Category Archives: Logic

Information = Comprehension × Extension • Selection 4

Posted on October 8, 2024 by Jon Awbrey

Selection 3 showed how it was possible to combine symbols in such a way as to end up with species of representation outside the class of genuine symbols and introduced the concepts of conjunctive terms and disjunctive terms to describe … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 5 Comments

Information = Comprehension × Extension • Selection 3

Posted on October 7, 2024 by Jon Awbrey

Selection 3 opens with Peirce remarking a critical property of genuine symbols — the class of symbols is not closed under combinations.  In particular, there are logical conjunctions of symbols and logical disjunctions of symbols which are not themselves genuine … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 6 Comments

Information = Comprehension × Extension • Selection 2

Posted on October 6, 2024 by Jon Awbrey

Over the course of Selection 1 Peirce introduces the ideas he needs to answer stubborn questions about the validity of scientific inference.  Briefly put, the validity of scientific inference depends on the ability of symbols to express superfluous comprehension, the … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 5 Comments

Information = Comprehension × Extension • Selection 1

Posted on October 5, 2024 by Jon Awbrey

Our first text comes from Peirce’s Lowell Lectures of 1866, titled “The Logic of Science, or, Induction and Hypothesis”.  I still remember the first time I read these words and the light that lit up the page and my mind. … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 8 Comments

Information = Comprehension × Extension • Preamble

Posted on October 4, 2024 by Jon Awbrey

Eight summers ago I hit on what struck me as a new insight into one of the most recalcitrant problems in Peirce’s semiotics and logic of science, namely, the relation between “the manner in which different representations stand for their … Continue reading →

Posted in Abduction, C.S. Peirce, Comprehension, Deduction, Extension, Hypothesis, Icon Index Symbol, Induction, Inference, Information = Comprehension × Extension, Inquiry, Intension, Logic, Peirce's Categories, Pragmatic Semiotic Information, Pragmatism, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , | 3 Comments

Pragmatic Cosmos • 1

Posted on September 21, 2024 by Jon Awbrey

Re: Michael Harris • Not About Fibonacci I have often reflected on the interminglings of the main three normative sciences.  In one of my earliest meditations I saw Beauty, Goodness, and Truth as the intersecting circles of a Venn diagram, with the … Continue reading →

Posted in Aesthetics, Anthem, Arete, Beauty, C.S. Peirce, Ethics, Knowledge, Logic, Mathematics, Normative Science, Pragmata, Pragmatic Cosmos, Pragmatism, Summum Bonum, Truth, Virtue | Tagged , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • Discussion 11

Posted on September 19, 2024 by Jon Awbrey

Re: Logical Graphs • Formal Development Re: Laws of Form • Lyle Anderson LA: What does it mean to assign a label or name to a node of the Logical Graph? In LoF, the variables of the algebra represent unknown … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Sign Relations, Spencer Brown, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • Discussion 10

Posted on September 18, 2024 by Jon Awbrey

Re: Logical Graphs • Formal Development Re: Laws of Form • Armahedi Mahzar AM: GSB took J1 : (a(a)) =   as the first algebraic primitive and the second one is transposition so he only need only 2 primitives for … Continue reading →

Posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Propositional Equation Reasoning Systems, Relation Theory, Semiotics, Sign Relations, Spencer Brown, Topology, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • Formal Development 8

Posted on September 16, 2024 by Jon Awbrey

Exemplary Proofs Using no more than the axioms and theorems recorded so far, it is possible to prove a multitude of much more complex theorems.  A number of all‑time favorites are linked below. Peirce’s Law Blog Series • (1) • … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments

Logical Graphs • Formal Development 7

Posted on September 15, 2024 by Jon Awbrey

Frequently Used Theorems (concl.) C3.  Dominant Form Theorem The third of the frequently used theorems of service to this survey is one Spencer Brown annotates as Consequence 3 (C3) or Integration.  A better mnemonic might be dominance and recession theorem (DART), but … Continue reading →

Posted in Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Deduction, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Visualization | Tagged , , , , , , , , , , , , , , , , | 4 Comments