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'''Methodeutic.'''  This subject, that C.S. Peirce gave the alternate titles of “speculative rhetoric” or “formal rhetoric”, because it is a science that ”would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants” (CP 1.444 and 1.559), and that he assigned the task to find “a method of discovering methods” (CP 2.108 and 3.364), is one that clearly has a special relevance to the pursuit of an inquiry into inquiry.

'''Methodeutic.'''  This subject, that C.S. Peirce gave the alternate titles of “speculative rhetoric” or “formal rhetoric”, because it is a science that “would treat of the formal conditions of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants” (CP 1.444 and 1.559), and that he assigned the task to find “a method of discovering methods” (CP 2.108 and 3.364), is one that clearly has a special relevance to the pursuit of an inquiry into inquiry.

In an effort to gradually begin formalizing these issues, I introduce the concept of a ''point of development'' (POD).  This notion is intended to capture a particular moment in the history of a system or its agent, as it is reflected in the systems of propositions associated with each POD.  Relative to a particular POD there can be distinguished, though neither exclusively nor exhaustively, two types of propositions that are said to be “associated” with it.  Roughly speaking, these types of propositions reflect the thoughts that are ''applied'' to a POD and the thoughts that are ''attached'' to a POD, respectively.

In an effort to gradually begin formalizing these issues, I introduce the concept of a "point of development" (POD).  This notion is intended to capture a particular moment in the history of a system or its agent, as it is reflected in the systems of propositions associated with each POD.  Relative to a particular POD there can be distinguished, though neither exclusively nor exhaustively, two types of propositions that are said to be "associated" with it.  Roughly speaking, these types of propositions reflect the thoughts that are "applied" to a POD and the thoughts that are "attached" to a POD, respectively.

1. A proposition that "applies" to a POD can be formulated in more detail as a "proposition about or on a POD" (PAO'POD).  This describes the corresponding POD as though observed from an outside perspective, stating features that locate it within a space of dynamic configurations or that place it in relation to some other medium of common description.  This manner of associating propositions with PODs is tantamount to adopting a third person POV on the system or its agent, and it is commonly used to convey an impression of objectivity, no matter whether this standpoint is well taken or not.

# A proposition that ''applies'' to a POD can be formulated in more detail as a ''proposition about or on a POD''.  This describes the corresponding POD as though observed from an outside perspective, stating features that locate it within a space of dynamic configurations or that place it in relation to some other medium of common description.  This manner of associating propositions with PODs is tantamount to adopting a third person POV on the system or its agent, and it is commonly used to convey an impression of objectivity, no matter whether this standpoint is well taken or not.

# A proposition that ''attaches'' to a POD can be formalized in more detail as a ''proposition at or in a POD''.  This represents what an agent thinks or believes, entertains or maintains, in sum, what an agent is aware of or willing to assert at a particular POD.  By way of filling out the formula, this type of proposition expresses thoughts and is expressed in signs that are likewise regarded as ''attached'' to the POD in question.  In general, propositions at a POD can be formed to express every conceivable modality.  Collectively, they can state anything that an agent notes or thinks, observes or imagines at a given moment of its developmental history.  They can reflect any aspect of an agent's awareness, belief, conjecture, doubt, expectation, intention, observation, or any other latitude of thought that is actively considered or faithfully preserved throughout the moment in question, and in this sense they are considered to be attached to, bound to, contained in, or localized at a particular POD.

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" (HOPs) 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.