Monthly Archives: October 2021

Relation Theory • 5

Relation Theory Two further classes of incidence properties will prove to be of great utility. Regional Incidence Properties The definition of a local flag can be broadened from a point to a subset of a relational domain, arriving at the … Continue reading

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 5 Comments

Relation Theory • 4

Relation Theory • Local Incidence Properties The next few definitions of local incidence properties of relations are given at a moderate level of generality in order to show how they apply to -place relations.  In the sequel we’ll see what … Continue reading

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 3

Relation Theory • Definition It is convenient to begin with the definition of a -place relation, where is a positive integer. Definition.  A -place relation over the nonempty sets is a -tuple where is a subset of the cartesian product Several … Continue reading

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 2

Relation Theory • Preliminaries Two definitions of the relation concept are common in the literature.  Although it is usually clear in context which definition is being used at a given time, it tends to become less clear as contexts collide, … Continue reading

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 6 Comments

Relation Theory • 1

Here’s an introduction to Relation Theory geared to applications and taking a moderately general view at least as far as finite numbers of relational domains are concerned (-adic or -ary relations). Relation Theory This article treats relations from the perspective … Continue reading

Posted in C.S. Peirce, Category Theory, Dyadic Relations, Logic, Logic of Relatives, Logical Graphs, Mathematics, Nominalism, Peirce, Pragmatism, Realism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , | 6 Comments

Zeroth Law Of Semiotics • Discussion 1

Re: Zeroth Law Of Semiotics • Comment 2 Re: Laws of Form • John Mingers JM: Hmmm Sounds terribly like analytic philosophy to me. There are not real philosophical problems, it’s all just a matter of misuse of words. Have … Continue reading

Posted in C.S. Peirce, Denotation, Extension, Information = Comprehension × Extension, Liar Paradox, Logic, Nominalism, Peirce, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Syntax, Zeroth Law Of Semiotics | Tagged , , , , , , , , , , , , , , , | Leave a comment

All Liar, No Paradox • Discussion 2

Re: Laws of Form • James Bowery • John Mingers Dear James, John, et al. The questions arising in the present discussion take us back to the question of what we are using logical values like and for, which takes … Continue reading

Posted in Bertrand Russell, C.S. Peirce, Epimenides, Laws of Form, Liar Paradox, Logic, Logical Graphs, Mathematics, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

All Liar, No Paradox • Discussion 1

Re: Laws of Form • John Mingers JM: Several people have referred recently to the idea that Laws of Form, and particularly Chapter 11 with imaginary logical values, provides an answer to the problems Russell found in Principia Mathematica leading to … Continue reading

Posted in Bertrand Russell, C.S. Peirce, Epimenides, Laws of Form, Liar Paradox, Logic, Logical Graphs, Mathematics, Paradox, Pragmatics, Rhetoric, Semantics, Semiositis, Semiotics, Sign Relations, Spencer Brown, Syntax, Visualization | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Logical Graphs, Iconicity, Interpretation • Discussion 2

Re: Logical Graphs, Iconicity, Interpretation • 2 Re: Laws of Form • John Mingers JM: The quote you have given does not match the standard Peircean trichotomy of icon, index, symbol.  See this quote from [CP 4.447 …] Dear John, I … 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, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes • 33

Re: Ontolog Forum • William Frank William Frank asked a question about propositional attitudes and presuppositions. WF: Are there any formal languages, such as Common Logic, that adequately represent statements about propositions — statements from which, in natural reasoning, one can … Continue reading

Posted in Analogy, Bertrand Russell, C.S. Peirce, Dyadic Relations, Fixation of Belief, Information, Information = Comprehension × Extension, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Pragmatic Maxim, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , | Leave a comment