This is the third part of the book framing comments, noted as Imaginary Heroes in the table of contents in the March posting. I may have been too harsh to call that other book attempt unpublishable, except that it had little original thought and was an application of Jungian archetype theory to science fiction and superheroes. I will review it and  consider parsing it up for this blog.

            From 1981, we must jump to 1992 when I wrote a properly unpublished book titled Imaginary Heroes in the Age of Science: Archetypes in Popular Culture. There was one good idea in it worthy of publication, which was developed into this collection’s first paper, ‘Mythic Spacetime.’ Once the framework developed in 1992, it took five years of idle contemplation before that set theory insight resulted one night. I now reproduce the few paragraphs, from the 1992 book, which were my first thoughts on and coining of the term mythic spacetime.

            In standard myths, where does a hero commit violence? In the land of adventure, the fantastic other realm outside of normal society. This is part of the constructive social meaning of archetypal models, which modern society tries to erase in its rational models of law and order, but which persists as part of human nature: there is a proper place for violence. In ancient times, it was on the hunt. In modern comics, it’s on the hunt for criminals or super villains. The mythic land is the place where violence is the correct thing to do, and anywhere a superhero is on the job becomes a mythic land for the duration of the fight. This fits in with why most of reality seems to ignore superheroes in the comic book stories.

            It also fits with the history and prehistory of real humanity. The hunting mentality can be thought of as a kind of ‘mythic time’ when men access the archetypes of violence. Coming back to the hearth, they would engage in entertainment to tell of their deeds, thus recalling when they were using their instinctive skills, i.e. accessing archetypes. The original boon that they brought back was the game that they killed. Of course, the women had the superior skill of producing a boon out of childbirth. Either sex has its own version of bloody violence in the mythic space-time.

            The would-be censors of violence on TV probably give less thought to sports. This is the usual mode for people to access the mythic space-time, far more popular than the pop cultures I consider in this book. The socially acceptable channeling of aggression and violent urges into competitive sports is no doubt completely satisfying for the participants. For some spectators, it’s not completely satisfying, and they have to start fights or riot. For other spectators, it may be the equivalent of reading a comic book, with the added experience of getting to shout from the stands. Or in the TV room.

            The notion of a separate space for superheroes to slug it out nagged at me, with its resemblance to Mircea Eliade’s description of making a ritual space. One night in my caregiver years, sitting on a couch by my sleeping mother, looking at a TV screen, the notion to represent the characters as set elements occurred. The consequent idea came that elements were mapping between sets. The further explication of these ideas is presented in the first three papers, all published in the Journal of Literary Semantics, thanks to the instant approval of its founding editor Trevor Eaton.

Continuing with the material as outlined in the table of contents from last month, we arrive next at Singular They, an unpublished paper on the set logic of pronouns used in the English language. As noted in the Introduction: Origins, this kind of thinking was a precursor to mythic algebra three decades later.    

            The following paper from 1981, ‘Set Theory and Some English Pronouns,’ was worked out after a much longer class paper on the use of singular ‘they,’ done for a communication course at Arizona State University in Tempe. That course paper was titled ‘Linguistic Neutralism: Everybody as They,’ and surveyed history and social use, briefly mentioning set theory implications.

Set Theory and Some English Pronouns

Abstract

The use of some third person pronouns corresponds with the mathematical rule for set unions. This leads to speculations about semantics and the place of mathematics among linguistic universals.

Descriptive linguists recognize a nonstandard use of a pronoun called the singular they, referring to uses of they, them, their, and theirs. An example is the sentence, ‘Somebody gave their donation anonymously.’ A prescriptive rule would have the sentence as, ‘Somebody gave his donation anonymously.’ for what is sometimes called the generic he. As for singular they, Ann Bodine (1975) traced its use through every recorded century of the English language, and showed how it filled a logical gap in the language, for a singular sex-indefinite pronoun.

Let us further pursue this logic, and state those principles of use: why do we say they when we mean either a he or a she? In our minds, we have two possibilities, of opposite sex. Only one of those possibilities will occur in reality, but that is irrelevant. The purpose is to communicate thoughts that consider both possibilities, so we use a plural pronoun. This is analogous to the mathematical formula for set union: a or b = a U b. Singular they indicates a union of two sets to compose a new set in which a member taken out of this new set could be from either of the two sets that combined.

It is as if we had two different semantic categories. The potential category indicates the basic complete picture of all elements. In mathematics that is the portrait of the sets and their union. The actual category is the result of performing some operation on the sets.  In mathematics that would be taking out one element, but in English grammar that becomes the use of the singular they. In the potential category, singular they is actually plural. The potential category is operated upon to become the actual category, and the proof that something has happened is shown by a plural pronoun becoming singular. This happens as long as the actual situation provides the context and not the hypothetical situation, in which case the pronoun would again have a plural meaning.

Pragmatics are involved in the use of singular they also. If a speaker had time to emphasize that either sex was meant, then ‘he or she’ may be spoken or written instead of they. However, if fast talking were going on, and the speaker didn’t want to call attention to such details, singular they may be spoken without awareness, just as a natural feature of the grammar.

As for syntax, singular they can show up as any kind of noun phrase function: subject, object, or modifier. Singular they encompasses four words. These words often show up with other indefinite pronouns, such as some-, any-, no-, or every- ending in –one or –body. A further example besides the one used at the start of this paper is the sentence, ‘If anybody shows up, give it to them.’

G.L. Brook (1964, 128) remarks upon the Old English adoption of the pronoun they from Scandinavia as a rare example of pronoun borrowing between languages. Jespersen (1938, 74) mentions other indefinite singular pronouns used in the history of the English language, including a contraction of them to ‘em, which is still in use today. The utility of they for indefinite singular usage may have contributed to its permanent establishment in the English language.

Perhaps other terms can cross over into other languages to fulfill set theoretic needs, or a language has a built-in flexibility to allow for such combinations among potential and actual categories. It would certainly be amazing if set theory principles from mathematics were not universal linguistic concepts. That might imply that any non-western language could create a different kind of set theory, and a totally foreign mathematics, to shatter our illusions of scientific truth. What we had thought was an unending universe of mathematics would turn out to be only one of many unending universes.

References

Bodine, Ann. ‘Androcentrism in prescriptive grammar: singular they, sex-indefinite he, and he or she.’ Language in Society. 1975(4): 129-146.

Brook, G.L. A History of the English Language. New York: W.W. Norton, 1964.

Jespersen, Otto. Growth and Structure of the English Language. Garden City, NY: Doubleday, 1938.

            Thirty years later, I can critique this paper as still valid even if the historical progression in usage is unclear. They was first used in English for uncertain singular or plural persons, then centuries-worth of prescriptive grammarians and school teachers have tried to limit it to plural only. Regardless of the origin of singular they, its modern use in violation of taught grammar shows a kind of set function where ‘male or female’ is thought of as plural, thus one selects a single choice from plural possibilities, so the taught label from plural comes to mind to use. Descriptive grammar is then vindicated by set theory, no matter which came first in history, single or plural they, or both together.

            This paper on they shows a first clue of sets and math processes turning up where they are not supposed to be, outside of mathematical topics. I did not pursue the matter further. After getting a Bachelor of Arts degree in mathematics, I got a master’s in library science and then a 13-year career in database publishing. Personal research and writing took other directions, but the new math works in mysterious ways.

This month's post is the beginning of the framing comments for an unpublished book idea to collect my six academic papers and related materials. Instead of pursuing that, my comic book trilogy resulted. 

Table of Contents

Introduction: Origins

     Singular They

     Imaginary Heroes

First Trio: Journal of Literary Semantics

     Mythic Spacetime
 
     Narrative Algebra

     More Features

Comments: Follow-up

     Hero Cycle

Second Trio: Semiotica

     Mythic Algebra Uses

     Numbers

     Laws of Association

Epilog: Future Directions



Introduction: Origins

     While this book reprints six academic papers and related material, its origins are not in the dry, technical world of academic theory. It started with comic books. Before I went to school, before I learned to read, I ‘read’ comic books at home. Four decades later I was again reading them at home, and developed mythic algebra from them.
     Mythic algebra is a hybrid system of various parts of basic mathematics, sets and algebra cobbled together to describe the symbolic processes of the mind. Originally derived from mythology and superhero comic book stories, the system has been aimed to cover all mental activity, incorporating non-mathematical processes like mental association. This led to the idea that mythic algebra is the ur-mathematics out of which true mathematics, and any other language, evolved.
     This collection of academic papers is based on a radical assumption, that the mind works on symbolic processes which are the same no matter how expressed. Today’s educators speak of different learning styles, which is no doubt true. Beyond this, everyone assumes that each field of thought, each subject area, involves different ways of thinking. How one does mathematics differs from how one understands the arts, stories, language, or any other mental activity. Yet we have one brain for all of this, and while scientists can identify different areas of higher brain activity depending on type of thought, all areas are said to be interconnected. There are also many different types of connection: chemical, electrical, physiological, organelle, and perhaps electromagnetic broadcast. But if all these are considered the building blocks, what structure do they make?
     Notwithstanding the actual variation of brain parts and connections, when they all work together, does it make a single, unified process? Obviously it does, since we are autonomous animals that think and move on our own. While this fact is easily conceded on the level of body motion and physiology, it is rejected at the level of thought. Our personal conflicts, our ambivalent desires, are taken as signs of the competing systems in the triune brain, the reptilian brainstem versus the mammalian midbrain versus the human frontal lobes. Yet the triune brain produces a single person, even if it is only a highly evolved radio box to receive a spirit. Leaving aside spiritual questions, how could any unity of process be recognized? How could this be described in a functional notation system?
     Enter ‘the new math,’ that abandoned approach to teaching grade school mathematics in the 1960s. I am a product of that, for I absorbed the emphasis upon sets as a basis of understanding the world. It has colored my thinking, becoming my natural viewpoint upon anything, long before it inserted itself into my way of thinking about comic books and the first published paper here (from 2000), ‘Mythic Spacetime.’ I get ahead of myself, and must retreat to earlier decades, to give an unpublished example of a worldview colored by sets.

The last of my Semiotica trilogy, and this was also given page one in the journal (Volume 2009, Issue 176:1-14) (Aug 2009). As an example of semiosis, or the creation of signs, the mental construction of a cargo cult is analyzed. The rest of the article analyzes the "laws of association" common to philosophy.

The final publication is available at www.degruyter.com

https://doi.org/10.1515/semi.2009.057