The ground of each distinction is an indistinct mass or state or condition, a kind of whole without parts or at least without parts that have been discerned. Every instance of the whole is at first, an instance of one mass or state or condition.
A unary distinction is a discernment of something out of a mass or state or condition of indistinction. The latter is the default state or condition, which is the ground from which something is distinguished.
For example, a forest of trees is, as far as has been stated, a mass of undistinguished trees. If one or a group of trees are distinguished out of this forest, a unary distinction has been made. Unless a tree is distinguished, it is uniform with the mass of trees that is the forest.
A contradiction is a unary distinction in logic. The mass of propositions has a default value, which is true or false depending on one’s logical stance. For the realist, all propositions are true unless shown to be false. For an anti-realist, all propositions are false unless shown to be true. If a set of propositions is shown to contradict propositions with the default value, a unary distinction has been made, and they are assigned the contradictory value.
A binary distinction is a division of the state or condition of indistinction into two parts or halves. The two parts are discerned relative to one another and entail one another; they are logical contraries. They make up a dichotomy.
Examples of binary distinctions abound: up and down, in and out, left and right, north and south, masculine and feminine, short and tall, small and large, negative and non-negative, etc. A reference to both parts of a binary distinction is a reference to the whole; it is a merism.
A ternary (or trinary) distinction is a division of the state or condition of indistinction into three parts or thirds. The three parts are discerned relative to one another and, together make up one whole. They make up a trichotomy.
Examples of ternary distinctions abound: small, medium, and large; masculine, feminine, and neuter; positive, negative, and zero; turn left, turn right, go straight; animal, vegetable, mineral; etc.
An N-ary distinction is a division of the state or condition of indistinction into N parts. The N parts are discerned relative to one another and together make up one whole. Examples are: a quaternary distinction of north, south, east, and west; Carl Jung distinguished eight psychological types, which is an 8-ary (octary?) distinction; G. K. Chesterton distinguished 12 types of people, a 12-ary distinction; Myers-Briggs distinguished 16 personality types, a 16-ary distinction.