Changes

<li>If ''partial <math>n\!</math>-tuples'' are admitted, and not permitted to be confused with ''<math>(< n)\!</math>-tuples'', then one arrives at the concept of an ''<math>n\!</math>-place relational complex''.</li></ol>

<li>If ''partial <math>n\!</math>-tuples'' are admitted, and not permitted to be confused with ''<math>(< n)\!</math>-tuples'', then one arrives at the concept of an ''<math>n\!</math>-place relational complex''.</li></ol>

'''Relational Complex?'''

Relational complex?

R = R(1) U ... U R(n)

{| align="center" cellspacing="8" width="90%"

| <math>L ~=~ L^{(1)} \cup \ldots \cup L^{(k)}\!</math>

Sign relational complex?

'''Sign Relational Complex?'''

R = R(1) U R(2) U R(3)

{| align="center" cellspacing="8" width="90%"

| <math>L ~=~ L^{(1)} \cup L^{(2)} \cup L^{(3)}\!</math>

It is possible to see two directions of remove that signs and concepts can take in departing from complete specifications of individual objects, and thus to see two dimensions of variation in the requisite varieties of partiality, each of which leads off into its own distinctive realm of abstraction.

It is possible to see two directions of remove that signs and concepts can take in departing from complete specifications of individual objects, and thus to see two dimensions of variation in the requisite varieties of partiality, each of which leads off into its own distinctive realm of abstraction.

1. In a direction of "generality", with "general" signs and concepts, one loses an amount of certainty as to exactly what object the sign or concept applies at any given moment, and thus this can be recognized as an extensional type of abstraction.

# In a direction of ''generality'', with ''general'' signs and concepts, one loses an amount of certainty as to exactly what object the sign or concept applies at any given moment, and thus this can be recognized as an extensional type of abstraction.

 

# In a direction of ''vagueness'', with ''vague'' signs and concepts, one loses a degree of security as to exactly what property the sign or concept implies in the current context, and thus this can be classified as an intensional mode of abstraction.

2. In a direction of "vagueness", with "vague" signs and concepts, one loses a degree of security as to exactly what property the sign or concept implies in the current context, and thus this can be classified as an intensional mode of abstraction.

The first order of business is to draw some distinctions, and at the same time to note some continuities, between the varieties of partiality that remain to be sufficiently clarified and the more mundane brands of partiality that are already familiar enough for present purposes, but lack perhaps only the formality of being recognized under that heading.

The first order of business is to draw some distinctions, and at the same time to note some continuities, between the varieties of partiality that remain to be sufficiently clarified and the more mundane brands of partiality that are already familiar enough for present purposes, but lack perhaps only the formality of being recognized under that heading.