Changes

In one sense, propositions about a POD are potentially the general case, since propositions at a POD can be incorporated within their formulation.  That is, a proposition about a POD is allowed to make assertions about the propositions at that POD, plus assertions about their relation to propositions at other PODs.  But propositions whose references are this involved, articulated as ''propositions about propositions at a POD'', for instance, are classed as ''higher order propositions'' and need to be inferred through processes of hypothesis and experiment, conjecture and confirmation, instead of being observed outright.  In another sense, propositions at a POD are intrinsically the prototype, since it is from their data that every other type must be constructed.

In one sense, propositions about a POD are potentially the general case, since propositions at a POD can be incorporated within their formulation.  That is, a proposition about a POD is allowed to make assertions about the propositions at that POD, plus assertions about their relation to propositions at other PODs.  But propositions whose references are this involved, articulated as ''propositions about propositions at a POD'', for instance, are classed as ''higher order propositions'' and need to be inferred through processes of hypothesis and experiment, conjecture and confirmation, instead of being observed outright.  In another sense, propositions at a POD are intrinsically the prototype, since it is from their data that every other type must be constructed.

Propositions about PODs naturally collect into theories about PODs, and at the next level of aggregation these constitute the familiar sorts of dynamic theories that are used to describe the state spaces of systems and the trajectories of agents through them.  Concentrating on these types of propositions leads to the kinds of theories about systems where a “neutral observer”, not involved in the system itself, is postulated or fancied to stand outside the dynamics of the “observable object system”:  where this “objective reasoner” is supposedly able to theorize about the observable system without essentially becoming a part of its operations or necessarily being involved as a participant in its actual workings, and where the same “passive agent” never finds itself forced to interact in an irreversible or irrevocable manner with the autonomous course of the object system's action.

Propositions about PODs naturally collect into theories about PODs, and at the next level of aggregation these constitute the familiar sorts of dynamic theories that are used to describe the state spaces of systems and the trajectories of agents through them.  Concentrating on these types of propositions leads to the kinds of theories about systems where a "neutral observer", not involved in the system itself, is postulated or fancied to stand outside the dynamics of the "observable object system":  where this "objective reasoner" is supposedly able to theorize about the observable system without essentially becoming a part of its operations or necessarily being involved as a participant in its actual workings, and where the same "passive agent" never finds itself forced to interact in an irreversible or irrevocable manner with the autonomous course of the object system's action.

The thoughts attached to a POD, the things an agent thinks or believes, entertains or maintains at one POD, in relation to what the agent thinks or believes, is aware of or willing to assert at another POD, is the very form of subject matter that is bound to come to light and bound to fall into play whenever one studies the development of a reflective system, whether the focus of interest is the course of a particular inquiry or the emergence of a generic intelligence.

The thoughts attached to a POD, the things an agent thinks or believes, entertains or maintains at one POD, in relation to what the agent thinks or believes, is aware of or willing to assert at another POD, is the very form of subject matter that is bound to come to light and bound to fall into play whenever one studies the development of a reflective system, whether the focus of interest is the course of a particular inquiry or the emergence of a generic intelligence.

It may be thought that there is an important distinction between belief and knowledge that ought to be recognized in the modes of maintaining propositions at or in a POD.  Given the pragmatic definition of belief, however, there is no local mark that can tell belief and knowledge apart.  That is, there is no practical difference that can be sustained, in the propositions attached to a single POD, between those that reflect items of contingent belief and those that reflect items of certain knowledge.  Even if the propositions at or in a POD are artificially marked in ways that can later be reliably detected, the problem of constantly updating so fleeting a form of distinction makes the accumulating profusion of ephemeral distinctions as immaterial and unenlightening as every other genre of eracist obliterature.

It may be thought that there is an important distinction between belief and knowledge that ought to be recognized in the modes of maintaining propositions at or in a POD.  Given the pragmatic definition of belief, however, there is no local mark that can tell belief and knowledge apart.  That is, there is no practical difference that can be sustained, in the propositions attached to a single POD, between those that reflect items of contingent belief and those that reflect items of certain knowledge.  Even if the propositions at or in a POD are artificially marked in ways that can later be reliably detected, the problem of constantly updating so fleeting a form of distinction makes the accumulating profusion of ephemeral distinctions as immaterial and unenlightening as every other genre of eracist obliterature.

A distinction between belief and knowledge appears to arise only in the interactions and comparisons that can be made between different PODs, either those enjoyed by a single agent in the history of a single system or those passed through by ostensibly different agents and systems.  The sense of the distinction can be sustained only if the order of its relational context continues to be recognized, which means that the mark of the distinction cannot be strained to the point of being an absolute.  In this context, different systems and their agents are said to be "at" comparable PODs precisely to the degree and exactly to the extent that the propositions "at" and "about" them, respectively, can be compared.  In many respects, the comparison of propositions at different PODs is equally complex and problematic whether it is one agent or several that is being considered.

A distinction between belief and knowledge appears to arise only in the interactions and comparisons that can be made between different PODs, either those enjoyed by a single agent in the history of a single system or those passed through by ostensibly different agents and systems.  The sense of the distinction can be sustained only if the order of its relational context continues to be recognized, which means that the mark of the distinction cannot be strained to the point of being an absolute.  In this context, different systems and their agents are said to be ''at'' comparable PODs precisely to the degree and exactly to the extent that the propositions ''at'' and ''about'' them, respectively, can be compared.  In many respects, the comparison of propositions at different PODs is equally complex and problematic whether it is one agent or several that is being considered.

With all this in mind, I can give a formulation of what the practical difference between belief and knowledge consists in.  Roughly speaking, an agent says that an agent "knows" something if and only if the one believes what the other believes.  More precisely, an agent at one POD has reason to say that an agent at another POD (possibly a former self) knows something about something (or knew something about something) if and only if the one believes what the other believes about it, all things being relative to the PODs that the agents are at.

With all this in mind, I can give a formulation of what the practical difference between belief and knowledge consists in.  Roughly speaking, an agent says that an agent ''knows'' something if and only if the one believes what the other believes.  More precisely, an agent at one POD has reason to say that an agent at another POD (possibly a former self) knows something about something (or knew something about something) if and only if the one believes what the other believes about it, all things being relative to the PODs that the agents are at.

Propositions associated with a POD are often found in organized bodies, forming more or less logical systems of more or less logical statements.  Whatever their type or modality with respect to a POD, "propositions of a feather gather together".  That is, they tend to collect into organized bodies of propositions that share compatible types of association and comparable modes of assertion.  In logic, an arbitrary collection of propositions is called a "theory", no matter how coherent, complete, or consistent it turns out to be when subjected in time to critical review.  Taking up this liberalized notion of a theory in the present setting, a bunch of PAI'PODs forms a "theory at or in a POD" (TAI'POD), while a bunch of PAO'PODs forms a "theory about or on a POD" (TAO'POD).

Propositions associated with a POD are often found in organized bodies, forming more or less logical systems of more or less logical statements.  Whatever their type or modality with respect to a POD, “propositions of a feather gather together”.  That is, they tend to collect into organized bodies of propositions that share compatible types of association and comparable modes of assertion.  In logic, an arbitrary collection of propositions is called a ''theory'', no matter how coherent, complete, or consistent it turns out to be when subjected in time to critical review.  Taking up this liberalized notion of a theory in the present setting, a bunch of ''propositions at or in a POD'' forms a ''theory at or in a POD'', while a bunch of ''propositions about or on a POD'' forms a ''theory about or on a POD''.

A reasonably organized system is amenable to having its propositions sorted further, forming collections of propositions that are intended to be interpreted in the same light, and constellating theories that bear on single modes of contemplation or declaration among their propositions.

A reasonably organized system is amenable to having its propositions sorted further, forming collections of propositions that are intended to be interpreted in the same light, and constellating theories that bear on single modes of contemplation or declaration among their propositions.