Towards the Full Digitalization of Language and Thought:

Final Definitions of All Types of Relative Clauses in Egyptian and in General, via Boole and Venn^[1]

It must be left to a special investigation to analyze the semantics of the explicative (parathetical) relative clause [in Coptic].^[2]

H.J. Polotsky,

In the decades of the twenty-first century lying ahead, it will become ever more important to analyze language—as well as thought, of which language serves as an expression—less as a product of the lips, teeth, and tongue than of brain waves. Since the electrochemical activity of the brain can probably be represented by electronic circuits as models, the description of language will need to turn more and more into something that is fully compatible with electrical engineering.

The design of the present investigation is to illustrate a particular mode of inquiry that aims to move decidedly in the direction of such a description. This bulk of this paper is concerned with a new analysis of one single phenomenon, the relative clause (see §§ 5–8). This is followed by a brief preliminary account of how the basic digital imprint perceived in the relative clause can be seen all over the linguistic system (see § 9). This digital imprint affords insight into a fundamental principle of how the mind seizes hold of the reality around itself and operates with it to reason about it. The two main parts are preceded by remarks of a general nature (§§ 1–4).

The present narrow focus on one specific phenomenon is inspired by the following consideration. In deductive efforts such as mathematics, the particular can shed light on the general in its entirety. "The knowledge of the laws of the mind does not require as its basis any extensive collection of observations,“ writes Boole^[3]". . . The general truth is seen in the particular instance, and it is not confirmed by the repetition of instances. . . . [A] truth is made manifest in all its generality by reflection upon a single instance of its application.“ I have earlier presented the mode of inquiry at hand in other publications. But it seems to me that the relative clause more transparently illustrates it than many other phenomena of language.

In dealing with language, a choice of specific languages imposes itself. The present choice is Egyptian, the longest attested of all languages, and more specifically Coptic Egyptian, its latest stage. There will also be much reference to English as the language of this paper and therefore the obvious language of translation. But what is said below should also apply to all other languages.

Perhaps, the most important property of the digital model proposed below is that its basic outline is fully exhaustive. An electronic circuit can do an exact number of things, not more, not less. One expects the same of the brain.^[4]

1. Linguistics and the Sciences

Academic fields are divided into the humanities and the sciences. Linguistics occupies a peculiar position in this respect. Departments of linguistics are typically part of the humanities. Indeed, F. de Saussure has taught us that languages are semiotic systems in which signifiers point to signifieds. Literature, music, art, and archeological artefacts constitute, like language, semiotic systems.^[5] A rose as signifier may point to love as a signified. And so may the sound pattern love. But linguistics can also be institutionally aligned with the sciences.^[6] Why can linguistics be aligned with both? An obvious answer would seem to be that, in the humanities, language serves as a tool and a medium. In the sciences, language is observed as an object. In a similar dichotomy, a single person can be both a speaker and an observer of his own speech.^[7] The question remains: Can linguistics be a science like biology and physics? And if it is not yet quite, what would make it fully so? I begin by two observations that put these questions into perspective. The first concerns what is missing. The second concerns the retrieval of what is missing.

The first observation is that something fundamental is missing in linguistics to make it one hundred percent a science. Language does not originate in the mouth or on the written page. Sounds or written symbols are not the prime mover. Everything is set into motion by events taking place inside the brain. Brocca’s and Wernicke’s centers located on the left side play crucial roles. How language is produced in the brain is virtually unknown. As a result, modern linguistics is like describing a car and its movement and function without being able to look under the hood to see what the engine looks like. Much that is useful and objective can be and has been written about language. But there is a final level to which the study of language has not penetrated. One imagines an intricate clockwork of the biochemical kind steering every linguistic event. What does this clockwork look like? In the Acta Eruditorum Lipsiensium of 1694, Leibniz writes, "I see that most people delighting in mathematical teachings abhor metaphysical ones" quod in illis lucem, in his tenebras animadvertant "because they observe light in the former and darkness in the latter."^[8] What is needed to bring linguistics out of its Platonic cave into the bright daylight?

The second observation is that linguistic communication works. When two people talk, they typically understand one another. It follows that the sound waves or written symbols transmitting linguistic purport from one mind to another ought to exhibit the full structure of the message. Only what the carrier contains is transmitted. There is therefore reason to believe that analyzing the spoken or written word can reveal some of what happens in the brain.

2. The Brain as Final Frontier

The twenty-first century is bound to be the century of brain science. It is when human existence will be turned inside out as it were, when we can watch ourselves function on the smallest scale as it happens. Genetics should make it possible to turn around the camera 180 degrees and watch ourselves function as a kind of organic clock-work down to the smallest scale. Boolean algebra should do much to make it possible to see the cogwheels of the mind turning and to observe thinking and speaking as it happens. George Boole fulfilled Leibniz’s dream of a scientia universalis or a calculus ratiocinator. Boole’s star is on the rise in mathematics and will take, I believe, its place among the first rank of mathematicians to which Archimedes, Newton, Euler, Laplace, and Gauss belong.

What are the gears and wheels of this clockwork? There are two facets of the problem to which I myself will hardly be able to contribute anything. I am neither a computer scientist nor a biochemist. Then again, for the time being, in order to establish what is going on in the mind in terms of language and thought, we are largely dependent on what comes out of the mouths of speakers. And since language is a tool of communication and we have a sense that messages we send to others mostly have their desired effect, there is reason to believe that, from the point of view of structure, much if not most of what is essential inside the mind is exteriorized audibly or visibly and transformed and transferred into the elements of spoken or written language. It is surely possible to be functional and useful in philology and grammar without being concerned too much with how the gray matter located under the skull operates. Then again, what comes out of the mouth is a secondary, derivative manifestation of what happens inside the mind. The brain is the final frontier.

Two tenets have guided my attempts to interpret phenomena of language against the larger background of language and thought. The word "tenet" derives from Latin tenere. They are statements that I hold onto. But they are also assumptions. They are briefly described in the next two sections (§§ 3–4).

3. The Digital Nature of Thought and Language

In the brain, most everything is On or Off, 1 or 0. Chemical reactions happen or they do not. Emotions are different. They increase and decrease on a continuous line. The flow of substances such as adrenaline, dopamine, and serotonin is not a matter of On or Off. On the other hand, neurons stimulated by neighboring neurons past a certain electrical threshold can give an "all-or-nothing“ signal. The signal has the same intensity no matter how strong the stimulation. That is On or Off. The hypothesis that language is fundamentally digital cannot be positively proven at this time. But it is easy to see from which angles opposition could arise to the notion of intelligence being merely a digital organism consisting of little switches flipped open and shut by microvoltages. Just consider the human imagination, which seems to be capable of just about anything, or the mysterious concept of consciousness or self-awareness.

In fact, it has been suggested that quantum effects play a role. In quantum theory, originated by Max Planck, not everything is On or Off. The presence of something in a place can be a matter of probability. Some adduce quantum theory to account for spirituality, the soul, consciousness. I myself hold a dimmer view of the sophistication of human intelligence, more like the opinion of the founder of computer science, Claude Shannon, who stated—perhaps partly in jest—that in the future we will be to robots what dogs are now to us.^[9] I also believe quantum theory cannot be intuitive because a mind in which everything is On or Off needs to grasp something that is somewhere in between.

Nothing prevents one from musing speculatively about higher forms of intelligence that rise above the human intellect. About such higher forms, Boole writes, "It is impossible for us, with our existing faculties, adequately to conceive [their real nature], but . . . we might still investigate [their laws] as an object of intellectual speculation.“^[10] By the same token, we are unable to understand why we think how we do and not in some other way. "It may, perhaps, be permitted to the mind,“ writes Boole,^[11] "to attain a knowledge of the laws to which it is itself subject, without its [sic] being also given to it to understand their ground and origin, or even, except in a very limited degree, to comprehend their fitness for their end, as compared with other and conceivable systems of law.“

By the afore-mentioned hypothesis, final linguistic definitions ought to make electrical engineers happy. My belief is that anything that can be reproduced in an electronic circuit using switches and magnetic coils can serve as the model for an analogous structure of the biochemical kind.^[12]

4. The Absolute Limitations of Thought and Language

The second tenet is that there are absolute limitations to what thought and language can do. Humility is an important concept in religion and morality. But rationality comes with its own brand of humility. This tenet involves its own kind of humility. Everyone will probably agree that we could be much smarter than we are. But where is the limit? In defining language and thought, the persistent search ought to be for what I would call final definitions. By "final,“ I do not mean that the definition might not be wrong, although every effort should be made to try and make it right. Rather, a final definition is one that has met an absolute limit. In that respect, perhaps the most important property of the theoretical model of relative clauses described in what follows is that there could not possibly be more types than the ones that are defined. Additional complexity is impossible because the instrumentation is not available. Without stipulation, the model cannot function. Only when we have a clear sense that we have reached the limits of thought and that there is no speaking and no thinking beyond what has been said is the description and explanation complete.

5. The Relative Clause Theoretically and Empirically

According to the two tenets described above, the search is for descriptions of language phenomena that are both digital and limited. The phenomenon chosen presently to illustrate the two tenets is the relative clause. The following argument has a theoretical component and an empirical component. In terms of theory, a general model will be proposed for the study of the relative clause. The principal aim of this model is to define all the possible types of relative clauses. They are three in number. It will be argued that there can not possibly be more than these three.

In terms of empirical data, the main focus will be on Coptic, the latest stage of Egyptian. The three types of relative clauses are empirically fully distinct in Coptic. One would expect to find these three types also in other languages. Importantly, one would expect to find everywhere no more than three. Then again, one might find fewer. The reason is as follows. Egyptian has the longest attested history of any language. As far as I can see, in the course of the long history of Egyptian, the articulation between the three types came into being only gradually. Accordingly, one might expect a certain lack of articulation of the three types in the earlier histories of languages. The way in which the brain operates with relative clauses had to mature over many centuries, as it were.

A more comprehensive study of the relative clause would also need to address matters not discussed in this paper.

First, students of Semitic and Egyptian are acquainted with the contrastive behavior involving indefinite and definite antecedents. From the perspective of modern European languages, this contrastive behavior may be described as follows. In both classical Arabic and later Egyptian, one says something like "the man who“ but "a man while“ or "a man when.“ There are two basic questions. First, does this so-called virtual relative clause, named Hâl in Arabic, point to the common Afrasian origin of Egyptian and Arabic? I believe the answer is "No.“ The second question is: What do indefinite expressions share with circumstantial clauses? I believe an answer is possible to this question as well. And the answer differs, as far as I can see, for Egyptian and Arabic. But I will need to reserve my proposed answers to both questions for another occasion.

A second phenomenon involving relative clauses is an association between relative clause and conditional clause, first extensively documented for Coptic by H.J. Polotsky.^[13] For example, the Greek of John 7:37 is:

Used only with express written permission

which contains a conditional clause. The Coptic translation is:

Used only with express written permission

which contains a relative clause. As I hope to show elsewhere, the association can be explained effortlessly in Boolean terms.

6. To Comma or not to Comma

When it comes to types of relative clauses, the key concern has always been to comma or not to comma, as it were. In the New York Times of February 16, 2008, page A4, one finds the expression "The diplomat, [comma] who spoke on condition of anonymity.“ I have not verified to what extent it is still taught in high school and college composition classes—I assume that it must be—that omitting the comma in front of this relative clause would produce a different purport. Without comma, "The diplomat who spoke on condition of anonymity“ would imply that there was another diplomat who did not so speak. A related distinction is the distinction between "that“ and "which.“ An overall correlation applies between "that“ and absence of comma, on the one hand, and "which“ and presence of comma, on the other hand.

7. The Three Types of Relative Clauses

The result is two types of relative clauses. Many terms have been proposed to name the two types. One type has been called "restrictive,“ "determinative,“ or "specifying.“ The other type has been called "appositive“ or "explicative.“

Restringere, determinare, specificare, apponere, and explicare are respectable Latin verbs. But what exactly do these verbs tell us about the two types of relative clauses?^[14]

Before proceeding with a definition, let us look at some of the facts. I will cite examples from Coptic, the latest stage of ancient Egyptian written, not in the hieroglyphic script, but with Greek letters supplemented with a few additional characters.^[15] Even to anyone less familiar with Coptic, the difference between the three types should be fairly obvious.

The following analysis of the relative clause is also supported by Boolean algebra. But within the confines of the present article, Boolean algebra will be kept to a minimum. The little that will be presented will not be essential to the argument. What follows are a list of conventions of Boolean algebra that will be mentioned below.

Used only with express written permission

A generic example in English of the first type, called "restrictive,“ is "French, that are doctors. is "French, who are Europeans. In this case, the coptic equivalent is unmarked.

TYPE 1 ("RESTRICTIVE“ "DETERMINATIVE“ "SPECIFYING“)

Example of the set ar: "French that are doctors.“Distinctive property of the set ar: The Boolean set ar (a × r) is unmarked.

COPTIC EXAMPLES

Used only with express written permission

A generic example of the second type, called "appositive,“ is "French, who are Europeans.“ In this case, the relative clause is augmented with a distinctive marker, which is in bold and in larger type.

TYPE 2 ("APPOSITIVE“ "EXPLICATIVE“)^[16]

Example of the set ar: "French,[comma!] who are Europeans.“Distinctive property of the set ar: The Boolean set ar is marked ("wired“) for the Boolean equation a = ar—that is, a is part of or a subset of r—in this case "The French are Europeans.“

COPTIC EXAMPLES

Used only with express written permission

The extra element is p. In the second example, the extra element is pai. pai is the near demonstrative pronoun meaning "this.“ But as a comparison with the original Greek shows, πλΙ does not have demonstrative meaning when it serves as the marker of the second type of relative clause. There is no demonstrative pronoun in the original Greek.

The third type is called "hermeneutical.“ One might also call it the "i.e.“ type. A generic example is "Paris, which is (i.e.) the capital of France.“ The essential characteristic of this type is that the two completely overlap. There is no Paris outside the capital of France and no capital of France outside of Paris.

TYPE 3 ("HERMENEUTICAL" "EXPLANATORY“)^[17]

Example of the set ar: "Paris, which is (i.e.) the capital of France.“Distinctive property of the set ar: The Boolean set ar is marked ("wired“) for the Boolean equation a = r—that is, a and r completely overlap—in this case "Paris is the capital of France and the capital of France is Paris.“

COPTIC EXAMPLE

Used only with express written permission

This third type is rare. But it is nevertheless essential in that it completes the model. Without this type, the theoretical model loses its cohesion. It matters greatly to the model that there can be no more than these three types. Now on to a definition of the three types.

8. Definition of the Three Types

8.1. Levels of Definition

There will be no time for a comprehensive definition. Such a comprehensive definition includes at least five levels, as follows: (1) Boolean algebra; (2) Venn diagrams; (3) the linguistic level; (4) the electromechanical level; and (5) the biochemical level. I believe that Boolean algebra provides the sharpest answers. Everything ultimately needs to be reduced to the mathematical level. Venn diagrams optimally visualize Boolean equations. But they exhibit limitations. The linguistic level involves identifying the exact morphemes as empirical components effecting the differences between the types. A description on the electromechanical level is inspired by the belief that everything biochemical in language can be mimicked by an equivalent electromechanical model. The fifth level, the biochemical level, is the final level. That is where things are really happening. But comparatively little can be said about this level at this time.

8.2. Properties of Definitions

The three types of relative clause transmit different kinds of information. In the realm of that which is On or Off, definitions of the kinds of information communicated by relative clauses ought to exhibit three properties.

First, they ought to be fully binary in structure in that everything is On or Off, to satisfy the electrical engineers among us. Second, there ought to be a sense of the absolute limits of the description. In other words, the number of On-and-Off toggles ought to be known exactly. Third, it ought to be known precisely what is On and what is Off.

Aristotelian logic and scholastic logic was mostly concerned with the Ons, hardly with the Offs. Such logic revolved mostly around the syllogism, which exhibits the structure "Human beings are mortal; Socrates is a human being. Therefore, Socrates is mortal.“ However, since Boole, it has become abundantly clear that the Offs are as important as the Ons. In reference to the example just cited, the Offs are "non-human,“"non-mortal,“ and "non-Socrates,“ or "the set of all that is not human,“ and so on. No one more than John Venn has emphasized that a precise calibration of what a certain item of information tells us requires measuring exactly which sets are available and which sets are non-available.

The difference in information between the types of relative clauses is not of the same kind as the difference between "This is a house“ and "This is a car“ or "This wall is red“ and 'This wall is green.“ There is a danger that definitions of concepts such as "restrictive“ and "explicative“ become needlessly abstract. Modern linguistics has on occasion been very theoretical and not all of it has stood the test of time.

The present theory of the relative clause has no chance of success if the differences in information between the types of relative clauses cannot be formulated in terms that are as empirically transparent as the difference between "This is a house“ and "This is a car.“ I realize that, with theoretical terms like "restrictive“ and "explicative,“ the prospects do not look good at the outset. The aim of the next two sections is to improve the prospects by two means. They are a metaphor and Venn diagrams.

8.3. Information Content of the Three Types

Illustrated by a Metaphor

A good way to show how the differences in information conveyed by the three types of relative clauses are very real and tangible is by means of a metaphor, even if metaphors come with limitations. The metaphor I would propose involves a person who always drinks either Pinot Grigio or Chardonnay when frequenting bars. The three types of relative clauses are like what happens in three bars. In each of the three bars, the man drinks a glass of Chardonnay. At the surface, the same thing happens three times. In the same way, the three types of relative clauses basically convey the same information. A clause is subordinated to an antecedent. So what is the difference? The difference is in what other exact information is known about what happens in the three bars.

The first bar corresponds to the so-called "restrictive“ relative clause, the one without the comma in English. The crucial piece of information is that both Pinot Grigio and Chardonnay are available. The man therefore selects Chardonnay.

The second bar corresponds to the so-called "explicative“ relative clause. In that bar, the crucial piece of information is that there is no Pinot Grigio available.

The two types of relative clause are equally informative. But the quality of the information just differs. In the first type, there is elimination of an option. In the second type, there is a non-availability of an option. The contrast between the two types of relative clauses is exactly the same as between elimination and non-availability. It is concepts like these that should inspire the terminology. However, as regards terminology, I have not made a commitment yet.

Elimination and non-availability are a kind of negative information. They belong rather to the Off than to the On of a digital structure. But again, in calibrating information, the Offs are as crucial as the Ons.

In relation to the absence or non-availability, one is reminded of the curious incident of the dog in the night-time, on which the plot of Arthur Conan Doyle’s story entitled Silver Blaze (1892) hinges. It is one of the most popular of the 56 Sherlock Holmes stories. A horse called Silver Blaze has vanished and someone has been killed. When the Scotland Yard inspector Gregory, who has gathered all the pertinent evidence, asks Holmes whether there is any point to which he would wish to draw attention, Holmes declares: "To the curious incident of the dog in the night-time.“ To which the inspector replies: "The dog did nothing in the night-time.“ Says Holmes: "That was the curious incident.“ That explained what happened.

Likewise, upon learning that the man drank Chardonnay in the second bar, one might be puzzled because he seemed to be in the mood for Pinot Grigio or it is Saturday and he always drinks Pinot Grigio on Saturday. In this case, the "curious incident“ is that there was no Pinot Grigio. That explains what happened.

In the same way, upon hearing "French, who are Europeans,“ behave in a certain way, someone geographically challenged who has not heard pause expressed by the comma in speech might ask how French who are not Europeans behave. In this case, the "curious incident,“ if one might call it that, is that there are no non-European French. Or, all French are Europeans.

But what about the third bar? The fundamental difference is that, in the first and second bars, there were other wines except Pinot Grigio and Chardonnay. But not in the case of the third bar. Chardonnay is the only wine available. In this case, there is a double non-availability.

8.4. The Information Contents of the Three Types

Illustrated by Venn Diagrams

Venn diagrams are a useful way of representing the digital character of relative clauses transparently. A relative clause and its antecedent involve two classes. In the realm in which everything is On or Off, 1 or 0, two sets involve four combination sets, which are represented by the four compartments of two overlapping circles in a Venn diagram. In the case of the set "French“ and the set "doctor,“ the four combination classes are "French doctors,“"non-French doctors,“"anything French things that is not a doctor,“ and "anything neither French nor doctor.“

This is how the mind seizes hold of reality (see § 9 below): (1) conceive of two sets in order to relate them to one another; (2) operate with both contraries in all four combinations of the two sets and the two contraries; and (3) shut down one or two combination sets or leave all combination sets occupied. It is easy to see how such operations can be expressed in an electronic circuit. Each compartment can correspond to a switch that can be On or Off.

In first type of relative clause, no compartment is shut down.

Used only with express written permission

As one progresses from the first type to the second and then to the third, what happens is that compartments get scratched out or blotted out or destroyed, as Venn would say. In an electronic circuit, switches are flipped. In "French, who are Europeans,“ one switch is flipped.

Used only with express written permission

This patterns is marked for the nexus f = fe“French are Europeans,” namely:

Used only with express written permission

In "Paris, which is the capital of France,“ two switches are flipped.

Used only with express written permission

This pattern is marked for the nexus p = c " Paris is France’s capital,“ namely:

Used only with express written permission

Flipping a third switch would mean that the universe of thought, everything that one could possibly think about, consists of what is both Paris and the capital of France, in addition to what else it might be. While this may be a pleasant thought to anyone who likes Paris, it is easy to see why this last possibility is not exploited in language.

8.5. Distinctive Linguistic Markers of the Three Types

How is the distinction between the three types achieved linguistically? Relative clauses are after also sound patterns that can be sent from the mouth of a speaker to the ear of a hearer. Some distinctive empirical part of that sound pattern needs to communicate or signal or mark that a relative clause belongs to one of the three types and not to the two others. What does one need to look for in all kinds of languages to identify the three types, to the extent that the three types are articulated?

According to the theoretical model proposed above, the second and third types are in a sense marked. One or two of four compartments are empty. One or two switches are turned off. For example, in the transition from the first type to the second type, a compartment is declared non-available on the level of logical purport. But how is this conveyed on the linguistic level? Which morphemes mark non-availability, and how? Consider the generic example "French, who are Europeans.“ Clearly, the information "French are Europeans“ is implied. Or, if one refers to the French by a pronominal representative, this information may be described as "They are Europeans.“ Chances are that some kind of pronominal representative like "they“ or "those“ marks the relative clause of the second type as a distinct type.

I believe that exactly such pronominal reference is the function of the extra pai pai or p- in the second type of relative clause in Coptic. Accordingly, as was noted above, pai pai does not have demonstrative function, as it otherwise always has. In the example Deuteronomy 1:32–33 cited in § 5, the expression petmooše "the one who is walking“ is a conversion of the nexus fmooše "He is walking,“ whose logical purport is "He is a member of the set of those that are walking.“^[18] The information conveyed by the nexus is fully preserved in the shift from "He is walking“ to "the one who is walking.“^[19] The elements p-"the one“ and f-"he“ convey the same information, that is, a reference to an entity involved in the event. It is this information that is needed to declare one of the four combination sets non-available and switch it off.

In English, the linguistic marker can be a slight pause, as marked by a comma in writing. A pause appears to have to the same effect as a pronominal element referring back to something previously mentioned. Therefore, two sentences such as "He arrived there, and that late“ and "He arrived there—late,“ the pronominal element "that,“ which refers back to something stated before, and the pause expressed by the Em-dash have roughly the same meaning.

In Coptic, the linguistic marker of the third type of relative clause is the expression ete pai pe p — "which is“ or "i.e.“ (literally: "about which one can say: that is the —[or another definite expression]“). Clearly, an expression such as "i.e.“ links two classes that completely overlap, which is the digital hallmark of the third type.

8.6. The Role of Negation

Negation has been a difficult beast to tame. E. Schröder, who taught at the Technische Hochschule in Karlsruhe and once was its director, evokes the tortured path of the study of negation from the time of Aristotle and even earlier when he describes it as^[20]

a field of investigation in which great caution is warranted, since the most renowned philosophers of all time—I mention in first place Aristoteles and Kant—widely diverge from one another in this regard, a field also in which even in most recent times authoritative voices have constructed untenable theories, theories that have entangled their creators in the greatest contradictions with themselves.^[21]

It was Boole who finally tamed the beast. Augustus De Morgan was an important precursor and Venn did much to make Boole’s ideas more accessible. One of Venn’s great merits, in my opinion, is to emphasize again and again how hardly anything more than the elimination or negation of classes among all possible combination classes gives the mind the power to engage reality and reason about it. The single most important step in domesticating negation, and also a main point of this paper, is that negation plays as important a role in affirmative statements as it does in negated statements. I believe that, without heeding this point, the analysis of language will never be pushed back to its final frontier.

9. How the Mind Digitally Seizes Control of Reality

Already from the mere contemplation of the relative clause, a picture emerges of how the mind in large part seizes hold of reality and molds it into information and reasons about it. This procedure is recognizable in all facets of language. Only a brief sketch will be presented here. The main steps are as follows.

First, reality presents itself to the senses as discrete elements. Second, these discrete elements are stored in the mind for what they are, namely discrete elements. Third, knowledge seriously takes off when two elements are related to one another. Fourth, in relating two elements to one another, the mind produces the four combination sets involving two elements and their contraries, that is, the two elements in both present or On (1) and absent or Off (0) state. The four combinations are obviously present/present, present/absent, absent/present, and absent/absent. Fifth, knowledge derives its principal strength from the shutting down or the switching off of one or two of these combinations. Switching off three or four is hardly informative.

The case of the relative clause is at length illustrated above. But the exact same switching off as a way of achieving knowledge is also found elsewhere. My provisional estimation is that this digital pattern can be found all over the structure of language and bears witness to the profoundly digital nature of thought and language. Two examples follow. For example, the information content of a sentence such as "Aristoteles is a philosopher,“ which would correspond to a nominal sentence in Coptic, is that one four combination sets is shut off, namely present/absent, or entities that are both Aristotle and not philosophers. Likewise in a conditional sentence such as "When it rains, I stay inside,“ exactly one of four combination sets is switched off, again present/absent, or instances when it rains and I do not stay inside. The three other combination sets remain On: instances when it rains and I stay inside; instances when it does not rain and I stay inside; and instance when it neither rains nor do I stay inside.

Notes

Citations