Changes

The practical use of Peirce's categories is simply to organize our thoughts about what sorts of formal models are demanded by a material situation, for instance, a domain of phenomena from atoms to biology to culture.  To say that "k-ness" is involved in a phenomenon is simply to say that we need k-adic relations to model it adequately, and that the phenomenon itself appears to demand nothing less.  Aside from this, Peirce's realization that k-ness for k = 1, 2, 3 affords us with a sufficient basis for all that we need to model is a formal fact that depends on a particular theorem in the logic of relatives.  If it weren't for that, there would hardly be any reason to single out three.

The practical use of Peirce's categories is simply to organize our thoughts about what sorts of formal models are demanded by a material situation, for instance, a domain of phenomena from atoms to biology to culture.  To say that "k-ness" is involved in a phenomenon is simply to say that we need k-adic relations to model it adequately, and that the phenomenon itself appears to demand nothing less.  Aside from this, Peirce's realization that k-ness for k = 1, 2, 3 affords us with a sufficient basis for all that we need to model is a formal fact that depends on a particular theorem in the logic of relatives.  If it weren't for that, there would hardly be any reason to single out three.

In order to discuss the various forms of iconicity that might be involved in the application of Peirce's logical graphs and their kind to the object domain of logic itself, we will need to bring out two or three "categories of structured individuals" (COSI's), depending on how we count.  These are called the "object domain", the "sign domain", and the "interpretant sign domain", which may be written '''O''', '''S''', '''I''', respectively, or ''X'', ''Y'', ''Z'', respectively, depending on the style that fits the current frame of discussion.

In order to discuss the various forms of iconicity that might be involved in the application of Peirce's logical graphs and their kind to the object domain of logic itself, we will need to bring out two or three ''categories of structured individuals'' (COSIs), depending on how one counts.  These are called the ''object domain'', the ''sign domain'', and the ''interpretant sign domain'', which may be written <math>O, S, I,\!</math> respectively, or <math>X, Y, Z,\!</math> respectively, depending on the style that fits the current frame of discussion.

For the time being, I will be considering systems where the sign domain and the interpretant domain are the same sets of entities, although, of course, their roles in a given "sign relation", say, '''L''' &sube; '''O''' &times; '''S''' &times; '''I''' or ''L'' &sube; ''X'' &times; ''Y'' &times; ''Z'', remain as distinct as ever.  I will tend to use the term "semiotic domain" for the common set of elements that constitute the signs and the interpretant signs in any setting where the sign domain and the interpretant domain are equal as sets.

For the time being, we will be considering systems where the sign domain and the interpretant domain are the same sets of entities, although, of course, their roles in a given ''[[sign relation]]'', say, <math>L \subseteq O \times S \times I</math> or <math>L \subseteq X \times Y \times Z,</math> remain as distinct as ever.  We may use the term ''semiotic domain'' for the common set of elements that constitute the signs and the interpretant signs in any setting where the sign domain and the interpretant domain are equal as sets.

At the "alpha level", "primary arithmetic", or "zeroth order" of consideration that we have so far introduced, the sign domain is any one of the several "formal languages" that we have placed in one-to-one correspondence with each other, namely, the languages of non-intersecting plane closed curves, well-formed parenthesis strings, or rooted trees.  The interpretant sign domain will for the present be taken to be any one of the same languages, and so I'll refer to any of them indifferently as the "semiotic domain".

With respect to the ''alpha level'', ''primary arithmetic'', or ''zeroth order'' of consideration that we have so far introduced, the sign domain is any one of the several ''formal languages'' that we have placed in one-to-one correspondence with each other, namely, the languages of non-intersecting plane closed curves, well-formed parenthesis strings, and rooted trees.  The interpretant sign domain will for the present be taken to be any one of the same languages, and so we may refer to any of them indifferently as the ''semiotic domain''.

Briefly if roughly put, icons are signs that denote their objects by virtue of sharing properties with them.  To put it a bit more fully, icons are signs that receive their interpretant signs on account of having specific properties in common with their objects.

Briefly if roughly put, icons are signs that denote their objects by virtue of sharing properties with them.  To put it a bit more fully, icons are signs that receive their interpretant signs on account of having specific properties in common with their objects.