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A step of formalization moves the active focus of discussion from the ''presentational object'' or ''source domain'' to the ''representational object'' or ''target domain'' that constitutes the relevant MOI.  If the structure in the source context is already formalized then the step of formalization can itself be formalized in an especially elegant and satisfying way as a structure-preserving map, homomorphism, or ''arrow'' of category theory.

A step of formalization moves the active focus of discussion from the ''presentational object'' or the source domain that constitutes the phenomenon of interest to the ''representational object'' or the target domain that makes up the relevant model of interest.  If the structure in the source context is already formalized then the step of formalization can itself be formalized in an especially elegant and satisfying way as a structure-preserving map, a homomorphism, or an ''arrow'' in the sense of mathematical category theory.

The test of a formalization being complete is that a computer could in principle carry out the steps of the process exactly as represented in the formal model or image.  It needs to be appreciated that this is a criterion of sufficiency to formal understanding and not of necessity relevant to material re-creation.  The ordinary agents of informal discussion who address the task of formalization do not disappear in the process of completing it, since it is precisely for their understanding that the step is undertaken.  Only if the phenomenon at issue were by its very nature solely a matter of form could its formal analogue constitute an authentic reproduction.  But this potential consideration is far from the ordinary case I need to discuss at present.

The test of a formalization being complete is that a computer program could in principle carry out the steps of the process being formalized exactly as represented in the formal model or image.  It needs to be appreciated that this test is a criterion of sufficiency to formal understanding and not of necessity directed toward a material re-creation or a concrete simulation of the formalized process.  The ordinary agents of informal discussion who address the task of formalization do not disappear in the process of completing it, since it is precisely for their understanding that the step is undertaken.  Only if the phenomenon or process at issue were by its very nature solely a matter of form could its formal analogue constitute an authentic reproduction.  However, this potential consideration is far from the ordinary case that I need to discuss at present.

In ordinary discussion, agents depend on the likely interpretations of others to give their common notions and shared notations a meaning in practice.  This means that a high level of implicit understanding is relied on to ground each informal inquiry in practice.  The entire framework of logical assumptions and interpretive activities that is needed to shore up this platform will itself resist analysis, since it is precisely to save the effort of repeating routine analyses that the whole infrastructure is built.

In ordinary discussion, agents of inquiry and interpretation depend on the likely interpretations of others to give their common notions and their shared notations a meaning in practice.  This means that a high level of implicit understanding is relied on to ground each informal inquiry in practice.  The entire framework of logical assumptions and interpretive activities that is needed to shore up this platform will itself resist analysis, since it is precisely to save the effort of repeating routine analyses that the whole infrastructure is built.

=====1.3.5.8. A Puckish Referee=====

=====1.3.5.8. A Puckish Referee=====