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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 5 (view source)
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Let me review the developments that bring me to this point. I began by describing my present inquiry, <math>y_0,</math> as an inquiry into inquiry, <math>y \cdot y.</math> Then I focussed on the activities of discussion, <math>d,</math> and formalization, <math>f,</math> as two components of the faculty or the process of inquiry, <math>y >\!\!= \{ d , f \}.</math> This led me to the present discussion of formalization, <math>f \cdot d.</math> Considered as classes of activities, the collective instances of formalization, <math>F,</math> appeared to be encompassed by the collective instances of discussion, <math>D,</math> thereby yielding the relationship <math>F \subseteq D.</math>
Let me review the developments that bring me to this point. I began by describing my present inquiry, <math>y_0,</math> as an inquiry into inquiry, <math>y \cdot y.</math> Then I focussed on the activities of discussion, <math>d,</math> and formalization, <math>f,</math> as two components of the faculty or the process of inquiry, <math>y >\!\!= \{ d , f \}.</math> This led me to the present discussion of formalization, <math>f \cdot d.</math> Considered as classes of activities, the collective instances of formalization, <math>F,</math> appeared to be encompassed by the collective instances of discussion, <math>D,</math> thereby yielding the relationship <math>F \subseteq D.</math>
I initially characterized discussion and formalization, in regard to each other, as being an “actively instrumental” versus a “passively objective” aspect, component, or “face” of the inquiry <math>y >\!\!= \{ d , f \}.</math> In casting them this way I clearly traded on the ambiguity of “-ionized” terms to force the issue a bit. In other words, I used the flexibility that is freely available within their “-ionic” construals, as processes or as products, to cast discussion and formalization into sundry molds, drawing out the patent energies that are manifested by the active process of discussion and placing them in contrast with the latent inertias that are immanent in the dormant product of formalization. In this partially arbitrary way, I decided on the one hand to treat discussion in respect of its ongoing process, the only thing that it has any assurance of accomplishing, but I decided on the other hand to treat formalization in respect of its end product, the abstract image or the formal model that constitutes its chief qualification and thus becomes the mark of what it is.
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By casting inquiry into the form y >= {d,f}, I made it more likely that my development of its self application, y.y >= {d,f}{d,f}, would first take up the application of discussion to formalization, f.d, and only later get around to the application of formalization to discussion, d.f, that brings the active side of the formalization process into a greater prominence. But the bias that I exploited in these readings does not seem at present to be a property of the incipient algebra that would determine the sense of the applications and the decompositions envisioned here. Thus, if I initially saw a difference between the two presentations {d,f} and {f,d}, then it must have been a purely interpretive and not a substantial one, and the task of giving explicit notice to these interpretive distinctions and working out their algebra or calculus yet remains to be carried out in any sort of convincing fashion.
By casting inquiry into the form y >= {d,f}, I made it more likely that my development of its self application, y.y >= {d,f}{d,f}, would first take up the application of discussion to formalization, f.d, and only later get around to the application of formalization to discussion, d.f, that brings the active side of the formalization process into a greater prominence. But the bias that I exploited in these readings does not seem at present to be a property of the incipient algebra that would determine the sense of the applications and the decompositions envisioned here. Thus, if I initially saw a difference between the two presentations {d,f} and {f,d}, then it must have been a purely interpretive and not a substantial one, and the task of giving explicit notice to these interpretive distinctions and working out their algebra or calculus yet remains to be carried out in any sort of convincing fashion.