  One set of distinctions among signs was introduced by Peirce in the early stages of his analysis. The distinctions in this set turn on whether the particular instance of the sign relation is “degenerate” or “non-degenerate.” The notion of “degeneracy” here is the standard mathematical notion, and as applied to sign theory non-degeneracy means simply that the triadic relation cannot be analyzed as a logical conjunction of any combination of dyadic relations and monadic relations. More exactly, a particular instance of the obtaining of the sign relation is degenerate if and only if the fact that a sign s means an object o to an interpretant i can be analyzed into a conjunction of facts of the form P(s) &amp; Q(o) &amp; R(i) &amp; T(s,o) &amp; U(o,i) &amp; W(i,s) (where not all the conjuncts have to be present). Either an obtaining of the sign relation is non-degenerate, in which case it falls into one class; or it is degenerate in various possible ways (depending on which of the conjuncts are omitted and which retained), in which cases it falls into various other classes.  Other distinctions regarding signs were introduced later by Peirce. Some of them will be discussed very briefly in the following section of this article.