The thesis of the arbitrariness of the sign (so grossly misnamed, and not only for the reasons Saussure himself recognizes) must forbid a radical distinction between the linguistic and the graphic sign. No doubt this thesis concerns only the necessity of relationships between specific signifiers and signifieds within an allegedly natural relationship between the voice and sense in general, between the order of phonic signifiers and the content of the signifieds (“the only natural bond, the only true bond, the bond of sound” ). Only these relationships between specific signifiers and signifieds would be regulated by arbitrariness. Within the “natural” relationship between phonic signifiers and their signifieds in general, the relationship between each determined signifier and its determined signified would be “arbitrary”.

Now from the moment that one considers the totality of determined signs, spoken, and a fortiori written, as unmotivated institutions, one must exclude any relationship of natural subordination, any natural hierarchy among signifiers or orders of signifiers. If “writing” signifies inscription and especially the durable institution of a sign (and that is the only irreducible kernel of the concept of writing), writing in general covers the entire field of linguistic signs. In that field a certain sort of instituted signifiers may then appear, “graphic” in the narrow and derivative sense of the word, ordered by a certain relationship with other instituted — hence “written,” even if they are “phonic” — signifiers. The very idea of institution — hence of the arbitrariness of the sign — is unthinkable before the possibility of writing and outside of its horizon. Quite simply, that is, outside of the horizon itself, outside the world as space of inscription, as the opening to the emission and to the spatial distribution of signs, to the regulated play of their differences, even if they are “phonic.”

The very idea of institution — hence of the arbitrariness of the sign — is unthinkable before the possibility of writing and outside of its horizon. Quite simply, that is, outside of the horizon itself, outside the world as space of inscription, as the opening to the emission and to the spatial distribution of signs, to the regulated play of their differences, even if they are “phonic.”

… only the signs called natural, those that Hegel and Saussure call “symbols,” escape semiology as grammatology. But they fall a fortiori outside the field of linguistics as the region of general semiology. The thesis of the arbitrariness of the sign thus indirectly but irrevocably contests Saussure's declared proposition when he chases writing to the outer darkness of language. This thesis successfully accounts for a conventional relationship between the phoneme and the grapheme (in phonetic writing, between the phoneme, signifier-signified, and the grapheme, pure signifier), but by the same token it forbids that the latter be an “image” of the former. Now it was indispensable to the exclusion of writing as “external system,” that it come to impose an “image,” a “representation,” or a “figuration,” an exterior reflection of the reality of language.

I'm better at prose than logic, but I would interpret it as something like this: if some property "x" applies to "a" and "b" equally, and both "a" and "b" are related through "x" as their fundamental property,

then a subordination in terms of "x" of "a" and/or "b" cannot be permitted for "a" or "b", because "a" and "b" include "x" equally.

So, if this is the case, then "a" and "b" in terms of "x" are interchangeable,

and if "b" has additional properties "p," but nonetheless is always "x" and all additional properties are differences in use, then we can say that b=a,

and as such, both b and a can be subsumed beneath a concept which permits no distinction in terms of "x,"

"n," and that "n" can be said to be the fundamental source of differences between "a" and "b" as well as their similarities.

Now we must think that writing is at the same time more exterior to speech, not being its “image” or its “symbol,” and more interior to speech, which is already in itself a writing. Even before it is linked to incision, engraving, drawing, or the letter, to a signifier referring in general to a signifier signified by it, the concept of the graphic [unit of a possible graphic system] implies the framework of the instituted trace, as the possibility common to all systems of signification.