Inquiry Into Inquiry

Re: Semiotics, Semiosis, Sign Relations • 5

It’s a common mistake to confound infinite with unbounded.  A process can continue without end and still be “bounded in a nutshell”.  So a sign process can pass from sign to interpretant sign to next interpretant sign ad infinitum without ever leaving a finite set of signs.

The number of questions I got about that statement tells me I should have delineated the context in which it was set a little more fully.

A sign process in this context is simply a sequence of signs, of the sort we might observe in communicational, computational, or experimental settings.  For people who remember the more ancient arts of AI, cognitive science, and cybernetics, it may help to recall the orders of considerations arising in protocol analysis.

It goes with this territory to assume the formal equivalent of categorical perception.  This means we can set aside the subtleties of token haecceity — the nominal distinctiveness of every individual sign instance — along with the possibility of signs being sampled from a continuous medium.

In this setting we are left with two interpretations for infinite and bounded, depending on whether the sign domain has a quantitative measure defined on it, or not.  In the first case, bounded means the sequence never exceeds a finite bound in the relevant measure.  In the second case, bounded means the sequence never leaves a finite set.

cc: Systems Science • Structural Modeling • Peirce (1) (2) • Ontolog • Cybernetics (1) (2)

Questions about the use of “semiotic triangles” and “semiotic triskelia” to represent triadic sign relations have come up again, as they often do in the wider world, prompting me to revisit an earlier comment on the subject and to tri, tri again to render the issues as clear as I can, otherwise we appear doomed never to get off triangle one.

Re: Semiotic Triangle • (1) • (2) | John Corcoran • (1) • (2)

Concepts for Peirce are mental symbols, so they fall under the general designation of signs.  For triadic sign relations in general, then, we are dealing with a triadic relation among (1) objects of signs, (2) signs of objects, and (3) what Peirce calls interpretant signs, or interpretants for short.  It is critical to regard the three designations of objects, signs, and interpretants as relational roles not ontological essences.  It is also critical to distinguish the following things:

• The extended sign relation as a subset of a cartesian product
• The elementary sign relation as an ordered triple in
• The places forming an ordered triple
• The elements filling those places.

Triangles like the one linked above have long been used to introduce the idea of a triadic sign relation.  They have the unintended consequence, however, of leading people to miss all the points I mentioned above.  So it’s wise to move quickly on to better pictures and more detailed descriptions.

Resources

• Survey of Semiotics, Semiosis, Sign Relations
• Semiotics, Semiosis, Sign Relations • (1) • (2) • (3) • (4) • (5)

cc: Systems Science • Structural Modeling • Peirce List • Ontolog • Cybernetics (1) (2)

Re: Richard Coyne • Recursion Again

It’s a common mistake to confound infinite with unbounded.  A process can continue without end and still be “bounded in a nutshell”.  So a sign process can pass from sign to interpretant sign to next interpretant sign ad infinitum without ever leaving a finite set of signs.

Resources

• Survey of Pragmatic Semiotic Information
• Semiotics, Semiosis, Sign Relations 🙞 (1) • (2) • (3) • (4)

cc: Systems Science • Structural Modeling • Peirce List • Ontolog • Cybernetics (1) (2)