Inquiry Into Inquiry

Re: Laws of Form • Leon Conrad

LC:

As someone who has worked on, teaches, and uses the CoI [Calculus of Indications] to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB’s work to logical tables, particularly if it does a similar thing.

Dear Leon,

Gauging the gap between entry-level formal systems like propositional calculi and calculi qualified to handle quantified predicates, functions, combinators, etc. is one of my oldest research pursuits and still very much a work in progress.  When I point people to the live edges of my understanding, the places where I break off in my searches, I usually end up numbering those episodes of risk-taking under the heading of “Failures to Communicate” — but it doesn’t stop me from trying.  So I’ll take a chance and post a few links along those lines in a little while but it may avert a measure of misunderstanding if I mention the main forces setting me on my present path.

I had already been studying Peirce’s Collected Papers from my first couple of years in college, especially fascinated by his approach to logic, his amphecks, his logical graphs, both entitative and existential, his overall visual and visionary way of doing mathematics.  And then a friend pointed me to the entry for Spencer Brown’s Laws of Form in the first Whole Earth Catalog and I sent off for a copy right away.  My computer courses and self-directed programming play rounded out the triple of primary impacts on the way I would understand and develop logical graphs from that point on.

To be continued …

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)

Re: Category Theory • Simon Burton

SB:

From what I’ve noticed there are two kinds of mathematical thinking:  manipulating abstract syntax, versus direct experience/perception of concrete mathematics.  These two are intertwined in various ways, but in my experience people generally excel in one of these two styles of thinking and not the other.  I think that many famous collaborations between two mathematicians are divided along these lines.

Dear Simon.

Susan Awbrey and I have worked a lot and written a little on a variety of “two-culture” and “cognitive style” questions from a broadly pragmatic perspective informed by the work of C.S. Peirce, John Dewey, and like-minded thinkers.  The three dimensional spaces of Peirce’s triadic sign relations afford a perspective on the ways diverse thinkers can specialize their thought to different planes or facets of a sign relation’s full volume.  Various issues along these lines are discussed in the following paper.

• Conceptual Barriers to Creating Integrative Universities

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)

Re: Category Theory • Henry Story

HS:

I place Logic within Mathematics and modal logic is a field of Logic,
and so of mathematics.  You will find that modal logic comes up a lot
working with machines, programs, and all state based systems.

Dear Henry,

Just by way of personal orientation, I tend to follow Peirce and assorted classical sources in viewing logic as a normative science whereas mathematics is a hypothetical descriptive science.  That gives a picture of their relationship like the one I drew in the following post.

Definition and Determination • 4

Normative science rests largely on phenomenology and on mathematics;
metaphysics on phenomenology and on normative science.

❧ Charles Sanders Peirce • Collected Papers, CP 1.186 (1903)
Syllabus • Classification of Sciences (CP 1.180–202, G-1903-2b)

The way I see it, then, logic is more an application of mathematics than a subfield of it.

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)

Re: Category Theory • Henry Story

HS:

If one were to think about maths and children’s education one would need to look at the needs of other subjects too.  It should be easy for people here to work out how cats ties in with physics and biology — having a maths of open systems could help a lot there.  But one would also want to help maths tie in with the humanities.  In France children sometime after 13 or so read Voltaire’s Candide published 1759, where Voltaire makes fun of Leibniz’ idea that we live in the best possible world, by having Candide go around the world and witness all the suffering known at the time.  It would be good if the maths department then also gave some introduction to fragments of contemporary modal logic, so that the children could see that the “best possible world” idea is abandoned by contemporary modal logics.

Dear Henry,

I’ve never found much use for modal logic in mathematics proper since mathematics is all about possible existence, in the sense of what is not inconsistent with a given set of premisses.  Of course, one can entertain modal logic as an endeavor to construct mathematical models of natural language intuitions about possibility, contingency, necessity, etc. but that is an application of mathematics to an empirical domain.

As far as best possibilities go we certainly do a lot of work on optimization in math and its applications to the special sciences and engineering.  For instance, a lot of physics begins with skiers on snowy slopes and their contemplation of gradients.  That very sort of thinking by Leibniz led to his personal discovery of differential calculus.

• Leibniz • The Present Is Big With The Future

Regards,

Jon

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)

Re: Laws of Form • Leon Conrad

LC:

As someone who has worked on, teaches, and uses the CoI [Calculus of Indications] to make classical syllogistic logic much easier to practice and more visually intuitive than any of the visualisations we have to date, I would be very interested in finding out more about your work in applying GSB’s work to logical tables, particularly if it does a similar thing.

Ahoy Leon!  Welcome aboard, a-synchronicity being what it is, it may be September before I get both my hands back on this deck myself as I’ve got a bunch of long-procrastinated home and garden and auto and health-related matters to deal with.

If you’re an old time web surfer like we all used to be way back when I could leave you with a link or two to follow up on your own recognizance — I know, I know, these days it’s more like you can link a horse to whatev but you can’t make em click it.

I will try to write something more coherent later today but failing that here’s a link to an omnibus Survey page for my blog, where you can find what’s been occupying my trains of
thought for the past half-century.  The last-numbered links under each topic include and update all the earlier entries.

• Inquiry Into Inquiry • Surveys

Best regards,

Jon

cc: Category Theory • Cybernetics • Ontolog • Structural Modeling • Systems Science
cc: FB | Inquiry Driven Systems • Laws of Form • Peirce List (1) (2) (3)