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| | sense that it represents an aspect of the structure that is present | | sense that it represents an aspect of the structure that is present |
| | in another object or domain. | | in another object or domain. |
| − | </pre>
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| − |
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| − | =====1.3.5.7. Steps and Tests of Formalization=====
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| − |
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| − | <pre>
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| − | | This same compulsion exists in the sense activities that support reason --
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| − | | by simplification, coarsening, emphasizing, and elaborating, upon which
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| − | | all "recognition", all ability to make oneself intelligible rests. Our
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| − | | needs have made our senses so precise that the "same apparent world"
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| − | | always reappears and has thus acquired the semblance of reality.
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| − | |
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| − | | (Nietzsche, 'The Will to Power', S 521, 282).
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| − |
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| − | A step of formalization moves the active focus of discussion from
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| − | the "presentational object" or the source domain that constitutes
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| − | the phenomenon of interest to the "representational object" or the
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| − | target domain that makes up the relevant model of interest. If the
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| − | structure in the source context is already formalized then the step
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| − | of formalization can itself be formalized in an especially elegant
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| − | and satisfying way as a structure-preserving map, a homomorphism,
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| − | or an "arrow" in the sense of mathematical category theory.
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| − |
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| − | The test of a formalization being complete is that a computer program could
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| − | in principle carry out the steps of the process being formalized exactly as
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| − | represented in the formal model or image. It needs to be appreciated that
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| − | this test is a criterion of sufficiency to formal understanding and not of
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| − | necessity directed toward a material re-creation or a concrete simulation
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| − | of the formalized process. The ordinary agents of informal discussion
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| − | who address the task of formalization do not disappear in the process
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| − | of completing it, since it is precisely for their understanding that
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| − | the step is undertaken. Only if the phenomenon or process at issue
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| − | were by its very nature solely a matter of form could its formal
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| − | analogue constitute an authentic reproduction. However, this
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| − | potential consideration is far from the ordinary case that
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| − | I need to discuss at present.
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| − |
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| − | In ordinary discussion, agents of inquiry and interpretation depend on
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| − | the likely interpretations of others to give their common notions and
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| − | their shared notations a meaning in practice. This means that a high
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| − | level of implicit understanding is relied on to ground each informal
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| − | inquiry in practice. The entire framework of logical assumptions and
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| − | interpretive activities that is needed to shore up this platform will
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| − | itself resist analysis, since it is precisely to save the effort of
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| − | repeating routine analyses that the whole infrastructure is built.
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| | </pre> | | </pre> |
