Animated Logical Graphs : 4

Re: Peirce List DiscussionHelmut Raulien

Although it’s fair to say that most of my university coursework leaned to the theoretical side of things, I did cobble together a respectable enough background in computing, statistics, and industrial-organizational styles of systems and simulation research that most of the work I actually got paid for later on, aside from teaching, involved getting down and dirty with real world empirical data, most of it from a wide variety of bio-sciences, health sciences, and social sciences.  These experiences kept practical applications to real world scientific inquiry in the forefront of my mind all through the time I developed my series of learning and reasoning programs.

As far as concrete examples go, I have a few.  The more complex ones tend to come from this or that highly specialized research study, and it’s been my experience over the years that applications like that tend to bore everyone to tears but the very specialists who love that precise sort of data.

So exposition is forced to begin with simple examples, very often falling into the class of “toy worlds” problems that AI researchers of old were wont to bandy about.

You may find a series of examples like that, proceeding from the very simplest to the moderately complex, in the User Guide that I wrote up for my Theme One Program toward the end of the 1980s.

Applications of my program to Constraint Satisfaction Problems (CSPs) are briefly detailed in the following project report from the mid 1990s.

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs : 3

Re: Peirce List DiscussionHelmut Raulien

I have a little more leisure now to begin the process of climbing back into the saddle, so let me see where we left off …

Try looking into the article I linked before:

Or my first couple of blog posts on Logical Graphs:

There are literally decades of thought and work that went into those, and if they do not engage the reader in the excitement of possible future developments then I would sorely appreciate any feedback on where and why they fail to do so.

George Spencer Brown is one of the few writers I’ve run across in the time since my first encounter with Peirce’s logical graphs who truly grasped the full depth of Peirce’s insight into logic, a vision that pierced the veil of logical interpretations, entitative and existential, to the deep formal unity between them.  That is one of the reasons I’ve made an effort to treat the two interpretations in parallel as far as I was able.  It is an extremely enticing research question to me whether that symmetry is necessarily broken as we pass from propositional to quantificational logic, or whether there is some way it may or need be maintained.

But that is a question for the future …

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Pragmatism About Theoretical Entities : 1

By theoretical entities I mean things like classes, properties, qualities, sets, situations, or states of affairs, in general, the putative denotations of theoretical concepts, formulas, sentences, terms, or treatises, in brief, the ostensible objects of signs.

A conventional statement of Ockham’s Razor is, “Entities shall not be multiplied beyond necessity.”

That is still good advice, as practical maxims go, but a pragmatist will read that as practical necessity or utility, qualifying the things that we need to posit in order to think at all, without getting lost in endless circumlocutions of perfectly good notions.

Nominalistic revolts are well-intentioned when they naturally arise, seeking to clear away the clutter of ostentatious entities ostensibly denoted by signs that do not denote.

But that is no different in its basic intention than what Peirce sought to do, clarifying metaphysics though the application of the Pragmatic Maxim.

Taking the long view, then, pragmatism can be seen as a moderate continuation of Ockham’s revolt, substituting a principled revolution for what tends to descend to a reign of terror.

Posted in Essentialism, Logic, Metaphysics, Method, Nominalism, Ockham, Ockham's Razor, Peirce, Philosophy, Philosophy of Science, Pragmatic Maxim, Pragmatism | Tagged , , , , , , , , , , , | Leave a comment

Animated Logical Graphs : 2

Re: Peirce List DiscussionJim Willgoose

It’s almost 50 years now since I first encountered the volumes of Peirce’s Collected Papers in the math library at Michigan State, and shortly afterwards a friend called my attention to the entry for Spencer Brown’s Laws of Form in the Whole Earth Catalog and I sent off for it right away.  I would spend the next decade just beginning to figure out what either one of them was talking about in the matter of logical graphs and I would spend another decade after that developing a program, first in Lisp and then in Pascal, that turned graph-theoretic data structures formed on their ideas to good purpose as the basis of its reasoning engine.  I thought it might contribute to a number of long-running and ongoing discussions if I could articulate what I think I learned from that experience.

So I’ll try to keep focused on that.

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Animated Logical Graphs : 1

For Your Musement …

Here are some animations I made up to illustrate several different styles of proof in an extended topological variant of Peirce’s Alpha Graphs for propositional logic.

Proof Animations

See the following article for a full discussion of this type of logical graph.

Logical Graphs

Additional Resources

Posted in Amphecks, Analogy, Animata, Automated Research Tools, Boolean Algebra, Boolean Functions, Cactus Graphs, Deduction, Diagrammatic Reasoning, Duality, Form, Graph Theory, Iconicity, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Model Theory, Peirce, Peirce's Law, Praeclarum Theorema, Pragmatism, Proof Theory, Propositional Calculus, Semiotics, Spencer Brown, Theorem Proving, Visualization | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Looking Back On 2014

The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.

Here's an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 25,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 9 sold-out performances for that many people to see it.

Click here to see the complete report.

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☝ What Ariadne Said To Theseus ☟

☞ You have to understand, the Minotaur is not clueless —
it just has a different goal than getting out of the maze. ☜

Posted in Mantra, Maxim, Maze, Myth | Tagged , , , | Leave a comment