Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 1

Posted on March 8, 2017 by Jon Awbrey

This is a Survey of blog and wiki posts on three elementary forms of inference, as recognized by a logical tradition extending from Aristotle through Charles S. Peirce.  Particular attention is paid to the way these inferential rudiments combine to form the more complex patterns of analogy and inquiry.

Blog Dialogs

More to be added later …

Posted in Abduction, Aristotle, C.S. Peirce, Deduction, Dewey, Discovery, Doubt, Fixation of Belief, Functional Logic, Icon Index Symbol, Induction, Inference, Information, Inquiry, Invention, Logic, Logic of Science, Mathematics, Morphism, Paradigmata, Paradigms, Pattern Recognition, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Scientific Inquiry, Scientific Method, Semiotics, Sign Relations, Surveys, Syllogism, Triadic Relations, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

Animated Logical Graphs • 10

Posted on March 3, 2017 by Jon Awbrey

Re: Peirce List Discussion • Charles 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 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 , , , , , , , , , , , , , , , , , , , , , , , , , | 11 Comments

The Difference That Makes A Difference That Peirce Makes • 3

Posted on February 28, 2017 by Jon Awbrey

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

Posted on February 27, 2017 by Jon Awbrey

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 obscuring the issue and fixed on what he called the “laws of information” as the 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 yet remains in a rough-hewn state, with Shannon’s paradigm so pervasively informing the ongoing revolution in our understanding and use of information, I have reason to believe Peirce’s idea is root and branch more general and has the potential, with due development, to resolve many mysteries still bedeviling our grasp of inference, information, and inquiry.

Inference, Information, Inquiry

Excursions

Blog Dialogs

Reference

Posted in Abduction, C.S. Peirce, Communication, Control, Cybernetics, Deduction, Determination, Discovery, Doubt, Epistemology, Fixation of Belief, Induction, Information, Information = Comprehension × Extension, Information Theory, Inquiry, Inquiry Driven Systems, Inquiry Into Inquiry, Interpretation, Invention, Knowledge, Learning Theory, Logic, Logic of Relatives, Logic of Science, Mathematics, Peirce, Philosophy, Philosophy of Science, Pragmatic Information, Probable Reasoning, Process Thinking, Relation Theory, Scientific Inquiry, Scientific Method, Semeiosis, Semiosis, Semiotic Information, Semiotics, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Uncertainty | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

The Difference That Makes A Difference That Peirce Makes • 2

Posted on February 8, 2017 by Jon Awbrey

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

Posted on January 17, 2017 by Jon Awbrey

In this Survey of 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 is distinct 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

Blog Series

Peirce’s 1870 “Logic of Relatives”

Peirce’s 1880 “Algebra of Logic” Chapter 3

Resources

Posted in Algebra, Algebra of Logic, C.S. Peirce, Category Theory, Combinatorics, Discrete Mathematics, Duality, Dyadic Relations, Foundations of Mathematics, Graph Theory, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Set Theory, Sign Relational Manifolds, Sign Relations, Surveys, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Peirce and Democracy • 2

Posted on December 30, 2016 by Jon Awbrey

Re: Peirce List • Gary Richmond • Helmut Raulien • John Sowa • Jon Awbrey

The essential reading for understanding the unbridled avarice of capitalism — how the Gospel Of Greed takes root in the hearts of those who set out initially seeking only, if a bit too desperately, some assurance of personal salvation, and how they come to wander lost in the spiritual wasteland of Moneytheism so ruling our nation today — is The Protestant Ethic and the Spirit of Capitalism by Max Weber.  There are a few 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 , , , , , , , , , , , , , , , , , , , | 2 Comments

Theory and Therapy of Representations • 2

Posted on December 19, 2016 by Jon Awbrey

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 govern your life, they 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 permitting 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.

cc: Conceptual Graphs • Cybernetics • Laws of Form • Ontolog Forum
cc: FB | Cybernetics • Structural Modeling • Systems Science

Posted in Cybernetics, Democracy, Economics, Education, Expectation, Governance, Information, Inquiry, Intention, Justice, Law, Logic, Observation, Plato, Representation, Science, Semiosis, Semiotics, Society, Statistics, Virtue | Tagged , , , , , , , , , , , , , , , , , , , , | 5 Comments

Time, Topology, Differential Logic • 6

Posted on November 30, 2016 by Jon Awbrey

Re: Peirce List • Edwina Taborsky • John Sowa • Jon Awbrey • Jeff Downard

Let me see if I can get back in the saddle on this topic, the dormitive virtues of tryptophan and a few pounds added notwithstanding.

I was addressing the following question from Jeffrey Brian Downard:

I wanted to see if anyone have might suggestions for thinking about the analogy between:

  1. mathematical models of the differentiation of spaces starting with a vague continuum of undifferentiated dimensions and trending towards spaces having determinate dimensions
  2. models for logic involving similar sorts of dimensions?

How might we understand processes of differentiation of dimensions in the case of logic?

By way of review, here are my blog posts on the discussion so far:

  • Time, Topology, Differential Logic • (1) • (2) • (3) • (4) • (5)

We can now get back to preparing the ground required to tackle Jeff’s question.

Resources

Posted in C.S. Peirce, Change, Differential Logic, Dynamical Systems, Inquiry, Inquiry Driven Systems, Logic, Logical Graphs, Mathematics, Peirce, Propositional Calculus, Semiotics, Systems Theory, Time, Topology | Tagged , , , , , , , , , , , , , , | 5 Comments

Peirce and Democracy • 1

Posted on November 23, 2016 by Jon Awbrey

Re: Peirce List • Gary Richmond • Jon Awbrey

In my mind the connection between Peirce and Democracy has long revolved around the concept of representation.

Representation in its semiotic sense has to do with signs that represent pragmatic objects to agents and communities of interpretation.

Representation in its political sense has to do with forms of government which address the res publica, the public concern, through elected representatives who represent, hopefully, the good will and the best information of the public at large in their stations at the rudders of the ship of state.  Here the twin senses of representation converge on the common root meaning of the words cybernetics and government.

I have written a lot about this twofold sense of representation over the years but weeks of watching “The Death of a Nation” on TV have left me too dispirited to say any more on the subject.

I did happen on a recent blog post that seems to fit here —

The question for our day remains —

  • What are the forces that distort our representations of what’s observed, what’s expected, and what’s intended?
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 , , , , , , , , , , , , , , , , , , , | 5 Comments