The Difference That Makes A Difference That Peirce Makes : 27

Re: Peirce ListJohn Sowa

It’s been my observation over many decades that people invoke the “ethics of terminology” mainly to inveigh against everyone’s innovations but their own, so these days I’ve shifted my attention to the “pragmatics of communication”, the critical case being communication across the boundaries and through the filters of diverse communities of usage.  In that spirit, I’ll copy here my last best attempt to construct a bridge between Peirce’s special sense of “formal” and the more generic construals we likely know.

The most general meaning of formal is concerned with form, but the Latin forma can mean beauty in addition to form, so perhaps a normative goodness of form enters at this root.

The Latin word norma literally means a carpenter’s square.  The Greek gnomon is a sundial pointer taking a similar form.  The most general meaning of normative is “having to do with what a person ought to do”, but a pragmatic interpretation of ethical imperatives tends to treat that as “having to do with what a person ought to do in order to achieve a given object”, so another formula might be “relating to the good that befits a being of our kind, and what must be done in order to bring that good into being, and how to tell the signs that show the way”.

Defining logic as formal or normative semiotic differentiates logic from other species of semiotic under the general theory of signs, leaving a niche open for descriptive semiotic, just to mention the obvious branch.  This brings us to the question:

How does a concern with form, or goodness of form, along with the question of what is required to achieve an object, modify our perspective on sign relations in a way that duly marks it as a logical point of view?

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Analogy, C.S. Peirce, Communication, Descriptive Science, Fixation of Belief, Formal Systems, Information, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Normative Science, Paradigms, Peirce, Pragmatic Maxim, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes : 26

Re: Peirce ListJohn Sowa

Questions about Peirce’s use of “formal” and “normative” in relation to logic and semiotic have come up again on the Peirce List, but I have to run off to another appointment, so for now I’ll just post a link to a relevant previous discussion.

In other recurring discussions, as far as my personal usage goes, I’ve always suggested there is a place for descriptive semiotics, whether of not that was Peirce’s way of drawing the distinctions.

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Analogy, C.S. Peirce, Communication, Descriptive Science, Fixation of Belief, Formal Systems, Information, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Normative Science, Paradigms, Peirce, Pragmatic Maxim, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

The Difference That Makes A Difference That Peirce Makes : 25

I’ve been detecting something approaching a mini-zeitgeist lately.  Ideas and issues popping up in my recent discussions and readings keep reminding me of themes I first encountered in Peirce’s early work, especially the Lectures on the Logic of Science (1865–1866) and the 1870 Logic of Relatives.  A number of Peirce’s potentially ground-breaking, paradigm-shifting ideas first saw the light of day in these early ventures.  I say “potentially” because what I regard as his most revolutionary ideas never saw their full development in Peirce’s lifetime, only to arise again in the press of mathematical and scientific advances later in the 20th Century.

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Analogy, C.S. Peirce, Communication, Descriptive Science, Fixation of Belief, Formal Systems, Information, Inquiry, Logic, Logic of Relatives, Logic of Science, Logical Graphs, Mathematics, Normative Science, Paradigms, Peirce, Pragmatic Maxim, Pragmatism, Relation Theory, Semiotics, Sign Relations, Triadic Relations, Triadicity | Tagged , , , , , , , , , , , , , , , , , , , , , , | Leave a comment

Peirce’s Categories • 12

Re: Peirce ListJFSJBD

Different minds are drawn to Peirce for different reasons and they tend to discover different stores of value there.  I was attracted to his work largely for his insights into logic, math, and science and because his articulations of their springs and catches ring true to the ways their own practitioners understand them in practice.

One consequence is my tendency to approach the question of categories from a particular angle, more through the logic and mathematics of relations than by way of phenomenology.

What follows from that approach gives me sufficient reason to pursue it, but I’ll have to save further motivation until I develop more material from the 1870 Logic of Relatives.

Resources

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 1 Comment

Peirce’s Categories • 11

Re: Peirce ListHelmut Raulien

There is a kind of “second cousin” kinship between category markers and grammatical aspects, moods, or tenses.  In several drafts of an earlier comment I experimented with grammatical terms like conjugation, declension, diacritic, inflection, etc.  to explain the function of category markers.  But I eventually decided this laid too much stress on their grammatical aspect and distracted from their main function, which is to focus the relation between formal expressions and formal objects.

Resources

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 1 Comment

Peirce’s Categories • 10

Re: CyberneticsBernard Cohen

I began that note on the Precursors of Category Theory as a purely exploratory sketch, plotting a few points on a single theme with no plans of making an exhaustive survey.  Even at that I never got time to get back to it.  I put in a pin for Kant but haven’t had a chance to map out any passages.  There are even “incitements” going back to my earliest days reading Russell and wrestling with his take on type theory but those inklings are too hazy in my memory to make clear at present.

Resources

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 1 Comment

Peirce’s Categories • 9

Re: Systems Sciences Facebook PageJAKAL

Scanning the spectrum of sources I sampled in my Precursors of Category Theory, there are many differences in the categorical paradigms different observers developed over the centuries.  Just for starters, the numbers of categories vary widely from system to system.  But there is a conceptual continuity in the function category markers perform in every system.  If we look to the role a category marker plays in the relation between formal expressions and their formal objects, in effect, if we look at the matter from a semiotic perspective, as Aristotle already did, then we see the job of a category marker is to reduce (“drive down”) the ambiguity of equivocal linguistic expressions to the point where they obey the laws of logic.

Resources

cc: Systems ScienceStructural ModelingOntolog ForumLaws of FormCybernetics

Posted in Abstraction, Aristotle, C.S. Peirce, Category Theory, Logic, Logic of Relatives, Mathematics, Peirce, Peirce's Categories, Phenomenology, Pragmatic Maxim, Relation Theory, Semiotics, Triadic Relations, Triadicity, Type Theory | Tagged , , , , , , , , , , , , , , , | 2 Comments