In this article, I set out to show how to interpret adjectives and why ru is a bad default for non-subordinating serial predicates.

Before we begin, in order to avoid confusion, it should be noted that when the term adjective is used throughout this article, it refers to predicates that are used in some way to modify other predicates. Toaq does not have adjectives as a separate part of speech, but it is a useful term to refer to the left part in a modifier-modified pair of predicates. With that said, we can begin our journey towards a better understanding of the logic of adjectives.

What is the meaning of a phrase like (A) “red car”? It seems to be quite simple: it’s a car and it’s red. It’s a red car. Surely, we say with conviction, the meaning of the phrase can be expressed by the following property:

red(x) ∧ car(x)

But is it really as simple as it seems? Let’s leave the color case for later and and let us look at another example: (B) “small elephant”. Well?

Consider this argument:

(1.1) [∀x : E(x)] A(x)

“Whatever is an E is an A”

(1.2) ⊨ [∀x : E(x) ∧ S(x)] A(x) ∧ S(x)

“Therefore, whatever is an E and is S is an A and is S”

(1.2) follows logically from (1.1). If we try to apply this to our small elephant, we get:

(2.1) [∀x : elephant(x)] animal(x)

“Whatever is an elephant is an animal.”

(2.2) ⊨ [∀x : elephant(x) ∧ small(x)] animal(x) ∧ small(x)

“Therefore, whatever is a small elephant is a small animal.”

This is clearly an invalid conclusion. A small elephant is still bigger than most animals. It must be, then, that the first argument (1.1 and 1.2) has a different logical form than the second argument (2.1 and 2.2). Since the first argument is logically sound (following basic rules of logic), it must be the second argument that is faulty. “small elephant” thus cannot logically be analyzed as the conjunction of the predicates “is small” and “is an elephant”.

Adjectives of this kind (i.e., adjectives which fail the above test) are called attributive adjectives. On the other hand, adjectives that do allow an analysis in terms of a conjunction of predicates are called predicate adjectives. These are not as common as may seem at first. The starting example “red car” seems to work out, but it is not telling the whole story about a predicate like “red”. Again, we will come back to this.

There is one more example needs to be looked at. How do we understand an expression like (C) “the alleged extraterrestrial”? It would be disastrous if we interpreted that phrase as in (2.1 and 2.2). It is not hard to see that an “alleged extraterrestrial” is not simply something that “is alleged” and “is extraterrestrial”. “alleged”, then, is also an attributive adjective.

Now that we have an understanding that there are different kinds of adjectives and have seen three different examples, we can begin to ask ourselves how they would be expressed in Toaq.

Assuming for now that “red” in example (A) is a predicative adjective, we have seen one example of a predicative adjective and two examples of attributive adjectives (examples (B) and (C)):

(A) “red car”

(B) “small elephant”

(C) “alleged extraterrestrial”

As a translation of (A), we will settle (for now) with ru:

(A.1) kỉa ru chảo

“is red and a car”

However, trying to express (B) and (C), we discover an important difference between the two. The word for “small”, nuı, is a monadic predicate (“___ is small”), but what about “alleged”? If you have developed some Toaq intuition, you would probably come up with the following solution for this word: ___ is alleged to satisfy property ___. And indeed, this intensional definition is exactly the correct approach. Toaq‘s serial predicate rules will turn the equivalent of “alleged extraterrestrial” into “alleged to be extraterrestrial”, which gives us the correct semantics automatically:

(C.1) rủaqnū bủıgājā

“be alleged to be extraterrestrial”

So back to (B). nuı “small”, as we said, does not have a property place. We would like to be able to say:

(B.1) nủı hẻlū

“small elephant” (?)

But the current rules are such that any non-subordinating serial predicate (i.e., those where the head predicate does not have any places that take subordinate clauses) has an implied ru, which corresponds to logical conjunction:

(B.2) nủı ru hẻlū

“small and an elephant”

Under the current rules, (B.1) and (B.2) are synonymous. I argue that they should not be and that a better default would be one that properly expresses the attributive semantics that we need. However, there are potentially two ways to go from here.

One way to handle attributive adjectives was exemplified in (C.1), and that is properties and the use of Toaq‘s serial predicate rules. The second way is to change the default connective that appeared in (B.2) to something else.

In the case of nuı “small”, the property approach would require adding a property place to the definition, something like “___ is small for something that satisfies property ___”.

There are, however, problems with having to rely on a property place:

Place structures become more complex throughout the lexicon.

It is dangerous because it puts a significant burden on word creators. Every word must be checked for the attributivity condition and if it fails, it must get an additional place. If this is not done, serial predicates using the word will end up having the wrong meaning. As such, this system is less robust because it leaves room for things to go wrong. I also think that word creation should remain as easy as it currently is. Requiring people to run every word they make through a logic test does not seem to go hand in hand with that.

Also, and this is just as relevant, many if not all words that are primarily predicate can be meaningfully used in an attributive way. The decision of whether or not to add a property place changes how a word behaves in serials, in a way forbidding the attributive use case if no property is added to the definition. This seems like the kind of philosophical prescriptivism that the language shouldn’t hard-code. It should be up to the speaker to use any predicate they want in an attributive fashion.

But then, adding a place to every single predicate when a simple compositional rule could take care of the correct semantics seems inefficient. It makes more sense then, to have attributivity be the default behavior of non-subordinating serial predicates instead.

As with other concepts in the language, something that applies or could potentially apply to every predicate should not be encoded in the predicate place structure. Everything can be viewed by a certain standard. Different standards of what counts as “asleep”, or “alive” for that matter, are conceivable. Since a standard can be applied to literally every predicate, it should be handled more globally. In this case, through attributive semantics of non-subordinating serials, or, in predicate sentences, via a prepositional phrase.

In short, all of the drawbacks mentioned above would be avoided by making the attributive interpretation the default.

I believe, therefore, that the attributive interpretation is a better default than the ru reading even in cases where ru would be semantically acceptable, because it is useful and offers more expressive possibilities than a mere ru, because it allows more contextually tuned meanings.

What is a “black cat”? One might think it satisfies the property black(x) ∧ cat(x), but in reality, there are no naturally occuring black cats – they are a very very dark brown – but for the purpose of classifying cats into groups by color, “black” is a useful name for a black cat. The attributive reading is more appropriate even with color words. Different things have different thresholds for when you would call them by a certain color.

Now, all this is not to say that ru is never useful. We would still use ru (explicitly) for some enumerated adjectives (“the beautiful happy painter”), and we would also use an explicit ru when we want to avoid the relativity provided by the attributive reading, which is going to be rare enough, but not inconceivable.

Instead of ru, we can also use a relative clause. For “scared white rabbit”, we can either say “white rabbit which is scared” (báo lẻpō těa), or the reverse, “the scared one which is a white rabbit” (téa bǎo lẻpō).

Verbs expressing (temporally limited) states of mind or states of being, like emotions, “to be happy”, or “to be alive”, “to be asleep”, usually work as predicative adjectives, so the use a relative clause or an explicit ru would be a common choice. However, even those could be used either way, and since the attributive reading is “never wrong” and ru often is, it should be clear what the better default must be at this point.

What remains to be explained is what the new default meaning actually is. We saw how adding the property place in “___ is small for something that satisfies property ___” would give the right semantics. The same semantics would be used as the implicit operator between two predicates in a non-subordinating serial.

nủı hẻlū

be small elephant

lủ nủı hóa pè báq hẻlū

be small for an elephant

(where pe is a predicate meaning “___ is the case for/by the standard of ___” used as a preposition)

Another expansion would use a predicate with two properties: “___ satisfies property ___ by the standard of things that satisfy property ___”. Because this predicate is rather impractical, it would only be used “under the hood” to explain the invisible function in formal terms, but it wouldn’t be used in conversation. I haven’t yet invented this predicate.

Anyway, with pe, we also acquire the ability to make predicative claims and then make them attributive in afterthought. So then, there are three ways to say “this elephant is small” in the sense of “this elephant is a small one” and at least two ways to say it in the predicate sense:

Nủı ní hẻlū.

“This elephant is small.” (predicative)

(compared to all salient things, all things in the domain. Maybe there are houses and dinosaurs in the domain, so the elephant counts as small. Whether it is small for an elephant is not being stated here!)

Nủı ru hẻlū ní.

“This is small and an elephant.” (predicative)

(explicit ru)



Nủı hẻlu ní.

“This is a small elephant” (attributive)

(the new default working nicely)

Nủı ní hẻlū pè báq hẻlū.

“This elephant is big for an elephant.” (attributive)

Nủı ní pè báq hẻlū.

“This one is small for an elephant.” (attributive)

(avoiding the repetition)

Whether there should be a function word that allows one to make the attributive function in nủı X hẻlu explicit (and if so, what that function word should be and to which class it should belong) remains to be seen. The main purpose of this article was to show why ru is not a good default and what the default should be instead. Further discussions deserve their own space.

And with that, I wish to thank all the skillful readers (predicative or attributive?) for having taken the time to read this long article (and here?).