Changes

§ 15.   There is an order of logical reasoning that is typically described as ''propositional'' or ''sentential'' and represented in a type of formal system that is commonly known as a ''propositional calculus'' or a ''sentential logic'' (SL).  Any one of these calculi forms an interesting example of a formal language, one that can be used to illustrate all of the preceding issues of style and technique, but one that can also serve this inquiry in a more instrumental fashion.  This section presents the elements of a calculus for propositional logic that I described in earlier work (Awbrey, 1989 and 1994).  The imminent use of this calculus is to construct and analyze logical representations of sign relations, and the treatment here focuses on the concepts and notation that are most relevant to this task.

§ 15.   There is an order of logical reasoning that is typically described as ''propositional'' or ''sentential'' and represented in a type of formal system that is commonly known as a ''propositional calculus'' or a ''sentential logic'' (SL).  Any one of these calculi forms an interesting example of a formal language, one that can be used to illustrate all of the preceding issues of style and technique, but one that can also serve this inquiry in a more instrumental fashion.  This section presents the elements of a calculus for propositional logic that I described in earlier work (Awbrey, 1989 and 1994).  The imminent use of this calculus is to construct and analyze logical representations of sign relations, and the treatment here focuses on the concepts and notation that are most relevant to this task.

The next four sections (§§ 16–19) treat the theme of self-reference that is invoked in the overture to a RIF.  To inspire confidence in the feasibility and the utility of well chosen reflective constructions and to allay a suspicion of self reference in general, it is useful to survey the varieties of self reference that arise in this work and to distinguish the forms of circular referrals that are likely to vitiate consistent reasoning from those that are relatively innocuous and even beneficial.

The next four sections (§§ 16–19) treat the theme of self reference that is invoked in the overture to a RIF.  To inspire confidence in the feasibility and the utility of well chosen reflective constructions and to allay a suspicion of self reference in general, it is useful to survey the varieties of self reference that arise in this work and to distinguish the forms of circular referrals that are likely to vitiate consistent reasoning from those that are relatively innocuous and even beneficial.

§ 16.   Recursive Aspects

§ 16.   Recursive Aspects

§ 20.   First, I discuss three distinct ways that the word ''system'' is used in this work, reflecting the variety of approaches, aspects, or perspectives that present themselves in dealing with what are often the same underlying objects in reality.

§ 20.   First, I discuss three distinct ways that the word ''system'' is used in this work, reflecting the variety of approaches, aspects, or perspectives that present themselves in dealing with what are often the same underlying objects in reality.

§ 21.   There is a general set of situations where the task arises to "build a bridge" between significantly different types of representation.  In these situations, the problem is to translate between the signs and expressions of two formal systems that have radically different levels of interpretation, and to do it in a way that makes appropriate connections between diverse descriptions of the same objects.  More to the point of the present project, formal systems for mediating inquiry, if they are intended to remain viable in both empirical and theoretical uses, need the capacity to negotiate between an "extensional representation" (ER) and an "intensional representation" (IR) of the same domain of objects.  It turns out that a cardinal or pivotal issue in this connection is how to convert between ERs and IRs of the same objective domain, working all the while within the practical constraints of a computational medium and preserving the equivalence of information.  To illustrate the kinds of technical issues that are involved in these considerations, I bring them to bear on the topic of representing sign relations and their dyadic projections in various forms.

§ 21.   There is a general set of situations where the task arises to “build a bridge” between significantly different types of representation.  In these situations, the problem is to translate between the signs and expressions of two formal systems that have radically different levels of interpretation, and to do it in a way that makes appropriate connections between diverse descriptions of the same objects.  More to the point of the present project, formal systems for mediating inquiry, if they are intended to remain viable in both empirical and theoretical uses, need the capacity to negotiate between an ''extensional representation'' (ER) and an ''intensional representation'' (IR) of the same domain of objects.  It turns out that a cardinal or pivotal issue in this connection is how to convert between ERs and IRs of the same objective domain, working all the while within the practical constraints of a computational medium and preserving the equivalence of information.  To illustrate the kinds of technical issues that are involved in these considerations, I bring them to bear on the topic of representing sign relations and their dyadic projections in various forms.

The next four sections (§§ 22–25) give examples of ERs and IRs, indicate the importance of forming a computational bridge between them, and discuss the conceptual and technical obstacles that will have to be faced in doing so.

The next four sections (§§ 22–25) give examples of ERs and IRs, indicate the importance of forming a computational bridge between them, and discuss the conceptual and technical obstacles that will have to be faced in doing so.