Functional Logic • Inquiry and Analogy

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Jon Awbrey

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Nov 14, 2021, 2:56:15 PMNov 14
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Cf: Functional Logic • Inquiry and Analogy • Preliminaries
http://inquiryintoinquiry.com/2021/11/14/functional-logic-inquiry-and-analogy-preliminaries/

All,

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, although normally in different orders.

Note on notation. The discussion to follow uses logical conjunctions, expressed in
the form of concatenated tuples e₁ … eₖ, and minimal negation operations, expressed in
the form of bracketed tuples (e₁, …, eₖ), 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 ( https://oeis.org/wiki/Logic_Syllabus )
• Boolean Function ( https://oeis.org/wiki/Boolean_function )
• Boolean-Valued Function ( https://oeis.org/wiki/Boolean-valued_function )
• Logical Conjunction ( https://oeis.org/wiki/Logical_conjunction )
• Minimal Negation Operator ( https://oeis.org/wiki/Minimal_negation_operator )

Regards,

Jon
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