In reading John Stuart Mill, A System of Logic (1843), it’s become clear to me that a lot of what I’ve found most useful in logic has been less what it’s ultimately trying to do and more what it must do as a means to its end.

In A System of Logic, Mill starts his analysis with names. For example, there are names like “country,” which are (in their spoken, written, and other forms) associated with indefinite “groups of individuals”—for the lack of a better term—and names like “England,” which are associated with definite “individuals.” What’s the difference, though, between a name and a word? A name is a kind of word. A name is always associated with an indefinite group of individuals, a definite group of individuals, or a definite individual, and a word is associated like that only insofar as it’s a name. For example:

1. “Country” is a name because it’s associated with England, Germany, and every other country (whether past, present, future, or hypothetical).
2. “The Axis” (in the context of the Second World War) is a name because it’s associated with Nazi Germany, Facist Italy, and Imperial Japan.
3. “England” is a name because it’s associated with that country.
4. “The” isn’t a name—at least it’s not a name in and of itself—because it’s not associated with an indefinite group of individuals, a definite group of individuals, or a definite individual. (“The country that I grew up in,” though, which has “the,” is a name.)

Mill also distinguishes between connotative and non-connotative names, “country” being an example of a connotative name because it connotes certain attributes (e.g., sovereignty) and “England” being an example of a non-connotative name. “Country” denotes England because England is sovereign etc., but “England” denotes that country regardless of its sovereignty etc.

After his analysis of names, Mill moves onto ontology, which is the analysis of the most fundamental categories: mind, body, etc. And then after ontology—I’ll forgo summarizing Mill’s ontological system in this essay—Mill moves onto an analysis of propositions (which presupposes names, for propositions are in part made of names): For example, in “snow is white,” the subject, which says what the proposition is about, is “snow,” and the predicate, which says something about what the proposition is about, is “white.” Such propositions, according to Mill, aren’t best analyzed as the category “snow” being included in the category “white things,” but as what’s in the category “snow” being attributed whiteness.

It’s only after analyzing names, ontology, and propositions (which gets at the form and substance of propositions) as a means to an end that Mill gets to what logic is ultimately trying to do: explain what propositions imply what other propositions, well what kinds of propositions imply what other kinds of propositions. I’ve always found the former more useful than the latter, whether in Mill or elsewhere.

In English, there are copular propositions (e.g., “swans are white”), copular-like propositions (e.g., “swans have wings”), and non-copular propositions (e.g., “drugs kill,” “drugs kill people”). What does it mean for swans to be white? If you see a swan, then you’ll see something white: the swan. And what does it mean for drugs to kill? If you see a drug, then you’ll see something that kills: the drug.

One of my goals for the artificial language is to integrate the copular, copular-like, and non-copular propositions. English uses “to be” for the copular, “to have” for the copular-like, and nothing for the non-copular: “Swans are white,” “swans have wings,” and “drugs kill.” In the artificial language, I’ll avoid that asymmetry. I’ll mark the subject, the predicate, and the kind of relationship between the subject and the predicate: the “to be” relationship, which is spatial whole-whole, temporal whole-whole, the “to have” relationship, which is spatial whole-part, temporal whole-whole, and the nothing relationship, which is the spatial whole-whole, temporal whole-part relationship. (Propositions take a subject a put it together with a predicate—that’s what propositions are. The questions are what the subject is, what the predicate is, and what the relationship is between the subject and the predicate.)

“Swans are white” means that if you see a swan, then you’ll see something white: the swan. And “white things are swans” means the opposite: that if you see a white thing, then you’ll see something that’s a swan: the white thing. The former proposition is false but not absurd, and the latter proposition is false and absurd.

English is asymmetrical:

1. “Swans are white,” “white things are swans”
2. “Swans have wings,” “things that have wings are swans”
3. “Drugs kill,” “things that kill are drugs”
4. “Drugs kill people,” “things that kill people are drugs”

In the artificial language, I’ll avoid that asymmetry. I’ll do something like:

1. “Swans are white,” “whites are swan”
2. “Swans have wings,” “wings have swans”
3. “Drugs kill,” “kills drug”
4. “Drugs kill people,” “kills people drug”

What are the semantic differences between “white swan” and “swans are white”? (a) One of the semantic differences is that “white swan” is non-propositional and “swans are white” is propositional. That is, “white swan” is neither true nor false but “swans are white” is the opposite: It’s either true or false. (b) The other semantic difference is that “white swan” asks you to imagine something that’s both white and a swan and “swans are white” tells you that if you see a white, then you’ll see something white: the swan. “White swan,” being non-propositional, doesn’t tell you anything about, say, “black swan,” but “swans are white,” being propositional, tells you that “swans aren’t black.”

That is:

1. “White swan” brings together in your imagination whiteness and swanness.
2. “Swans are white” not only brings together in your imagination whiteness and swanness but also proposes that whiteness and swanness go together.

(It’s important to point out that “swans are white” tells you that with swanness comes whiteness, not the opposite: that with whiteness comes swanness. That is, s < w, not w < s.)

With the double labels ab, ~ab, a~b, and ~a~b:

1. It’s possible to bring together in your imagination ab, ~ab, a~b, or ~a~b.
2. It’s also possible to propose that ab, ~ab, a~b, or ~a~b go together. (That’s what the copula does.)

In The WEIRDest People in the World (2020), Joseph Henrich argues that over a millennium, the Catholic Church simplified the kinship system of the West from clannishness to the nuclear family. People stopped marrying in a narrow circle, which results in narrow genetic loyalty—clannishness—and started marrying in a wide circle, which results in wide genetic loyalty. Cooperation scaled, and the West, with its big-scale civilization, took over.

Henrich doesn’t argue this, but my understanding is:

1. There have always been clannish holdouts (e.g., royalty, the aristocracy, the Jews, the mafia).
2. The clannish holdouts end up with a lot of power.

What was monarchy but that? That is, what was monarchy but the clannish holdouts controlling the non-clannish? The non-nuclear families controlling the nuclear families?

And what was the aftermath of the World Wars but the end of royalty and the aristocracy?

When introducing the technical side of my work, I used to lead with: “I’m designing an artificial language.” Now I lead with: “I’m designing notation for logic and linguistics à la the best mathematical notation: arithmetical, algebraic, etc.” I used to get bad reactions, and now I get good reactions. Why? I’ve been working on my artificial language, my logico-linguistic notational system, for a long time. I started in my late teens. In changing the term that I lead with from “artificial language,” which makes most people skeptical, to “notation,” which doesn’t, I didn’t change anything about the substance, about what I’ve been working on for so long. I just changed my strategy for explaining what I’m working on.

Why it worked to change the term:

1. It sounds utopian, even schizophrenic, to be serious about designing an “artificial language,” to seriously believe that designing an “artificial language” could revolutionize communication. By contrast, it sounds modest to say that you’re designing “notation.” It sounds scientific.
2. In designing an artificial language, it would be possible to prioritize the phonological and orthographical aesthetics, to prioritize making the artificial language sound and look beautiful. In designing notation, however, (a) there’s no phonology—the term “notation” refers to +, -, and other international written symbols, their countless spoken counterparts throughout the world (e.g., “plus,” “minus”) notwithstanding, for those spoken symbols aren’t notation but natural language—and (b) although it would be possible to prioritize the orthographical aesthetics, people associate the term “notation” not with art but with science. My project has no phonology, and my artistic vision for the orthography is secondary to my scientific vision. Thus, the term “artificial language” is more misleading association-wise, and the term “notation” is less misleading.

The software would:

1. Be a better way to learn languages (which would be the direct goal).
2. (Indirectly) teach the user how to abstract out the logical substructure of natural language (in practice).
3. (Indirectly) teach the user the skeleton for an artificial language.
4. With enough users, (indirectly) flesh out the skeleton of the artificial language.

Imagine that you’re studying Japanese with flashcard software (e.g., Anki), with the front of each flashcard being the Japanese (whether spoken, written, or both) and the back of each flashcard being the English translation (again whether spoken, written, or both). My software would also be flashcard software, the difference being:

1. The software would guess what it should test you on. Its guesses would get better over time, and eventually it would be able to guess how much vocabulary you know, how much grammar you know, how good your ear is, etc. (That would be motivating because the software would show your language-learning progress in real time. The more you immerse and the more you study the flashcards, the faster you see your vocabulary growing etc.)
2. The back of each flashcard wouldn’t be an English translation but a translation into the artificial language.

On #2: Imagine again that you’re studying Japanese. You try to understand the Japanese on the front of the flashcard, and then you check the back in order to check whether you were right. By default, the software would show you only the translation into the 1-dimensional modality of the artificial language. You’d have various options:

1. Generate the 2-dimensional-modality artificial-language transliteration.
2. Hover your cursor over anything in the Japanese on the front of the card or the artificial-language translation/transliteration on the back of the card, which would show you which chunks, whether bigger or smaller, in the Japanese, correspond to which chunks, again whether bigger or smaller, in either the 1-dimensional translation or the corresponding 2-dimensional transliteration.
3. Click any of those chunks, whether a word, phrase, or sentence, in order to AI-generate a visualization of a prototypical example. Click again in order to generate another visualization. Gradually, the visualizations would go from more prototypical to less.

Besides letting the user study flashcards, the software would also let users input the 1-dimensional and 2-dimensional modalities of the artificial language themselves in order to write either to themselves or other users. Most importantly, they could message other users in artificial language (not to mention English, Japanese, or any other natural language popular enough to be easy to include). With enough users who (indirectly) know the artificial language, an international Republic of Letters could come about. If, say, a monolingual Japanese person learns English with the software and a monolingual Korean person learns German, then they have no shared natural language. The artificial language would be the easiest way to communicate, which could naturally make the artificial language into their lingua franca.

The artificial language could also just end up being (like arithmetical, algebraic, and other mathematical notation) a useful supplement to natural language: an international notational system (for laying bare the logical substructure of natural language). (Another possibility: It could also just end up being a tool for formalizing logic, linguistics, and the relationship between logic and linguistics.)

But how would I make the artificial language more natural? The software would let the users add new symbols to the open-class vocabulary, which would let them naturally change the artificial language in practice.