Sometimes the tetrachotomy results from the combination of two dichotomies, like the Aristotelian vision of the 4 elements:

Other times, a tetrachotomy originates from two successive dichotomies, like is the case for the one appearing in the main page. Very often these kind of tetrachotomies can be easily traced back to a single dichotomy. In that example, most can agree on the artificiality of the distinction between Love and Friendship and of the one between Art & Science (i.e. they'll agree that Love=Friendship and Science=Art).

And, of course, there are tetrachotomies in their own right, coming from no dichotomy at all.
E.g. the division of the year in four seasons would be very artificially and subjectively grouped two-by-two into a dichotomy (first part of year|second part of year? colder|warmer? happy|sad?).

The human mind seems very much oriented towards dichotomies, towards dividing the world in black & white, dead & alive, sky & earth, good & bad. The absence or presence of a property often leads the separating scalpel.

Alternatives to this view are possible (and encouraged). Tri- Tetra- Penta- (and more) divisions.

Or no division at all.
Zen philosophy is one of the masterpieces in refuting and refusing dichotomies, expecially subject-object ones.
The yin and the yang (female|male, black|white principles) melt together in one.
The FiliusMortis symbol (at the bottom of the page) is composed of four parts (they are in reality just two, as can be easily shown when the symbol is folded around a cylinder to unite the two edges) that all meet in the center, melting in one.

MU (the famous "third way") is another way out of the dichotomy:

'The teacher Joshu was asked by a student, "Does a dog have Buddha nature ?", to which Joshu replied, "Mu !"'.
Commenting on this many years later, the teacher known as Mumon wrote,
'The dog, and the Buddha nature. Joshu's answer is perfect and final. When you can say whether it has it or not, you will be walking hand in hand with the patriarchs'.
'Mu' does not mean that a dog cannot have Buddha nature, but that the question itself is a 'nothing' question (that is, a question without profit, since no answer is profitable). By replying 'mu', he "unasks" the question.