# Why is binarity emphasized so much in linguistics?

I'm an aspiring linguistics student, not a professional, so my thinking may be misguided or elementary.

In my personal research about linguistics, I have discovered many important theories and frameworks which seem to emphasize something binary, i.e., they divide things into two elements. For example:

1. In distinctive feature theory, binarity is a principal property, with two values for each feature (+ and -). Even the unary features feel binary with values of present and not present.
2. In X-Bar syntax, binary branching seems to be emphasized excessively. Elements that might otherwise be categorized as one of three+ branches in a node are placed at a different level on the tree so the binarity can be maintained.
3. Finally, I know that generative grammarians love recursion through the Merge operation, which combines two objects into a bigger one.

I'm aware that formalists love to reduce language down to the simplest axioms possible, which may be a reason for binarity. However, I don't understand why it is necessarily better to give features only two values, divide constituents into only two branches, and merge only two items. {a} + {b} -> {a, b} + {c} -> {a, b, c} seems much more complicated to me than {a} + {b} + {c} -> {a, b, c} (I'm aware my notation is probably terrible).

What is the reason for the emphasis on binary structures and distinctions in linguistics?

• I prefer binary opposition. Anyway, binary [structure] is important in structuralism which a lot of folks around here do not like. In any event, it is just a tool. Nov 6, 2023 at 16:29
• Your question is good. I think it is touching on a weakness in much linguistic theory. There is something scientifically satisfying about binarity, even though the binary oppositions may complicate the use and application of the theory that they are intended to simplify. Most who have studied the strictly binary branching tree structures associated with "Minimalism" know that those tree structures are terribly complex and anything but simple and easy to learn. Nov 7, 2023 at 12:57

Binarity is favored over alternatives by general scientific logic, therefor to the extent that a linguist is concerned with scientific logic, that is the expcted tendency. However the specific details depend on the particular application. The general principle is Occam’s Razor, specifically the principle that given an unnecessary proposition, the theory without the unnecessary proposition is to be chosen (xref the classical Aristotelian, Aquinian and Newtonian statements).

However, the concrete application of this logic varies substantially in linguistic theory. In the case of phonological features (which preceded generative theory by many years), the initial position was that there is a small set of orthogonal properties which are present or not, which can define all human language sounds. The Jakobsonian branch introduced a specific notion of plus and minus values for features, which is the underlying premise adopted by genertive grammarians. This is analogous to computer representations of positive integers from 0 to 65535, that each integer can be represented as a unique configuration of 1 and 0 bits within a field of 16 bits. The computer guys could have tried for a base 3 representation of numerals where the values yes, no and meh yield integers from 0 to 59049 within a field of 10 bits. The two theories are similar, but where the binary theory posits the bit-entities ‘0, 1’, the ternary theory posits the bit-entities ‘0, 1, 2’, making the binary theory a simpler subset of the ternary theory. This prejudices the scientist in favor of the binary theory.

Further however, straight binary theory in phonology soon was actually replaced with ternary theory (the names were “+, –, 0”) then later a virtually unbounded set of values (+,–,u,m,0,1,2,3,4…). The propositional complexity of the theory changed by expanding the range of possible values associated with a given feature. This is in clear violation of Occam’s Razor, which does not allow expansion of entities unless it is shown to be necessary.

Phonological theory later (in the mid 80’s) rediscovered Trubetzkovian privativity, so there has been a retreat in this expansion of entities. Part of this retraction was the removal of u, m and integers as values, because phonologists rejected various aspects of the SPE theory of computation and representation. The elimination of integers (or reals) stems from the rejection of the SPE premise that there is no phonetic component to grammar, where is where integer values might be of some unique use. Therefore, rather than positing that there are two values for every features, we would now say that a given feature is present or not present. In binary theory, you have three concepts: feature, attribute, and value. In privative theory, you have only one concept: feature. This is an instance of intensional reasoning, that is, focusing on the logic of the theory rather than the class of things that can cranked out with a particular theory. Linguistics in the 70’s-90’s was more highly focused in extensional thinking, in terms of classes of outputs, but current thinking is more focused on the fundamental nuts and bolts of the theory. So in fact privative theory is not binary theory. (I should point out that neither binary nor privative theory has carried the day in contemporary phonology, instead agnosticism rules).

A touch of extensional reasoning likewise underlies the syntactic claim of binary branching. It is well known that N-ary trees allow uncomputably many ways of arranging 15 words into a single tree, therefore a child cannot possibly learn a language that allows sentences that are at least 15 words long (i.e. all languages), because there are too many hypotheses to entertain and reject. The added premise that all branching is binary vastly reduces the acquisition problem, and imposing a single direction of branching carries you even further. If you only allow binary branching, you complicate the theory by positing that there is a limit on the number of branches allowed, but your theory of upper bounds is the simplest possible (0 and 1). Some complication is necessary (for reasons of acquisition), binary branching is the logically-simplest complication.

Complexity is defined at the level of the theory itself, and cannot be intuited from the superficial behavior of the system. To understand complexity arguments, you have to know what propositions define theory A versus theory B. The problem is that people tend to bypass the step of explicitly stating the propositions that constitute A vs B, therefore there is a mistaken tendency to think of complexity in terms of reified “steps” in a pseudo-computation. If it is simpler to smash {a} + {b} + {c} together in a single more-powerful step, rather than two steps, imagine how much simpler it would be to smash {a}+{b}+{c}+{d}+{e}+{f}+{g} into {a, b, c, d, e, f, g}, and yet even simpler to just start with {a, b, c, d, e, f, g} and forego the smashing-together step entirely.

• I can comment here concerning binary branching in syntax. The notion you put forward here that it is the logically simplest way to conceive of sentence structures is poppycock in an important way. By positing strict binarity of branching in syntax, the number of nodes in the tree structure reaches its upper limits. N-ary branching results in fewer nodes and hence fewer constituents and hence simpler and easier to learn syntactic structures. Nov 7, 2023 at 12:40
• Calling something poppycock does not make it so. Nov 10, 2023 at 14:04
• @Keelan, the statement is "poppycock in an important way", and then the qualification comes. Do you disagree? Why? I would enjoy engaging with your answer. Nov 10, 2023 at 16:48

{a} + {b} -> {a, b} + {c} -> {a, b, c} seems much more complicated to me than {a} + {b} + {c} -> {a, b, c}

Complexity and difficulty are different problems. A recursive algorithm may have a fairly low complexity, as in this example, and repeated application to the results is basicly free.

For reference, the number of permutations for a + b is low, either {a, b} or {b, a}. This remains true in recursive application. The number of possible results for a + b + ... n on the other hand grows exponentially (factorial n).

Conversely, one could argue that the number of functions involved is higher in the former case (rec and some operator) than in the latter (some operator).

The values of variables depends on whatever theory you are working with. However, almost all theories agree on true and false statements. They might not agree on particular truth values, but they agree on an infinite number of statements being false, which they can disregard.

In this view, the premise of the question is not correct:

In my personal research about linguistics, I have discovered many important theories and frameworks which seem to emphasize something binary, i.e., they divide things into two elements.

The vast majority of theories like to define X is Y. Perhaps this is the uniformitarian principle at work. In set theory it is called the identity operator.

In linguistics, no universal formalism has been obtained. E.g. a) the binary contrast in feature theory can concern two features present in three phonemes or not, b) in branching trees of dependency syntax, the elements are made up of those phonemes, c) in universal grammar's merge, recursion is simply not an example of binary branching, if the operation is carried out by a parallel architecture (Jackendoff). Subdigitization e.g. adding roman numerals I + II = III requires no permutation or sequencing.

It's just that sequentially written text appears to be very sequential, except that anyone who has gone back to edit a text knows that this isn't even true.