Is the arbitrary symmetrical?

Arbitrariness is commonly seen as a major concept in Saussure’s thought, and it even receives the status of a “principle” in his theory. It is not only the characteristic feature of the relation between the signifier and the signified (the semiological relation is arbitrary), but moreover it is constitutive of this very relation (the relation is semiological because it is arbitrary; there is a so-called “semiological relation” established between a signifier and a signified because of the principle of arbitrariness). And when linguists and other Saussurean interpreters comment on the concept of arbitrariness, they usually imply a binary relation: the semiological relation is arbitrary due to the fact that the signifier is arbitrarily chosen vis-à-vis the signified, and vice versa. I will be questioning the latter assertion in this paper. In my opinion, the symmetry of the semiological relation has not been properly demonstrated. The signifier can be seen as arbitrary with regard to the signified, but no reason has been provided to recognize the converse. Instead a number of arguments can be put forth to see arbitrariness as a concept that implies a non-symmetrical relation.