Animated Logical Graphs : 10

Re: Peirce List DiscussionCharles Pyle

Let’s consider Peirce’s logical graphs at the alpha level, the abstract forms of which can be interpreted for propositional logic.  I say “can be interpreted” advisedly because the system of logical graphs itself forms an uninterpreted syntax, the formulas of which have no fixed meaning until interpreted.  As it happens, the forms themselves do not determine their interpretations uniquely.  There is at minimum a degree of freedom that allows them to be interpreted in two different ways, corresponding to what Peirce called his entitative graphs and his existential graphs.

Bringing this to bear on the empty sheet of assertion we have the following facts:

The blank SA is a symbol and wants interpretation to give it a meaning.  Under the entitative reading (En) it means “false”.  Under the existential reading (Ex) it means “true”.  What in turn these “interpretants” mean requires a further, denotative interpretation relative to the universe of discourse at hand, “true” denoting the whole universe and “false” denoting the empty set.

Posted in Abstraction, Amphecks, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Complementarity, Computational Complexity, Constraint Satisfaction Problems, Diagrammatic Reasoning, Duality, Graph Theory, Interpretation, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Semiotics, Spencer Brown, Theorem Proving, Visualization, Zeroth Order Logic | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes : 3

It was fifty years ago this month that I first came North to Michigan, prospecting for a college to enter in the Fall.  I reached East Lansing in the middle of what would later be regaled as the Blizzard of ’67 and spiting all that various twists of fate led me to enroll the next Summer Term at Michigan State.

To be continued …

Posted in C.S. Peirce, Chemistry, Complementarity, Inquiry, Laws of Form, Logic, Mathematics, Peirce, Philosophy, Physics, Pragmatism, Quantum Mechanics, Relativity, Science, Scientific Method, Semiotics, Spencer Brown | Tagged , , , , , , , , , , , , , , , , | Leave a comment

Survey of Semiotic Theory Of Information • 2

This is a Survey of previous blog and wiki posts on the Semiotic Theory Of Information.  All my projects are exploratory in essence but this line of inquiry is more open-ended than most.  The question is:

What is information and how does it impact the spectrum of activities that answer to the name of inquiry?

Setting out on what would become his lifelong quest to explore and explain the “Logic of Science”, C.S. Peirce pierced the veil of historical confusions enclosing the issue and fixed on what he called the “laws of information” as the needed key to solving the puzzle.  This was in 1865 and 1866, detailed in his lectures at Harvard University and the Lowell Institute.

Fast forward to the present and I see the Big Question as follows.  Having gone through the exercise of comparing and contrasting Peirce’s theory of information, however much it remains in a rough-hewn state, with Shannon’s paradigm that so pervasively informs the ongoing revolution in our understanding and use of information today, I have reason to believe that Peirce’s idea is root and branch more general and has the potential, with due development, to resolve many mysteries that still bedevil our grasp of inference, information, and inquiry.

Inference, Information, Inquiry

Excursions

Blog Dialogs

Reference

  • Peirce, C.S. (1867), “Upon Logical Comprehension and Extension”.  Online.
Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Entropy, Epistemology, Fixation of Belief, Ignorance, Illusion, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Interpretive Frameworks, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Mental Models, Objective Frameworks, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Thirdness, Triadic Relations, Triadicity, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes : 2

Re: A Flash From The Past ⚡⚡⚡

My mind keeps flashing back to the days when I first encountered Peirce’s thought.  It was so fresh, it spoke to me like no other thinker’s thought I knew, and it held so much promise of setting aside all the old schisms that boggled the mind through the ages.

I feel that way about it still but communicating precisely what I find so revolutionary in Peirce’s thought remains a work in progress for me.

Many readers of Peirce share the opinion that there is something truly novel in his thought, a difference that makes a critical difference in the way we understand our thoughts and undertake our actions in its light.  The question has arisen once again, just what that difference might be.

So I’ll make another try at answering that …

Posted in C.S. Peirce, Inquiry, Logic, Mathematics, Peirce, Philosophy, Pragmatism, Science, Scientific Method, Semiotics | Tagged , , , , , , , , , | Leave a comment

Survey of Relation Theory • 3

In this Survey of previous blog and wiki posts on Relation Theory, relations are viewed from the perspective of combinatorics, in other words, as a topic in discrete mathematics, with special attention to finite structures and concrete set-theoretic constructions, many of which arise quite naturally in applications.  This approach to relation theory, or the theory of relations, is distinguished from, though closely related to, its study from the perspectives of abstract algebra on the one hand and formal logic on the other.

Elements

Relational Concepts

Relation Construction Relation Composition Relation Reduction
Relative Term Sign Relation Triadic Relation
Logic of Relatives Hypostatic Abstraction Continuous Predicate

Illustrations

Peirce’s 1870 “Logic of Relatives”

Peirce’s 1880 “Algebra of Logic” Chapter 3

Blog Dialogs

Resources

Posted in Algebra, C.S. Peirce, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Logic, Logic of Relatives, Mathematics, Model Theory, Peirce, Proof Theory, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Teridentity, Thirdness, Triadic Relations, Triadicity, Type Theory, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce and Democracy • 2

Re: Peirce List Discussion • GRHRJFSJA

The essential reading for answering that question — how the Protestant Ethic takes root in the hearts of those who set out merely seeking, if a bit too desperately, some assurance of personal salvation, and how they come to wander lost in the spiritual wasteland of Moneytheism that so rules our nation today — is The Protestant Ethic and the Spirit of Capitalism by Max Weber.  There are some links on the following pages:

  • Peirce and Democracy • (1)
  • Readings on Moneytheism • (1)(2)
  • Theory and Therapy of Representations • (1)(2)
Posted in C.S. Peirce, Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Max Weber, Observation, Peirce, Peirce List, Plato, Representation, Science, Semiotics, Society, Statistics | Tagged , , , , , , , , , , , , , , , , , , , | Leave a comment

Theory and Therapy of Representations • 2

December 19, 2011

In a complex society, people making decisions and taking actions at places remote from you have the power to affect your life in significant ways.  Those people are your government, no matter what spheres of influence they inhabit, private or public.  The only way you get a choice in that governance is if there are paths of feedback that allow you to affect the life of those decision makers and action takers in significant ways.  That is what accountability, response-ability, and representative government are all about.

Naturally, some people are against that.

In the United States there has been a concerted campaign for as long as I can remember — but even more concerted since the Reagan Regime — to get the People to abdicate their hold on The Powers That Be and just let some anonymous corporate entity send us the bill after the fact.  They keep trying to con the People into thinking they can starve the beast, to limit government, when what they are really doing is feeding the beast of corporate control, weakening their own power over the forces that govern their lives.

That is the road to perdition as far as responsible government goes.  There is not much of anything one leader or one administration can do unsupported if the People do not constantly demand a government of, by, and for the People.

Posted in Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Max Weber, Observation, Plato, Representation, Science, Semiotics, Society, Statistics | Tagged , , , , , , , , , , , , , , , , | 2 Comments