="mention hashtag" rel="tag">#BooleanFunction</a> <a href="https://mathstodon.xyz/tags/BooleanValuedFunction" class="mention hashtag" rel="tag">#BooleanValuedFunction</a> <a href="https://mathstodon.xyz/tags/Peirce" class="mention hashtag" rel="tag">#Peirce</a> <a href="https://mathstodon.xyz/tags/LogicalGraph" class="mention hashtag" rel="tag">#LogicalGraph</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperator" class="mention hashtag" rel="tag">#MinimalNegationOperator</a> <a href="https://mathstodon.xyz/tags/ExclusiveDisjunction" class="mention hashtag" rel="tag">#ExclusiveDisjunction</a> <a href="https://mathstodon.xyz/tags/XOR" class="mention hashtag" rel="tag">#XOR</a> <a href="https://mathstodon.xyz/tags/CactusLanguage" class="mention hashtag" rel="tag">#CactusLanguage</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#PropositionalCalculus</a> <a href="https://mathstodon.xyz/tags/RadioButtonLogic" class="mention hashtag" rel="tag">#RadioButtonLogic</a> <a href="https://mathstodon.xyz/tags/TruthTable" class="mention hashtag" rel="tag">#TruthTable</a>

Jon AwbreyLogic Syllabus • 3 • <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/logic-syllabus/</a>Logical Concepts • <a href="https://oeis.org/wiki/Logic_Syllabus#Logical_concepts" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Logic_Syllabus#Logical_concepts</a>Ampheck • <a href="https://oeis.org/wiki/Ampheck" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Ampheck</a> Boolean Domain • <a href="https://oeis.org/wiki/Boolean_domain" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Boolean_domain</a> Boolean Function • <a href="https://oeis.org/wiki/Boolean_function" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Boolean_function</a> Boolean-Valued Function • <a href="https://oeis.org/wiki/Boolean-valued_function" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Boolean-valued_function</a> Differential Logic • <a href="https://oeis.org/wiki/Differential_logic" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Differential_logic</a> Logical Graph • <a href="https://oeis.org/wiki/Logical_Graphs" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Logical_Graphs</a> Minimal Negation Operator • <a href="https://oeis.org/wiki/Minimal_negation_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Minimal_negation_operator</a> Multigrade Operator • <a href="https://oeis.org/wiki/Multigrade_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Multigrade_operator</a> Parametric Operator • <a href="https://oeis.org/wiki/Parametric_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Parametric_operator</a> Peirce's Law • <a href="https://oeis.org/wiki/Peirce%27s_law" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Peirce%27s_law</a> Propositional Calculus • <a href="https://oeis.org/wiki/Propositional_calculus" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Propositional_calculus</a> Sole Sufficient Operator • <a href="https://oeis.org/wiki/Sole_sufficient_operator" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Sole_sufficient_operator</a> Truth Table • <a href="https://oeis.org/wiki/Truth_table" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Truth_table</a> Universe of Discourse • <a href="https://oeis.org/wiki/Universe_of_discourse" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Universe_of_discourse</a> Zeroth Order Logic • <a href="https://oeis.org/wiki/Zeroth_order_logic" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://oeis.org/wiki/Zeroth_order_logic</a><a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicSyllabus" class="mention hashtag" rel="tag">#LogicSyllabus</a> <a href="https://mathstodon.xyz/tags/Ampheck" class="mention hashtag" rel="tag">#Ampheck</a> <a href="https://mathstodon.xyz/tags/BooleanDomain" class="mention hashtag" rel="tag">#BooleanDomain</a> <a href="https://mathstodon.xyz/tags/BooleanFunction" class="mention hashtag" rel="tag">#BooleanFunction</a> <a href="https://mathstodon.xyz/tags/BooleanValuedFunction" class="mention hashtag" rel="tag">#BooleanValuedFunction</a> <a href="https://mathstodon.xyz/tags/DifferentialLogic" class="mention hashtag" rel="tag">#DifferentialLogic</a> <a href="https://mathstodon.xyz/tags/LogicalGraph" class="mention hashtag" rel="tag">#LogicalGraph</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperator" class="mention hashtag" rel="tag">#MinimalNegationOperator</a> <a href="https://mathstodon.xyz/tags/MultigradeOperator" class="mention hashtag" rel="tag">#MultigradeOperator</a> <a href="https://mathstodon.xyz/tags/ParametricOperator" class="mention hashtag" rel="tag">#ParametricOperator</a> <a href="https://mathstodon.xyz/tags/PeircesLaw" class="mention hashtag" rel="tag">#PeircesLaw</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#PropositionalCalculus</a> <a href="https://mathstodon.xyz/tags/SoleSufficientOperator" class="mention hashtag" rel="tag">#SoleSufficientOperator</a> <a href="https://mathstodon.xyz/tags/TruthTable" class="mention hashtag" rel="tag">#TruthTable</a> <a href="https://mathstodon.xyz/tags/UniverseOfDiscourse" class="mention hashtag" rel="tag">#UniverseOfDiscourse</a> <a href="https://mathstodon.xyz/tags/ZerothOrderLogic" class="mention hashtag" rel="tag">#ZerothOrderLogic</a>

Jon Awbrey<a href="https://mathstodon.xyz/tags/ThemeOneProgram" class="mention hashtag" rel="tag">#ThemeOneProgram</a> • <a href="https://mathstodon.xyz/tags/JetsAndSharks" class="mention hashtag" rel="tag">#JetsAndSharks</a> 2.1 • <a href="https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/</a>Our <a href="https://mathstodon.xyz/tags/CactusGraph" class="mention hashtag" rel="tag">#CactusGraph</a> bears a vocabulary of \(41\) <a href="https://mathstodon.xyz/tags/LogicalTerms" class="mention hashtag" rel="tag">#LogicalTerms</a>, each denoting a <a href="https://mathstodon.xyz/tags/BooleanVariable" class="mention hashtag" rel="tag">#BooleanVariable</a>, so our proposition, call it \(``q",\) is a <a href="https://mathstodon.xyz/tags/BooleanFunction" class="mention hashtag" rel="tag">#BooleanFunction</a> \(q:\mathbb{B}^{41}\to\mathbb{B}.\) Since \(2^{41}=2,199,023,255,552,\) its <a href="https://mathstodon.xyz/tags/TruthTable" class="mention hashtag" rel="tag">#TruthTable</a> has \(>\) 2 trillion rows and its <a href="https://mathstodon.xyz/tags/VennDiagram" class="mention hashtag" rel="tag">#VennDiagram</a> has that many cells. There are \(2^{2^{41}}\) functions \(f:\mathbb{B}^{41}\to\mathbb{B}\) and \(q\) is just one of them.<a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalGraphs" class="mention hashtag" rel="tag">#LogicalGraphs</a>

Jon Awbrey<a href="https://mathstodon.xyz/tags/LogicSyllabus" class="mention hashtag" rel="tag">#LogicSyllabus</a> • <a href="https://inquiryintoinquiry.com/logic-syllabus/" target="_blank" rel="nofollow noopener noreferrer" translate="no">https://inquiryintoinquiry.com/logic-syllabus/</a>This page serves as a focal node for a collection of related resources.<a href="https://mathstodon.xyz/tags/Logic" class="mention hashtag" rel="tag">#Logic</a> <a href="https://mathstodon.xyz/tags/LogicalOperators" class="mention hashtag" rel="tag">#LogicalOperators</a><a href="https://mathstodon.xyz/tags/LogicalConjunction" class="mention hashtag" rel="tag">#LogicalConjunction</a> <a href="https://mathstodon.xyz/tags/LogicalDisjunction" class="mention hashtag" rel="tag">#LogicalDisjunction</a> <a href="https://mathstodon.xyz/tags/ExclusiveDisjunction" class="mention hashtag" rel="tag">#ExclusiveDisjunction</a> <a href="https://mathstodon.xyz/tags/LogicalEquality" class="mention hashtag" rel="tag">#LogicalEquality</a> <a href="https://mathstodon.xyz/tags/LogicalImplication" class="mention hashtag" rel="tag">#LogicalImplication</a> <a href="https://mathstodon.xyz/tags/LogicalNegation" class="mention hashtag" rel="tag">#LogicalNegation</a> <a href="https://mathstodon.xyz/tags/LogicalNAND" class="mention hashtag" rel="tag">#LogicalNAND</a> <a href="https://mathstodon.xyz/tags/LogicalNNOR" class="mention hashtag" rel="tag">#LogicalNNOR</a><a href="https://mathstodon.xyz/tags/LogicalConcepts" class="mention hashtag" rel="tag">#LogicalConcepts</a><a href="https://mathstodon.xyz/tags/Ampheck" class="mention hashtag" rel="tag">#Ampheck</a> <a href="https://mathstodon.xyz/tags/SoleSufficientOperator" class="mention hashtag" rel="tag">#SoleSufficientOperator</a> <a href="https://mathstodon.xyz/tags/BooleanDomain" class="mention hashtag" rel="tag">#BooleanDomain</a> <a href="https://mathstodon.xyz/tags/UniverseOfDiscourse" class="mention hashtag" rel="tag">#UniverseOfDiscourse</a> <a href="https://mathstodon.xyz/tags/LogicalGraph" class="mention hashtag" rel="tag">#LogicalGraph</a> <a href="https://mathstodon.xyz/tags/PropositionalCalculus" class="mention hashtag" rel="tag">#PropositionalCalculus</a> <a href="https://mathstodon.xyz/tags/MinimalNegationOperator" class="mention hashtag" rel="tag">#MinimalNegationOperator</a> <a href="https://mathstodon.xyz/tags/TruthTable" class="mention hashtag" rel="tag">#TruthTable</a> <a href="https://mathstodon.xyz/tags/BooleanFunction" class="mention hashtag" rel="tag">#BooleanFunction</a> <a href="https://mathstodon.xyz/tags/BooleanValuedFunction" class="mention hashtag" rel="tag">#BooleanValuedFunction</a>

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