## Semiotics, Semiosis, Sign Relations • Discussion 7

MR:
Okay, this is hard to parse, but I’ve looked at it a few times now framed with discussion from a few different sources, and it seems that if we fix some sets $A$ of signs, $B$ of interpretants and $C$ of objects, and treating the sign relation as $R \subseteq A \times B \times C,$ there are some reasonable restrictions/assumptions we could place on $R.$  For example:

1a.
$\forall a \in A, \, \forall b \in B, \, \exists c \in C, \, (a,b,c) \in R,$
“every sign means something to every interpretant”,
1b.
$\forall a \in A, \, \exists b \in B, \, \exists c \in C, \, (a,b,c) \in R,$ a weaker alternative,
“every sign means something to some interpretant”,
2a.
$\forall c \in C, \, \forall b \in B, \, \exists a \in A, \, (a,b,c) \in R,$
“every interpretant has a name for every object”,
2b.
$\forall c \in C, \, \exists b \in B, \, \exists a \in A, \, (a,b,c) \in R,$ a weaker alternative,
“every object has at least one name assigned to it by each interpretant,”

and so on.

However, none of these seem strictly necessary to me;  there could be meaningless symbols or nameless objects.  Does Peirce assume any of these things or similar?  If not, I suspect the answer to my question regarding mathematical distinguishing features of sign relations is that there aren’t any:  that any ternary relation can be understood as a sign relation if one squints hard enough.

As far as meaningless signs go, we do encounter them in theoretical analysis (“resolving conundra” and “steering around nonsense”) and empirical or computational applications (“missing data” and “error types”).  The defect of meaning can affect either denotative objects or connotative interpretants or both.  In those events we have to generalize sign relations to what are called sign relational complexes.

Signless objects are a different matter since cognitions and concepts count as signs in pragmatic semiotics and Peirce maintains we have no concept of inconceivable objects.

If you fancy indulging in a bit of cosmological speculation you could imagine the whole physical universe to be a sign of itself to itself, making $O = S = I,$ but this far downstream from the Big Bang we mortals usually have more pressing business to worry about.

In short, what we need sign relations for is not for settling big questions about cosmology or metaphysics but for organizing our thinking about object domains and constructing models of what goes on and what might go better in practical affairs like communication, inquiry, learning, and reasoning.

cc: Category Theory • Cybernetics (1) (2)
cc: Ontolog ForumStructural ModelingSystems Science
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