Changes

In order to continue formalizing the discussion of POVs and PODs within the text that uses them, I introduce the following notations:

In order to continue formalizing the discussion of POVs and PODs within the text that uses them, I introduce the following notations:

<pre>

j :  x | y, x |j y, x | y  : j,

<math>\begin{array}{lcccr}

j : (x , y), (x , y)j, (x , y) : j.

j :  x \ne y

</pre>

& , &

x \ne_j y

& , &

x \ne y  : j

j : (x ~,~ y)

& , &

(x ~,~ y)_j

& , &

(x ~,~ y) : j

\end{array}</math>

All of these expressions are intended to indicate a set of circumstances that could otherwise be rendered as follows:

All these expressions are intended to indicate a set of circumstances that could otherwise be described as follows:

# <math>j\!</math> appears to see a distinction between <math>x\!</math> and <math>y.\!</math>

# <math>j\!</math> partitions a dimension of discourse between <math>x\!</math> and <math>y.\!</math>

| <math>j ~\text{appears to see a distinction between}~ x ~\text{and}~ y.</math>

# <math>j\!</math> sees <math>x\!</math> and <math>y\!</math> as mutually exclusive and exhaustive possibilities.

| <math>j ~\text{partitions a dimension of discourse between}~ x ~\text{and}~ y.</math>

| <math>j ~\text{sees}~ x ~\text{and}~ y ~\text{as mutually exclusive and exhaustive possibilities.}</math>

In this scheme, <math>{}^{\backprime\backprime} x {}^{\prime\prime}</math> and <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> indicate logical dimensions of variation or propositional features of description that govern an agent's possibilities of action and perception.  Used as primitive logical terms they denote the distinctive features that determine an agent's spaces of performance and experience.  In combination with logical operators they generate a descriptive framework that encompasses both:  (1) the methodological ''approaches'' or ''perspectives'' toward objects that an agent can adopt, and (2) the categorical ''aspects'' of objects, the independently coherent systems of properties and qualities that characterize the hypothetically unified object system.

In this scheme, <math>{}^{\backprime\backprime} x {}^{\prime\prime}</math> and <math>{}^{\backprime\backprime} y {}^{\prime\prime}</math> indicate logical dimensions of variation or propositional features of description that govern an agent's possibilities of action and perception.  Used as primitive logical terms they denote the distinctive features that determine an agent's spaces of performance and experience.  In combination with logical operators they generate a descriptive framework that encompasses both:  (1) the methodological ''approaches'' or ''perspectives'' toward objects that an agent can adopt, and (2) the categorical ''aspects'' of objects, the independently coherent systems of properties and qualities that characterize the hypothetically unified object system.