Changes

==Factoring Sign Relations==

==Factoring Sign Relations==

Let us now apply the concepts of factorization and reification, as they are developed above, to the analysis of sign relations.

Let us now apply the concepts of factorization and reification,

as they are developed above, to the analysis of sign relations.

Suppose that we have a sign relation L c O x S x I, where the sets

Suppose we have a sign relation <math>L \subseteq O \times S \times I,</math> where <math>O\!</math> is the object domain, <math>S\!</math> is the sign domain, and <math>I\!</math> is the interpretant domain of the sign relation <math>L.\!</math>

O, S, I are the domains of the Object, Sign, Interpretant domains,

respectively.

Now suppose that the situation with respect to

Now suppose that the situation with respect to the ''denotative component'' of <math>L,\!</math> in other words, the projection of <math>L\!</math> on the subspace <math>O \times S,</math> can be pictured in the following manner, where equal signs written between ostensible nodes identify them into a single actual node.

the "denotative component" of L, in other words,

the "projection" of L on the subspace O x S, can

be pictured in the following manner, where equal

signs, like "=", written between ostensible nodes,

like "o", identify them into a single actual node.

o-----------------------------o

o-----------------------------o

| Denotative Component of L  |

| Denotative Component of L  |

|                            |

|                            |

o-----------------------------o

o-----------------------------o

This depicts a situation where each of the three objects,

This depicts a situation where each of the three objects,

x_1, x_2, x_3, has a "proper name" that denotes it alone,

x_1, x_2, x_3, has a "proper name" that denotes it alone,