Cell Language Theory, The: Connecting Mind And Matter

The Universality of the Irreducible Triadic Relation 379

“6x9” b2861 The Cell Language Theory: Connecting Mind and Matter

The concept of “information” seems to occur naturally in Figure 9.1

in connection with mapping h. Since Figure 9.1 is a diagrammatic repre-

sentation of the sign as defined by Peirce, it would be logical to refer to

the information associated with mapping h as the “Peircean information”

to be denoted as IPeirce, with the following definition:

The Peircean information, IPe, is the information that is transferred

from the object to its interpretant mediated by a sign. (9.6)

Thus defined, IPe can be distinguished from the Planckian information,

IPl discussed in Sections 2.2.3 and 8.5 and the Shannon information, ISh,

discussed in Section 2.2.2, as follows:

Just as IPe can be associated with mapping h, so it is possible that ISh

and IPl can be associated with mappings, f and g, respectively. (9.7)

The multiplicity of different kinds of information appearing in

Statement (9.7) is consistent with the parametric definition of information

recently advanced by Burgin [37], according to which there are at least

35 different ways of measuring the amount of information.

One of the fundamental aspects of the sign theory of Peirce is that the

relation among sign, representamen, and interpretant cannot be reduced

to any combinations of two or less of the three nodes of the network

shown in Figure 9.1. This idea of Peirce is often referred to as the irreduc-

ible triadic relation (ITR). ITR, in the form of Figure 9.1, is also involved

in the definition of a category in mathematics as indicated in Figure 9.3(g)

and Table 9.1.

9.2 Peirce’s Simple Concepts Applicable to Every Subject

In [372], Peirce predicted the existence of “simple concepts applicable to

every subject”. For convenience, the “simple concepts” described in [372]

will be referred to as “Peirce’s simple concepts” (PSCs). In addition to the

concept of double articulation that belongs to the group of PSCs, there are

at least two more that have been discussed in this book extensively. They

are (a) Peirce’s own concept of “irreducible triadicity” discussed in

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