Sign relations are just special cases of triadic relations, in much the same way that binary operations in mathematics are special cases of triadic relations.  It does amount to a minor complication that we participate in sign relations whenever we talk or think about anything else, but it still makes sense to try and tease the separate issues apart as much as we possibly can.

As far as relations in general go, relative terms are often expressed by slotted frames like “brother of __”, “divisor of __”, and “sum of __ and __”.  Peirce referred to these kinds of incomplete expressions as rhemes or rhemata and Frege used the adjective ungesättigt or unsaturated to convey more or less the same idea.

Switching the focus to sign relations, it’s a fair question to ask what kinds of objects might be denoted by pieces of code like “brother of __”, “divisor of __”, and “sum of __ and __”.  And while we’re at it, what is this thing called denotation, anyway?

Resources

• Relation Theory
• Triadic Relations
• Sign Relations
• Peirce’s 1870 Logic Of Relatives