Changes

The relationship between a POD and an OM at an IM can be understood as follows.  …

The relationship between a POD and an OM at an IM can be understood as follows.  …

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:

j :  x | y, x |j y,  x | y  : j,

j :  x | y, x |j y,  x | y  : j,

j :  x / y, x /j y,  x / y  : j,

j :  x / y, x /j y,  x / y  : j,

j : (x , y), (x ,  y)j, (x , y) : j.

j : (x , y), (x ,  y)j, (x , y) : j.

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

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

1. j appears to see a distinction between x and y.

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

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, "x" and "y" 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 practice, it does not matter whether one regards x and y as logical features or as boolean variables, so long as the full set of positive and negative features { x, (x), y, (y) } is initially available to classify the relevant space of object perceptions or interpretive actions.  Analogous to its role in the staging relations { < , > }, the label "j" indicates the active interpreter, that is, the system and moment of interpretation or the state of the interpretive system that is held to be responsible for finding, making, testing, or following through the consequences of posing the contemplated distinctions.

In practice, it does not matter whether one regards x and y as logical features or as boolean variables, so long as the full set of positive and negative features { x, (x), y, (y) } is initially available to classify the relevant space of object perceptions or interpretive actions.  Analogous to its role in the staging relations { < , > }, the label "j" indicates the active interpreter, that is, the system and moment of interpretation or the state of the interpretive system that is held to be responsible for finding, making, testing, or following through the consequences of posing the contemplated distinctions.