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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
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===6.17. Patterns of Self-Reference===
===6.17. Patterns of Self-Reference===
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In setting out the plan of a full scale RIF there is an unspoken promise to justify eventually the thematic motives that experimentally tolerate its indulgence in self reference, and it seems that this implicit hope for a full atonement in time is a key to the tensions of the work being borne. This section, in order to inspire confidence in the prospects of a RIF being achievable, and by way of allaying widespread suspicions about all types of self reference, examines several forms of circular referral and notes that not all contemplation of self reference is incurably vicious.
In this section I consider signs, expressions, sign relations, and systems of interpretation (SOI's) that involve forms of self reference. Because it is the abstract forms of self reference that constitute the chief interest of this study, I collect this whole subject matter under the heading "patterns of self reference" (POSR's). With respect to this domain I entertain the classification of POSR's in two different ways.
In this section I take notice of a broad family of formal structures that I refer to as "patterns of self reference" (POSR's), because they seem to have in common the proposed description of a formal object by means of recursive or circular references. In their basic characters, POSR's range from the familiar to the strange, from the obvious to the problematic, and from the legitimate to the spurious. Often a POSR is best understood as a formal object in its own right, or as a formal sign that foreshadows a definite object, but occasionally a POSR can only be interpreted as something in the character of a syntactic pattern, one that goes into the making of a questionable specification and represents merely a dubious attempt to indicate or describe an object. All in all, POSR's range from the kinds of functions and objects, or programs and data structures, that are successfully defined by recursion to the sorts of vitiating circles that doom every attempt to define an unknown term in terms of itself.
Because POSR's span the spectrum from the moderately straightforward to the deliberately misleading, there is a need for ways to tell them apart, at least, before pursuing their consequences too far. Of course, if one cannot rest without having all computable functions at one's command, then no program can tell all the good and bad programs apart. But if one can be satisfied with a somewhat more modest domain, then there is hope for a way, an experimental, fallible, and incremental way, but a way nonetheless, that eventually leads one to know the good and ultimately keeps one away from the bad.
When it comes to their propriety, POSR's are found on empirical grounds to fall into two varieties: the "exculpable" and the "indictable" kinds. Thus, it is reasonable to attempt an empirical distinction, proposing to let experience mark each POSR as an "excusable self reference" (ESR) or an "improper self reference" (ISR), as the case may be. But empirical grounds can be a hard basis to fall back on, since a recourse to actual experience with POSR's can risk an agent's participation in pretended sign relations and promissory representations that amount in the end to nothing more than forms of interpretive futility. Therefore, one seeks an arrangement of methods in general or an ordering of options in these special cases that makes the empirical trial a court of last resort and that avoids resorting to the actual experience of interpretation as a routine matter of course.
First, I recognize an "empirical distinction" that seems to exist between the less problematic and the more problematic varieties of self reference, allowing POSR's to be sorted according to the consequential features that they have in actual experience. There are the "good" sorts, those cleared up to the limits of accumulated experience as innocuous usages and even as probable utilities, and then there are the "bad" sorts, those marked by hard experience as definitely problematic.
Next, I search for an "intuitive distinction" that can be supposed to exist between the good and the bad sorts of POSR's, invoking a formal character or computable predicate of a POSR whose prior inspection can provide interpreters with a definitive indication or a decisive piece of information as to whether a POSR is good or bad, without forcing them to undergo the consequences of its actual use.
Before I can pin down what is involved in finding these intuitive characters and distinctions, it is necessary to discuss the concept of "intuition" that is relevant here. This issue requires a substantial digression and is taken up in the next section. After that, the concrete examples I take to be acceptable POSR's are presented.
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===6.18. Practical Intuitions===
===6.18. Practical Intuitions===