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In this setting, it is possible to bring about an accommodation between the mathematical and the psychological concepts of ''projection'' and to reconcile their discordant uses of the term within a concerted paradigm.  For example, in dealing with the joint configuration space of a multiple agent system, one considers this ''yoked extension space'' (YES) to fall within a ''common extension'' (CE) of all the single agent state spaces.  Each agent involved in such a system ''projects'', in a geometric sense, the total action of the system on its own ''section'' of the whole CE, its ''local outlook'', ''mental plane'', personal ''frame of reference'' (FOR), or ''point of view'' (POV).

In this setting, it is possible to bring about an accommodation between the mathematical and the psychological concepts of ''projection'' and to reconcile their discordant uses of the term within a concerted paradigm.  For example, in dealing with the joint configuration space of a multiple agent system, one considers this ''yoked extension space'' (YES) to fall within a ''common extension'' (CE) of all the single agent state spaces.  Each agent involved in such a system ''projects'', in a geometric sense, the total action of the system on its own ''section'' of the whole CE, its ''local outlook'', ''mental plane'', personal ''frame of reference'' (FOR), or ''point of view'' (POV).

What does the POV of an agent consist in?  Generally speaking, agents are not dumb.  They are not limited to a single view of their situation, nor are they restricted to a single scenario for its ongoing development.  They can entertain many different possibilities as candidates for the so-called and partly self-describing “objective situation” and they can envision many different ways that these potential situations might be developing, both before and after their passage through the moment in question.  Furthermore, under circumstances favorable to reflection, agents can invoke POVs that help them to contemplate many different possible developments in the constitution of these very same POVs.

What does the POV of an agent consist in?  Generally speaking, agents are not dumb.  They are not limited to a single view of their situation, nor are they restricted to a single scenario for its ongoing development.  They can entertain many different possibilities as candidates for the so called and partly self describing "objective situation" and they can envision many different ways that these potential situations might be developing, both before and after their passage through the moment in question.  Furthermore, under circumstances favorable to reflection, agents can invoke POVs that help them to contemplate many different possible developments in the constitution of these very same POVs.

Now, it is conceivable that all the POVs entertained by a single agent are predetermined as having the same collection of generic characters, and thus that this invariant constitution is what really limits the range of all possible POVs for the agent in question.  If so, it leads to the idea that this invariant constitution defines a "uniquely general POV", a "highest order meta POV", or a "consummate POV" of the agent involved.  Still, the only points of access and the only paths of approach that an agent can have to its own consummate POV, if indeed such a goal does make sense, are through the agency and the medium of whatever POVs it happens to have at each passing moment in its developmental history.  Consequently, a persistent enough search for a good POV opens up the investigation of each agent's prevailing "point of develoment" (POD).

Now, it is conceivable that all the POVs entertained by a single agent are predetermined as having the same collection of generic characters, and thus that this invariant constitution is what really limits the range of all possible POVs for the agent in question.  If so, it leads to the idea that this invariant constitution defines a ''uniquely general POV'', a ''highest order meta-POV'', or a ''consummate POV'' of the agent involved.  Still, the only points of access and the only paths of approach that an agent can have to its own consummate POV, if indeed such a goal does make sense, are through the agency and the medium of whatever POVs it happens to have at each passing moment in its developmental history.  Consequently, a persistent enough search for a good POV opens up the investigation of each agent's prevailing ''point of development'' (POD).

In the best of all possible worlds, then, being under the influence of one POV does not render an agent incapacitated for considering others.  Of course, there are practical limitations that affect both the capacity and the flexibility of a particular POV, and there can be found in force both logical constraints and resource constraints that leave a POV with a narrowly fixed and impoverished character, one that the agent opting for it can fail to represent reflectively enough within the scope of this POV itself.  In particular, the "finite information constructions" (FICs) that are accessible from a computational standpoint are especially limited in the kinds of POVs they are able to attain.

In the best of all possible worlds, then, being under the influence of one POV does not render an agent incapacitated for considering others.  Of course, there are practical limitations that affect both the capacity and the flexibility of a particular POV, and there can be found in force both logical constraints and resource constraints that leave a POV with a narrowly fixed and impoverished character, one that the agent opting for it can fail to represent reflectively enough within the scope of this POV itself.  In particular, the ''finite information constructions'' (FICs) that are accessible from a computational standpoint are especially limited in the kinds of POVs they are able to attain.

This means that POVs and PODs have recursive constitutions and recursive involvements with one another, calling on and referring to other POVs and PODs, both for the exact definitions that are needed and also for the more illuminating elaborations that might be possible, both those belonging to the same agent, reflexively, and those possessed by other agents, vicariously.  A large part of the task of building a RIF is taken up with formalizing POVs and PODs, in part by analyzing their intuitive notions in terms of their implicit recursive structures and their referential involvements with each other, and in part by exploring their potential relationships with the previously formalized concepts of "objective concerns" (OCs).

This means that POVs and PODs have recursive constitutions and recursive involvements with one another, calling on and referring to other POVs and PODs, both for the exact definitions that are needed and also for the more illuminating elaborations that might be possible, both those belonging to the same agent, reflexively, and those possessed by other agents, vicariously.  A large part of the task of building a RIF is taken up with formalizing POVs and PODs, in part by analyzing their intuitive notions in terms of their implicit recursive structures and their referential involvements with each other, and in part by exploring their potential relationships with the previously formalized concepts of ''objective concerns'' (OCs).

In settings where recursion is contemplated, it is possible to conceive of a distinction between "well founded" recursions, that lead to determinate definitions of the entities in question, and "buck passing" recursions, that lead one down the "garden path" to an interminable "run around".  The catch, of course, is that it is not always possible to implement an effective procedure that can accomplish what it is possible to conceive.  Thus, there are cases where the imagined distinction does not apply and times when the putative difference is not always detectable in practice.

In settings where recursion is contemplated, it is possible to conceive of a distinction between ''well-founded'' recursions, that lead to determinate definitions of the entities in question, and ''buck-passing'' recursions, that lead one down the “garden path” to an interminable “run-around”.  The catch, of course, is that it is not always possible to implement an effective procedure that can accomplish what it is possible to conceive.  Thus, there are cases where the imagined distinction does not apply and times when the putative difference is not always detectable in practice.

In this connection, there are two or three fundamental questions that need to be addressed by this project:

In this connection, there are two or three fundamental questions that need to be addressed by this project:

1. What makes a POV or a POD "well founded"?

# What makes a POV or a POD well-founded?

# How should they be treated and regulated, if tolerated?

A tentative approach to these questions is tendered by the pragmatic theory of sign relations, where the ''definitive'' and the ''elaborative'' aspects of recursion correspond to the denotative and the connotative components of reference, respectively.  Although it is always useful to organize the connotative realm in the species of a determinate ordering or a well-founded hierarchy, there is found in these parts generally a greater tolerance for the baroque proliferation of circuitous references and a broader acceptance of provincial, dialectic, and private coinages.

 

 

A tentative approach to these questions is tendered by the pragmatic theory of sign relations, where the "definitive" and the "elaborative" aspects of recursion correspond to the denotative and the connotative components of reference, respectively.  Although it is always useful to organize the connotative realm in the species of a determinate ordering or a well founded hierarchy, there is found in these parts generally a greater tolerance for the baroque proliferation of circuitous references and a broader acceptance of provincial, dialectic, and private coinages.

If all thought takes place in signs, as a tenet of pragmatism holds, then mental space is a space of signs and their interpretants, in other words, it is a connotative realm.

If all thought takes place in signs, as a tenet of pragmatism holds, then mental space is a space of signs and their interpretants, in other words, it is a connotative realm.