Consider the following passage, about phonological features:

I have not seen any convicing justification for the doctrine that all features must be underlyingly binary rather than ternary, quaternary, etc. The proponents of the doctrine often realize it needs defending, but the calibre of the defense is not unfairly represented by the subordinary clause devoted to the subject in SPE (297): ‘for the natural way of indicating whether or not an item belongs to a particular category is by means of binary features.’ The restriction to two underlying specifications creates problems and solves none. (Sommerstein 1977: 109)

Similarly, I had a recent conversation by someone who insisted certain English multi-object constructions in syntax are better handled by assuming the possibility of ternary branching.

I disagree with Sommerstein, though: a logical defense of the assumption of binarity—both for the specification of phonological feature polarity and for the arity of syntactic trees—is so obvious that it fits on a single page. Roughly: 1) less than two is not enough, and; 2) two is enough.

Less than two is not enough. This much should be obvious: theories in which features only have one value, or syntactic constituents cannot dominate more than one element, have no expressive power whatsover.^1,2

Two is enough. Every time we might desire to use a ternary feature polarity, or a ternary branching non-terminal, there exists a weakly equivalent specification which uses binary polarity or binary branching, respectively, and more features or non-terminals. It is then up to the analyst to determine whether or not they are happy with the natural classes and/or constituents obtained, but this possibility is always available to the analyst. One opposed to the this strategy has a duty to say why the hypothesized features or non-terminals are wrong.

Endnotes

1. It is important to note in this regard that privative approaches to feature theory (as developed by Trubetzkoy and disciples) are themselves special cases of the binary hypothesis which happen to treat absence as a non-referable. For instance, if we treat the set of nasals as a natural class (specified [Nasal]) but deny the existence of the (admittedly rather diverse) natural class [−Nasal]—and if we further insist rules be defined in terms of natural classes, and deny the possibility of disjunctive specification—we are still working in a binary setting, we just have added an additional stipulation that negated features cannot be referred to by rules.
2. I put aside the issue of cumulativity of stress—a common critique in the early days—since nobody believes this is done by feature in 2023.

References

Sommerstein, A. 1977. Modern Phonology. Edward Arnold.