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# Eventually, it is necessary to develop a formal concept and even a mathematical model of this relationship.  To do this, I adopt the intuitive notions of a ''point of view'' (POV) and its ''point of development'' (POD), gradually turning them into formal concepts of a very general character.  This requires distinguishing between two kinds of propositions that are associated with POVs and PODs, namely:  (a) the propositions that are ''attached to'' or ''contained in'' them, and (b) the propositions that are ''applied to'' or ''maintained about'' them.

# Eventually, it is necessary to develop a formal concept and even a mathematical model of this relationship.  To do this, I adopt the intuitive notions of a ''point of view'' (POV) and its ''point of development'' (POD), gradually turning them into formal concepts of a very general character.  This requires distinguishing between two kinds of propositions that are associated with POVs and PODs, namely:  (a) the propositions that are ''attached to'' or ''contained in'' them, and (b) the propositions that are ''applied to'' or ''maintained about'' them.

Just to give a rough idea of how these two distinctions relate to each other, the ''matter'' of a thought corresponds to an ''attached'' proposition, ''in'' a POV or ''at'' a POD, while the ''manner'' of a thought corresponds to an ''applied'' proposition, ''on'' a POV or ''about'' a POD.  Employing this language to describe the case of an inquiry successfully self-applied, one can say the following things.  An agent of inquiry has a POV that changes from one POD to the next in a series of developments, and this can be a POV that concerns itself with the question of inquiry, among other things, and thus with the topics of uncertainty and certainty, or doubt and belief.  In such a case, as the POV moves from an initial POD to a terminal POD, a part of its matter stays fixed on ''doubt'', while its whole manner is transformed from one of ''doubt'' toward one of ''belief''.

Just to give a rough idea of how these two distinctions relate to each other, the matter of a thought corresponds to an "attached" proposition, "in" a POV or "at" a POD, while the manner of a thought corresponds to an "applied" proposition, "on" a POV or "about" a POD.  Employing this language to describe the case of an inquiry successfully self applied, one can say the following things.  An agent of inquiry has a POV that changes from one POD to the next in a series of developments, and this can be a POV that concerns itself with the question of inquiry, among other things, and thus with the topics of uncertainty and certainty, or doubt and belief.  In such a case, as the POV moves from an initial POD to a terminal POD, a part of its matter stays fixed on "doubt", while its whole manner is transformed from one of "doubt" toward one of "belief".

It is not always necessary to distinguish a POV from each of its POD's, except when one needs to emphasize the dynamic aspect of these ideas, especially the fact that a single POV can pass through or incorporate many different POD's in the course of its development.  It is legitimate to say that the POV is present at each of its POD's, or that the POD's are incorporated in their overall POV.  Accordingly, it is not always necessary to lose sight of the successive POD's in a series, so long as they are amenable to being incorporated in the last POD, or final POV.

It is not always necessary to distinguish a POV from each of its PODs, except when one needs to emphasize the dynamic aspect of these ideas, especially the fact that a single POV can pass through or incorporate many different PODs in the course of its development.  It is legitimate to say that the POV is present at each of its PODs, or that the PODs are incorporated in their overall POV.  Accordingly, it is not always necessary to lose sight of the successive PODs in a series, so long as they are amenable to being incorporated in the last POD, or final POV.

When one says that a POV is associated with a particular proposition, whether containing it or instancing it, one always means a POV as it exists at a particular POD, or through a particular range of its POD's.  For example, if I say that "J thinks K is smarter than L", then I am implicating a POV that J has at a particular POD, assumed to be capable of specification.  Moreover, I am relying on the specific information inherent in this POD to index the particular persons named "K" and "L" that I am assuming J has in mind at that POD.  In technical terms, this requires the "intentional context" that is signaled by the verb "thinks", normally "opaque" to all distributions of contextual information from any point outside its frame, to be treated as "transparent" to the packet of information that is assumed to be represented by the POD in question.

When one says that a POV is associated with a particular proposition, whether containing it or instancing it, one always means a POV as it exists at a particular POD, or through a particular range of its PODs.  For example, if I say <math>{}^{\backprime\backprime}J ~\text{thinks}~ K ~\text{is smarter than}~ L{}^{\prime\prime},\!</math> then I am implicating a POV that <math>J\!</math> has at a particular POD, assumed to be capable of specification.  Moreover, I am relying on the specific information inherent in this POD to index the particular persons <math>K\!</math> and <math>L\!</math> that I am assuming <math>J\!</math> has in mind at that POD.  In technical terms, this requires the &ldquo;intentional context&rdquo; that is signaled by the verb ''thinks'', normally &ldquo;opaque&rdquo; to all distributions of contextual information from any point outside its frame, to be treated as &ldquo;transparent&rdquo; to the packet of information that is assumed to be represented by the POD in question.

In the application of mediate interest to this project, a POV corresponds to a computational system, while a POD corresponds to one of its states.  It is desirable to have a way of referring to the system as a whole, but in ways that are implicitly quantified by the relevant classes of states.  For example, I want to have a system of interpretation in place where it is possible to write "j : x = y" to mean that "j sets x equal to y", to read this as a statement about a system j and two of its stores x and y, and to understand this as a statement that implicitly refers to a set of states that makes it true.  Further, I want to recognize this statement as the "active" voice, "attributed" account, or "authorized" version of the more familiar, but "passive", "anonymous", or "unavowed" species of assignment statement "x := y".

In the application of mediate interest to this project, a POV corresponds to a computational system, while a POD corresponds to one of its states.  It is desirable to have a way of referring to the system as a whole, but in ways that are implicitly quantified by the relevant classes of states.  For example, I want to have a system of interpretation in place where it is possible to write "j : x = y" to mean that "j sets x equal to y", to read this as a statement about a system j and two of its stores x and y, and to understand this as a statement that implicitly refers to a set of states that makes it true.  Further, I want to recognize this statement as the "active" voice, "attributed" account, or "authorized" version of the more familiar, but "passive", "anonymous", or "unavowed" species of assignment statement "x := y".