Signification

Another fact of everyday life is the ability of human persons (and even some animals) to associate sign material $\sigma \in \Sigma^{*}$ with something else, other kinds of objects or even sign material. This 'something else' will be called the 'signified' or the 'designatum' $d \in DSGN$, which finally are some phenomena in the consciousness. While the association does not exist as 'real' relation in the 'real' world or as a 'primary' phenomenon in the consciousness, our consciousness is able to create such a meaning association out of nothing only triggered by the simultaneous occurence. Thus we have the ability of associating phenomena originally separated. Because the meaning association is so important we give a special name to it: $assoc_{s}$ for sign relation.

$$\sigma \in \Sigma^{*}$$ (6.34)

$$assoc : 2^{Ph} \times 2^{Ph} \rightleftarrows 2^{Ph}$$ (6.35)

$$assoc_{m} : \Sigma^{*} \times 2^{Ph} \rightleftarrows Ph$$ (6.36)

Thus one can 'name' some phenomena with a signature $\sigma$, and because every signature with its meaning is again a phenomenon one can again 'name' the resulting meaning relation with a new signature. And so on. Similarly one can create different meaning associations with different signatures $\{\sigma_{1}, ..., \sigma_{n} \}$ and then one can combine these different individual signatures to one new signature $\sigma = \sigma_{1}\curlywedge ... \curlywedge\sigma_{n}$ with the sign ' $\curlywedge$' representing 'concatenation' of signs.