Symbolic logic and the Nicelys

FOR five days, three winters ago, I sat in a Cincinnati motel room while my husband took a course in antique clock repair in a building across the parking lot. I had come with plenty to do: a fiction story to write and a book to read, ``An Introduction to Symbolic Logic,'' by the American philosopher Susanne K. Langer. I had picked the book with care. For one thing, I knew it couldn't be a fiction book that I'd take into that cell with me. Not unless I wanted my story to come out sounding just like it. Styles are highly contagious. An anthology might have worked. One writer's words may be taken as the antidote for another's. Chekhov cancels out Austen, for example.

But I wanted to take advantage of the solid block of time to digest something meatier than snippets, something all of a piece. A nonfiction book on another subject might have done as well, but very likely I would have finished it too soon. Besides, I wanted not necessarily to read, but to study -- to take a course in something myself, as my husband was doing.

This winter, my story, begun in that motel room, will be published. And looking back on notes from my journal of that year, I see that the Langer book did exert its influence, but in a way quite unlike another fiction writer's work might have.

``In what ways does the family cohere ?'' I wrote at a table by a huge picture window that dominated the tiny room. I was writing to myself about my chosen subject, a family called the Nicelys. They are not the most genteel of families, but they are a family. That fact cannot be altered. ``How are its parts related?'' I queried myself in language taken straight from Langer.

In another part of the journal I see a doodle of sorts. Actually it's the working out of symbols for a logical system: d=int``daughter''| s=int``son''| M=int``Mother''| F=int``Father''| GM=int``Grandmother''| GF=int``Grandfather''| sr=int``sister''| br=int``brother''|

(A Langer notation, ``=int'' stands for ``is identical with.'')

Thumb through the Langer book, first published in 1937, reissued in 1952 and again in 1967, and you'll see that it literally swarms with configurations that seem to have little enough to do with philosophy, much less fiction. Chosen at random:

Theorem 10a: -(a + b) = -a x -b.

Yet symbolic logic is a prime tool of philosophers. As Langer states it: ``There is something uncanny about the power of a happily chosen ideographic language; for it often allows one to express relations which have no names in natural language and have therefore never been noticed by anyone. Symbolism, then, becomes an organ of discovery rather than mere notation.''

A system which is a substitute for ``natural language,'' the fiction writer's stock in trade, would seem to hold no attraction for one constructing narratives out of words. But a fiction writer's difficulties with any particular piece may start long before there is any attempt to actually arrange the words on the pages. The raw material of fiction is often such strong stuff, so hot to handle that sometimes I take to drawing pictures of my scenes -- stick figures and boxes, that is -- to try making sense of what in fact my characters are doing. This use of ideographic language as an instrument of vision is what Langer's symbolic language is all about.

Why should the act of expressing widely divergent pieces of reality as a homogenous, abstract system help someone to think more clearly about them? The aim, to paraphrase Langer, is to see things in proportion to each other, in some order, as a system, as a whole. Manipulation of symbols can be easier than manipulation of the complex ideas they stand for.

It's also economical, in the best sense of that word. A map is a logical picture of the sort I'm referring to here. So is an architect's blueprint. Or a piece of choreography. Like language -- a logical picture in itself -- these systems of notation copy as closely as possible the logical form of our thought.

The act of reducing different things to mere differences of appearance -- lines, circles, and other shapes to stand for complex conceptions like love and irony, for example -- can also aid us in recognizing transformations. A transformation is a change, specifically a change from one form to another, as the word itself implies. Thus, a change of season may transform the ideal fishing spot into the town skating pond. The birth of a daughter transforms a daughter into a mother. Or a series of visits by ghosts may transform a character like Scrooge into another, better, kind of man.

The notion of transformation is the keynote of the science, because, as Langer says, ``The only way we can do business at all with a rapidly changing, shifting, surprising world is to discover the most general laws of its trans-formations.''

Ultimately, then, symbolic logic is a way of getting at the truth. For that reason, five days spent on it can only be a beginning, as that period was only the beginning of the writing of the Nicelys' story. As for my husband, he struggles with clock repair nightly.

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