Cell Language Theory, The: Connecting Mind And Matter

Key Terms and Concepts 13

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

reduced, just as the irreducible triad of object, sign, and interpretant can

be viewed as the minimal irreducible triad to which all other more

complex signs can be reduced (see Section 6.3 and Figure 9.1). Figures 2.1

and 2.2 can be viewed as geometric (or iconic) representations of the irre­

ducible triadic relation (ITR) [33] (see Chapter 9), which would be their

symbolic representation.

The origin of the concept of ITR may be traced to Peirce’s definitions

of the sign, especially Definition #30 in [34]. As evident in Table 2.1, the

ur­category (and hence ITR) can be applied to various processes in both

natural (see layers 3–6) and human sciences (see layers 1–3), with layer

3 covering both natural and human sciences. It is surprising that the ur­

category can be applied even to Einstein’s general relativity theory of

motion [35] (see the legend to layer 6). Thus, if we can treat each of these

disciplines as a mathematical category, then ITR and the ur­category may

be viewed as “functors” in the category theory [30–32].

The ur­category has three steps or “transformations”, labeled f, g,

and h. Steps f and g can be associated with physicochemical interactions

and hence with constructor­theoretic information [36] or Shannon infor­

mation [38], the latter being characterized by selection processes. In con­

trast, step h does not involve any direct physicochemical interaction

between the source and the receiver nor between the object and the inter­

pretant. In other words, steps f and g represent interactions, while the

combined effects of steps of f, g, and h constitute communication. Steps f

and g are dyadic in that they each implicate a 2­node network, i.e., “two

nodes connected by one arrow”, whereas steps f, g, and h are parts of a

triadic unit that cannot be reduced to any network with less than three

nodes connected with three arrows forming the so­called “commutative

triangle” [30–32].

f g

BAC

h

Figure 2.2 A simplified diagram of the commutative triangle or the ur-category. The

same diagram is used to represent the ITR in semiotics (see Figure 9.1).

b2861_Ch-02.indd 13 17-10-2017 11:38:57 AM