Re: Peter Cameron • Discovery and Invention
Between the discovery and the invention,
Falls the Shadow, who knows, you know,
By tracking backward, retracing the steps
Of the tourist, who comes not to conquer,
But to enjoy the winding stair to the place.
That all invention is discovery recalls the Platonic idea that all learning is recollection.
Re: Peirce List • Matt Faunce • Jon Awbrey • Jon Awbrey
Though my present object has more to do with the logical and mathematical aspects of triadic relations than it does with their psychological embodiments, the following exchange on the matter of consciousness from earlier last Fall keeps intruding on my thoughts.
Question: Matt Faunce
Response: Jon Awbrey
In which my thought was this —
If mind is grounded in triadic relations and reality is grounded in triadic relations then what remains is to study the ways more mindful materials and less mindful materials differ within the variety of triadic relations.
Now back to my regularly scheduled program …
The core insight of Peirce’s conceptual system is the recognition that triadic relations are sui generis, constituting a class by themselves. Understanding the properties of triadic relations and the consequences of their irreducibility is critical to understanding Peirce’s thought and work. Every attempt to reconstruct Peirce’s system on a different basis must eventually fall like a house of cards.
Re: Peter Cameron • Mathematics and Logic
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.
Red-breasted robins and brown-speckled starlings
Mobbing the crab-apple tree outside my window,
Stretching their necks for the frozen red berries —
The snow-sprinkled branches saved them for now.
Jon Awbrey
31 Dec 2012
Re: Peirce List • Gary Richmond
The program I wrote for my M.A. in Psych was barely a prototype, a “test of concept”, as they say, but I continued to develop and apply the underlying collection of ideas to a number of concrete problems throughout the ensuing years.
Here is a paper describing the associated program of research Susan Awbrey and I presented at a conference the following year.
or in a place where it might be understood?
or to a person who might understand it?
Re: Peirce List • Christophe Menant • Jon Awbrey • Christophe Menant
The system-theoretic concept of constraint is one that unifies a manifold of other notions — definition, determination, habit, information, law, predicate, regularity, and so on. Indeed, it is often the best way to understand these concepts.
Entwined with the concept of constraint is the concept of information, the power signs bear to reduce uncertainty and advance inquiry. Asking what consequences those ideas have for Peirce’s theory of triadic sign relations led me some years ago to the following thoughts.
Here I am thinking of the concept of constraint that constitutes one of the fundamental ideas of classical cybernetics and mathematical systems theory.
For example, here is how Ashby introduces the concept of constraint in his Introduction to Cybernetics (1956).
A most important concept, with which we shall be much concerned later, is that of constraint. It is a relation between two sets, and occurs when the variety that exists under one condition is less than the variety that exists under another. Thus, the variety of the human sexes is 1 bit; if a certain school takes only boys, the variety in the sexes within the school is zero; so as 0 is less than 1, constraint exists. (1964 ed., p. 127).
At its simplest, then, constraint is just an aspect of the subset relation.
The objective of an agent, organism, or similar regulator is to keep within its viable region, a particular subset of its possible state space. That is the constraint of primary interest to the agent.
Incidentally, Ashby’s book, in my estimation still the best introduction to classical cybernetics going, is available online in PDF form:
Inquiry Into Inquiry 