Pragmatic Semiotic Information • Discussion 19

Re: Differential Logic and Dynamic Systems
Re: FB | Systems SciencesKenneth Lloyd

An exchange on Facebook took me back to recent discussions of pragmatic truth and long-running discussions of pragmatic semiotic information.  Just by way of a note to myself and anyone who’s interested, I’ll copy my comment here and add a few links to keep the relevant gray cells warm.

Concepts of belief, fact, knowledge, opinion, etc. look rather different from a Peircean pragmatic perspective, in other words, when analyzed in terms of the pragmatic maxim.  In time the traditional conceptions begin to strike us as increasingly clumsy tools, better supplanted by Peirce’s concept of information.

Resources

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Posted in Abduction, Aristotle, C.S. Peirce, Comprehension, Deduction, Definition, Determination, Extension, Hypothesis, Induction, Inference, Information, Information = Comprehension × Extension, Inquiry, Intension, Intention, Logic, Logic of Science, Mathematics, Measurement, Observation, Peirce, Perception, Phenomenology, Physics, Pragmatic Semiotic Information, Pragmatism, Probability, Quantum Mechanics, Scientific Method, Semiotics, Sign Relations | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Cybernetics • Requisite Variety • Selection 13

Our venture into cybernetics, the study of systems whose time evolution signifies an object, brings us to the point of seeing how pragmatic, semiotic, and systems thinking all have triadic relations at their core.

Recall the game between R and D determined by the following data:

Ashby Cybernetics Table 11.3.1

We continue with Ashby’s analysis of how the game plays out.

Requisite Variety

11/3.[cont.]   Examination of the table soon shows that with this particular table R can win always.  Whatever value D selects first, R can always select a Greek letter that will give the desired outcome.  Thus if D selects 1, R selects \beta;  if D selects 2, R selects \alpha;  and so on.  In fact, if R acts according to the transformation

Ashby Cybernetics Figure 11.3.2

then he can always force the outcome to be a.

R\text{'s} position, with this particular table, is peculiarly favourable, for not only can R always force a as the outcome, but he can as readily force, if desired, b or c as the outcome.  R has, in fact, complete control of the outcome.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Posted in Adaptive Systems, Ashby, C.S. Peirce, Communication, Control, Cybernetics, Evolution, Information, Inquiry Driven Systems, Learning, Logic, Mathematics, Peirce, Purpose, Regulation, Survival, Truth Theory, W. Ross Ashby | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Cybernetics • Requisite Variety • Selection 12

Ashby now invites us to consider a series of games, beginning as follows.

Requisite Variety

11/3.   Play and outcome.  Let us therefore forget all about regulation and simply suppose that we are watching two players, R and D, who are engaged in a game.  We shall follow the fortunes of R, who is attempting to score an a.  The rules are as follows.  They have before them Table 11/3/1, which can be seen by both:

Ashby Cybernetics Table 11.3.1

D must play first, by selecting a number, and thus a particular row.  R, knowing this number, then selects a Greek letter, and thus a particular column.  The italic letter specified by the intersection of the row and column is the outcome.  If it is an a, R wins;  if not, R loses.

I’ll pause the play here and give readers a chance to contemplate strategies.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

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Posted in Adaptive Systems, Ashby, C.S. Peirce, Communication, Control, Cybernetics, Evolution, Information, Inquiry Driven Systems, Learning, Logic, Mathematics, Peirce, Purpose, Regulation, Survival, Truth Theory, W. Ross Ashby | Tagged , , , , , , , , , , , , , , , , , | Leave a comment

Pragmatic Theory Of Truth • 21

Re: Cybernetic CommunicationsKlaus Krippendorff

I appreciate the way Klaus Krippendorff immediately extracted one of the overarching themes of Peirce’s whole paper, indeed of his whole work.  That allows us to tread lightly past a lot of verbal nit-picking about the differences among traditional concepts like belief, fact, knowledge, opinion, etc. and get right down to systems-theoretic ideas about states of information and inquiry as a process that revises those states.

Here’s a bit I wrote a few years back rubricizing Peirce’s four ways of moving from doubt to belief — from a state of information so unsettled it puzzles the will to one secure enough on which to act, should the need for action arise.

My favorite polymathematician, Charles Sanders Peirce, gave a fourfold classification of what he called “methods of fixing belief”, or “settling opinion”, most notably and seminally in his paper, “The Fixation of Belief” (1877).  Adjusting his nomenclature very slightly, if only for the sake of preserving a mnemonic rhyme scheme, we may refer to his four types as Tenacity, Authority, Plausibility (à priori pleasing praiseworthiness), and full-fledged Scientific Inquiry.

Reference

Resource

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Posted in Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Pragmatic Theory Of Truth • 20

Re: Renaissance MathematicusThony Christie
Re: Cybernetic CommunicationsLouis Kauffman
Re: FB | Charles S. Peirce SocietyJohn Corcoran

Various conceptions of belief in relation to pragmatic theories of inquiry, signs, and truth have come up recently in several discussion groups.  Some of the variations are too far off my present track but if I stay the pragmatic course I’d naturally recommend the novel fork taken by Peirce’s 1877 paper, “The Fixation of Belief”.

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Posted in Aristotle, C.S. Peirce, Coherence, Concordance, Congruence, Consensus, Convergence, Correspondence, Dewey, Fixation of Belief, Information, Inquiry, John Dewey, Kant, Logic, Logic of Science, Method, Peirce, Philosophy, Pragmatic Maxim, Pragmatism, Semiotics, Sign Relations, Triadic Relations, Truth, Truth Theory, William James | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Differential Logic • Comment 4

Re: Cybernetic CommunicationsStephen Paul King

SPK:
Is it possible that beliefs can propagate almost completely contrary to facts, seen by those that are not infected with those beliefs?

Can we have complex waves in the domains of binary truth tables?

Patterns of change in multi-dimensional Boolean spaces is what Differential Logic is all about.  I’ll say more on that as I get time but here’s a collection of resource links for now.

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Posted in Amphecks, Boole, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Cybernetics, Differential Analytic Turing Automata, Differential Logic, Discrete Dynamical Systems, Fixation of Belief, Graph Theory, Hill Climbing, Hologrammautomaton, Inquiry, Laws of Form, Leibniz, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Peirce, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown | Tagged , , , , , , , , , , , , , , , , , , , , , , , , ,

Cybernetics • Requisite Variety • Selection 11

Ashby now takes a few steps back from the picture of regulation in biological systems, setting out the framework he needs for a broader perspective on regulation in general.

Requisite Variety

11/1.   In the previous chapter we considered regulation from the biological point of view, taking it as something sufficiently well understood.  In this chapter we shall examine the process of regulation itself, with the aim of finding out exactly what is involved and implied.  In particular we shall develop ways of measuring the amount or degree of regulation achieved, and we shall show that this amount has an upper limit.

11/2.   The subject of regulation is very wide in its applications, covering as it does most of the activities in physiology, sociology, ecology, economics, and much of the activities in almost every branch of science and life.  Further, the types of regulator that exist are almost bewildering in their variety.  One way of treating the subject would be to deal seriatim with the various types;  and chapter 12 will, in fact, indicate them.  In this chapter, however, we shall be attempting to get at the core of the subject — to find what is common to all.

What is common to all regulators, however, is not, at first sight, much like any particular form.  We will therefore start anew in the next section, making no explicit reference to what has gone before.  Only after the new subject has been sufficiently developed will we begin to consider any relation it may have to regulation.

Reference

  • Ashby, W.R. (1956), An Introduction to Cybernetics, Chapman and Hall, London, UK.  Republished by Methuen and Company, London, UK, 1964.  Online.

cc: CyberneticsOntolog ForumStructural ModelingSystems Science

Posted in Adaptive Systems, Ashby, C.S. Peirce, Communication, Control, Cybernetics, Evolution, Information, Inquiry Driven Systems, Learning, Logic, Mathematics, Peirce, Purpose, Regulation, Survival, Truth Theory, W. Ross Ashby | Tagged , , , , , , , , , , , , , , , , , | Leave a comment