Changes

When is enough enough?  What measure can I use to tell if my effort is working?  What information is critical in deciding whether my exercise of the method is advancing my state of knowledge toward a solution of the problem?

When is enough enough?  What measure can I use to tell if my effort is working?  What information is critical in deciding whether my exercise of the method is advancing my state of knowledge toward a solution of the problem?

Given that the problem is "inquiry" and the method is "inquiry", the test of progress and eventual success is just the measure of any inquiry's performance.  According to my current understanding of inquiry, and the tentative model of inquiry that will guide this project, the criterion of an inquiry's competence is how well it succeeds in reducing the uncertainty of its agent about its object.

Given that the problem is ''inquiry'' and the method is ''inquiry'', the test of progress and eventual success is just the measure of any inquiry's performance.  According to my current understanding of inquiry, and the tentative model of inquiry that will guide this project, the criterion of an inquiry's competence is how well it succeeds in reducing the uncertainty of its agent about its object.

What are the practical tests of whether the results of inquiry succeed in reducing uncertainty?  Two gains are often cited:  Successful results of inquiry provide the agent with increased powers of prediction and control as to how the object system will behave in given circumstances.  If a common theme is desired, at the price of a finely equivocal thread, it can be said that the agent has gained in its power of determination.  Hence, more certainty is exhibited by less hesitation, more determination is manifested by less vacillation.

What are the practical tests of whether the results of inquiry succeed in reducing uncertainty?  Two gains are often cited:  Successful results of inquiry provide the agent with increased powers of prediction and control as to how the object system will behave in given circumstances.  If a common theme is desired, at the price of a finely equivocal thread, it can be said that the agent has gained in its power of determination.  Hence, more certainty is exhibited by less hesitation, more determination is manifested by less vacillation.

Discussion is easy in general because its termination criterion is relaxed to the point of becoming otiose.  A discussion of things in general can be pursued as an end in itself, with no consideration of any purpose but persevering in its current form, and this accounts for the virtually perpetual continuation of many a familiar and perennial discussion.

Discussion is easy in general because its termination criterion is relaxed to the point of becoming otiose.  A discussion of things in general can be pursued as an end in itself, with no consideration of any purpose but persevering in its current form, and this accounts for the virtually perpetual continuation of many a familiar and perennial discussion.

There's a catch here that applies to all living creatures:  In order to keep talking one has to keep living.  This brings discussion back to its role in inquiry, considered as an adaptation of living creatures designed to help them deal with their not so virtual environments.  If discussion is constrained to the envelope of life and required to contribute to the trend of inquiry, instead of representing a kind of internal opposition, then it must be possible to tighten up the loose account and elevate the digressionary narrative into a properly directed inquiry.  This brings an end to my initial discussion of "discussion".

There's a catch here that applies to all living creatures:  In order to keep talking one has to keep living.  This brings discussion back to its role in inquiry, considered as an adaptation of living creatures designed to help them deal with their not so virtual environments.  If discussion is constrained to the envelope of life and required to contribute to the trend of inquiry, instead of representing a kind of internal opposition, then it must be possible to tighten up the loose account and elevate the digressionary narrative into a properly directed inquiry.  This brings an end to my initial discussion of ''discussion''.

====1.3.3.  Discussion of Formalization : General Topics====

====1.3.3.  Discussion of Formalization : General Topics====

=====1.3.3.3.  A Formalization of Discussion?=====

=====1.3.3.3.  A Formalization of Discussion?=====

The previous section took the concept of "formalization" as an example of a topic that a writer might try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader.  In either case the formalization process, that aims to translate a concept from informal to formal discussion, is itself mediated by a form of discussion:  (1) that interpreters conduct as a part of their ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue with a reader (hearer).  In view of this, I see no harm in letting the concept of discussion be stretched to cover all attempted processes of formalization.  F ? D.

The previous section took the concept of "formalization" as an example of a topic that a writer might try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader.  In either case the formalization process, that aims to translate a concept from informal to formal discussion, is itself mediated by a form of discussion:  (1) that interpreters conduct as a part of their ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue with a reader (hearer).  In view of this, I see no harm in letting the concept of discussion be stretched to cover all attempted processes of formalization.

In this section, I step back from the example of "formalization" and consider the general task of clarifying and communicating concepts by means of a properly directed discussion.  Let this kind of "motivated" or "measured" discussion be referred to as a "meditation", that is, "a discourse intended to express its author's reflections or to guide others in contemplation" (Webster's).  The motive of a meditation is to mediate a certain object or intention, namely, the system of concepts intended for clarification or communication.  The measure of a meditation is a system of values that permits its participants to tell how close they are to achieving its object.  The letter "M" will be used to annotate this form of meditation.  F ? M ? D.

:: '''<code>F &sube; D</code>'''

This brings the discussion around to considering the intentional objects of measured discussions and the qualifications of a writer so motivated.  Just what is involved in achieving the object of a motivated discussion? Can these intentions be formalized?  y0 = y.y >= {d, f}{d, f} >= {d}{f}.

In this section, I step back from the example of ''formalization'' and consider the general task of clarifying and communicating concepts by means of a properly directed discussion.  Let this kind of ''motivated'' or ''measured'' discussion be referred to as a ''meditation'', that is, "a discourse intended to express its author's reflections or to guide others in contemplation" (Webster's).  The motive of a meditation is to mediate a certain object or intention, namely, the system of concepts intended for clarification or communication.  The measure of a meditation is a system of values that permits its participants to tell how close they are to achieving its object. The letter "M" will be used to annotate this form of meditation.

The writer's task is not to create meaning from nothing, but to construct a relation from the typical meanings that are available in ordinary discourse to the particular meanings that are intended to be the effects of a particular discussion.

:: '''<code>F &sube; M &sube; D</code>'''

In case there is difficulty with the meaning of the word "meaning", I replace its use with references to a "system of interpretation" (SOI), a technical concept that will be increasingly formalized as this project proceeds.  Thus, the writer's job description is reformulated as follows.

The writer's task is not to create a system of interpretation (SOI) from nothing, but to construct a relation from the typical SOI's that are available in ordinary discourse to the particular SOI's that are intended to be the effects of a particular discussion.

 

 

 

In case there is difficulty with the meaning of the word ''meaning'', I replace its use with references to a ''system of interpretation'' (SOI), a technical concept that will be increasingly formalized as this project proceeds.  Thus, the writer's job description is reformulated as follows.

 

* The writer's task is not to create a system of interpretation (SOI) from nothing, but to construct a relation from the typical SOI's that are available in ordinary discourse to the particular SOI's that are intended to be the effects of a particular discussion.

 

This assignment begins with an informal system of interpretation (SOI₁), and builds a relation from it to another system of interpretation (SOI₂).  The first is an informal SOI that amounts to a shared resource of writer and reader.  The latter is a system of meanings in practice that is the current object of the writer's intention to recommend for the reader's consideration and, hopefully, edification.  In order to have a compact term for highlighting the effects of a discussion that ''builds a relation'' between SOI's, I will call this aspect of the process ''narration''.

It is the writer's ethical responsibility to ensure that a discourse is potentially edifying with respect to the reader's current SOI, and the reader's self-interest to evaluate whether a discourse is actually edifying from the perspective of the reader's present SOI.

It is the writer's ethical responsibility to ensure that a discourse is potentially edifying with respect to the reader's current SOI, and the reader's self-interest to evaluate whether a discourse is actually edifying from the perspective of the reader's present SOI.

Formally, the relation that the writer builds from SOI to SOI can always be cast or recast as a three-place relation, one whose staple element of structure is an ordered or indexed triple.  One component of each triple is anchored in the interpreter of the moment, and the other two form a connection with the source and target SOI's of the current assignment.

Formally, the relation that the writer builds from SOI to SOI can always be cast or recast as a three-place relation, one whose staple element of structure is an ordered or indexed triple.  One component of each triple is anchored in the interpreter of the moment, and the other two form a connection with the source and target SOI's of the current assignment.

Once this relation is built, a shift in the attention of any interpreter or a change in the present focus of discourse can leave the impression of a transformation taking place from SOI1 to SOI2, but this is more illusory (or allusory) than real.  To be more precise, this style of transformation takes place on a virtual basis, and need not have the substantive impact (or import) that a substantial replacement of one SOI by another would imply.  For a writer to affect a reader in this way would simply not be polite.  A moment's consideration of the kinds of SOI-building worth having leads me to enumerate a few characteristics of "polite discourse" or "considerate discussion".

Once this relation is built, a shift in the attention of any interpreter or a change in the present focus of discourse can leave the impression of a transformation taking place from SOI1 to SOI2, but this is more illusory (or allusory) than real.  To be more precise, this style of transformation takes place on a virtual basis, and need not have the substantive impact (or import) that a substantial replacement of one SOI by another would imply.  For a writer to affect a reader in this way would simply not be polite.  A moment's consideration of the kinds of SOI-building worth having leads me to enumerate a few characteristics of ''polite discourse'' or ''considerate discussion''.

If this form of SOI-building narrative is truly intended to edify and educate, whether pursued in monologue or dialogue fashion, then its action cannot be forcibly to replace the meanings in practice a sign already has with others of an arbitrary nature, but freely to augment the options for meaning and powers for choice in the resulting SOI.

If this form of SOI-building narrative is truly intended to edify and educate, whether pursued in monologue or dialogue fashion, then its action cannot be forcibly to replace the meanings in practice a sign already has with others of an arbitrary nature, but freely to augment the options for meaning and powers for choice in the resulting SOI.

At this point, the discussion has touched on a topic, in one of its manifold aspects, that it will encounter repeatedly, under a variety of aspects, throughout this work.  In recognition of this circumstance, and to prepare the way for future discussion, it seems like a good idea to note a few of the aliases that this protean topic can be found lurking under, and to notice the logical relationships that exist among its several different appearances.

At this point, the discussion has touched on a topic, in one of its manifold aspects, that it will encounter repeatedly, under a variety of aspects, throughout this work.  In recognition of this circumstance, and to prepare the way for future discussion, it seems like a good idea to note a few of the aliases that this protean topic can be found lurking under, and to notice the logical relationships that exist among its several different appearances.

On several occasions, this discussion of inquiry will arrive at a form of "aesthetic deduction", in general terms, a piece of reasoning that ends with a design recommendation, in this case, where an analysis of the general purposes and interests of inquiry leads to the conclusion that a certain property of discussion is an admirable one, and that the quality in question forms an essential part of the implicit value system that is required to guide inquiry and make it what it is meant to be, a method for advancing toward desired forms of knowledge.  After a collection of admirable qualities has been recognized as cohering together into a unity, it becomes natural to ask:  What is the underlying reality that inheres in these qualities, and what are the logical relations that bind them together into the qualifications of inquiry and a definition of exactly what is desired for knowledge?

On several occasions, this discussion of inquiry will arrive at a form of ''aesthetic deduction'', in general terms, a piece of reasoning that ends with a design recommendation, in this case, where an analysis of the general purposes and interests of inquiry leads to the conclusion that a certain property of discussion is an admirable one, and that the quality in question forms an essential part of the implicit value system that is required to guide inquiry and make it what it is meant to be, a method for advancing toward desired forms of knowledge.  After a collection of admirable qualities has been recognized as cohering together into a unity, it becomes natural to ask:  What is the underlying reality that inheres in these qualities, and what are the logical relations that bind them together into the qualifications of inquiry and a definition of exactly what is desired for knowledge?

=====1.3.3.4.  A Concept of Formalization=====

=====1.3.3.4.  A Concept of Formalization=====

The concept of formalization is intended to cover the whole collection of activities that serve to build a relation between casual discussions, those that take place in the ordinary context of informal discourse, and formal discussions, those that make use of completely formalized models.  To make a long story short, formalization is the narrative operation or active relation that construes the situational context in the form of a definite text.  The end product that results from the formalization process is analogous to a snapshot or a candid picture, a relational or functional image that captures an aspect of the casual circumstances.

The concept of formalization is intended to cover the whole collection of activities that serve to build a relation between casual discussions, those that take place in the ordinary context of informal discourse, and formal discussions, those that make use of completely formalized models.  To make a long story short, formalization is the narrative operation or active relation that construes the situational context in the form of a definite text.  The end product that results from the formalization process is analogous to a snapshot or a candid picture, a relational or functional image that captures an aspect of the casual circumstances.

Relations between casual and formal discussion are often treated in terms of a distinction between two languages, the "meta-language" and the "object language", linguistic systems that take complementary roles in filling out the discussion of interest.  In the usual approach, issues of formalization are addressed by postulating a distinction between the meta-language, the descriptions and conceptions from ordinary language and technical discourse that can be used without being formalized, and the object language, the domain of structures and processes that can be studied as a completely formalized object.

Relations between casual and formal discussion are often treated in terms of a distinction between two languages, the ''meta-language and the ''object language'', linguistic systems that take complementary roles in filling out the discussion of interest.  In the usual approach, issues of formalization are addressed by postulating a distinction between the meta-language, the descriptions and conceptions from ordinary language and technical discourse that can be used without being formalized, and the object language, the domain of structures and processes that can be studied as a completely formalized object.

=====1.3.3.5.  A Formal Approach=====

=====1.3.3.5.  A Formal Approach=====

I plan to approach the issue of formalization from a slightly different angle, proceeding through an analysis of the medium of interpretation and developing an effective conception of "interpretive frameworks" or "interpretive systems".  This concept refers to any organized system of interpretive practice, ranging from those used in everyday speech, to the ones that inform technical discourse, to the kinds of completely formalized symbol systems that one can safely regard as mathematical objects.  Depending on the degree of objectification that it possesses from one's point of view, the same system of conduct can be variously described as an interpretive framework (IF), interpretive system (IS), interpretive object (IO), or object system (OS).  These terms are merely suggestive - no rigid form of classification is intended.

I plan to approach the issue of formalization from a slightly different angle, proceeding through an analysis of the medium of interpretation and developing an effective conception of ''interpretive frameworks'' or ''interpretive systems''.  This concept refers to any organized system of interpretive practice, ranging from those used in everyday speech, to the ones that inform technical discourse, to the kinds of completely formalized symbol systems that one can safely regard as mathematical objects.  Depending on the degree of objectification that it possesses from one's point of view, the same system of conduct can be variously described as an interpretive framework (IF), interpretive system (IS), interpretive object (IO), or object system (OS).  These terms are merely suggestive - no rigid form of classification is intended.

Many times, it is convenient to personify the interpretive organization as if it were embodied in the actions of a typical user of the framework or a substantive agent of the system.  I will call this agent the "interpreter" of the moment.  At other times, it may be necessary to analyze the action of interpretation more carefully.  At these times, it is important to remember that this form of personification is itself a figure of speech, one that has no meaning outside a fairly flexible interpretive framework.  Thus, the term "interpreter" can be a cipher analogous to the terms "X", "unknown", or "to whom it may concern" appearing in a system of potentially recursive constraints.  As such, it serves in the role of an indeterminate symbol, in the end to be solved for a fitting value, but in the mean time conveying an appearance of knowledge in a place where very little is known about the subject itself.

Many times, it is convenient to personify the interpretive organization as if it were embodied in the actions of a typical user of the framework or a substantive agent of the system.  I will call this agent the ''interpreter'' of the moment.  At other times, it may be necessary to analyze the action of interpretation more carefully.  At these times, it is important to remember that this form of personification is itself a figure of speech, one that has no meaning outside a fairly flexible interpretive framework.  Thus, the term ''interpreter'' can be a cipher analogous to the terms ''X'', ''unknown'', or ''to whom it may concern'' appearing in a system of potentially recursive constraints.  As such, it serves in the role of an indeterminate symbol, in the end to be solved for a fitting value, but in the mean time conveying an appearance of knowledge in a place where very little is known about the subject itself.

A meta-language corresponds to what I call an "interpretive framework".  Besides a set of descriptions and conceptions, it embodies the whole collective activity of unexamined structures and automatic processes that are trusted by agents at a given moment to make its employment meaningful in practice.  An interpretive framework is best understood as a form of conduct, that is, a comprehensive organization of related activities.

A meta-language corresponds to what I call an ''interpretive framework''.  Besides a set of descriptions and conceptions, it embodies the whole collective activity of unexamined structures and automatic processes that are trusted by agents at a given moment to make its employment meaningful in practice.  An interpretive framework is best understood as a form of conduct, that is, a comprehensive organization of related activities.

In use, an interpretive framework operates to contain activity and constrain the engagement of agents to certain forms of active involvement and dynamic participation, and manifests itself only incidentally in the manipulation of compact symbols and isolated instruments.  In short, though a framework may have pointer dials and portable tools attached to it, it is usually too incumbent and cumbersome to be easily moved on its own grounds, at least, it rests beyond the scope of any local effort to do so.

In use, an interpretive framework operates to contain activity and constrain the engagement of agents to certain forms of active involvement and dynamic participation, and manifests itself only incidentally in the manipulation of compact symbols and isolated instruments.  In short, though a framework may have pointer dials and portable tools attached to it, it is usually too incumbent and cumbersome to be easily moved on its own grounds, at least, it rests beyond the scope of any local effort to do so.

The supposition that there is a meaningful and well-defined distinction between object language and meta-language ordinarily goes unexamined.  This means that the assumption of a distinction between them is de facto a part of the meta-language and not even an object of discussion in the object language.  A slippery slope begins here.  A failure to build reflective capacities into an interpretive framework can let go unchallenged the spurious opinion that presumes there can be only one way to draw a distinction between object language and meta-language.

The supposition that there is a meaningful and well-defined distinction between object language and meta-language ordinarily goes unexamined.  This means that the assumption of a distinction between them is de facto a part of the meta-language and not even an object of discussion in the object language.  A slippery slope begins here.  A failure to build reflective capacities into an interpretive framework can let go unchallenged the spurious opinion that presumes there can be only one way to draw a distinction between object language and meta-language.

The next natural development is to iterate the supposed distinction.  This represents an attempt to formalize and thereby "objectify" parts of the meta-language, precipitating it like a new layer of pearl or crystal from the resident medium or "mother liquor", and thereby preparing the decantation of a still more pervasive and ethereal meta-meta-language.  The successive results of this process can have a positivistically intoxicating effect on the human intellect.  But a not so happy side-effect leads the not quite mindful cerebration up and down a blind alley, chasing the specious impression that just beyond the realm of objective nature there lies a unique fractionation of permeabilities and a permanent hierarchy of effabilities in language.

The next natural development is to iterate the supposed distinction.  This represents an attempt to formalize and thereby ''objectify'' parts of the meta-language, precipitating it like a new layer of pearl or crystal from the resident medium or ''mother liquor'', and thereby preparing the decantation of a still more pervasive and ethereal meta-meta-language.  The successive results of this process can have a positivistically intoxicating effect on the human intellect.  But a not so happy side-effect leads the not quite mindful cerebration up and down a blind alley, chasing the specious impression that just beyond the realm of objective nature there lies a unique fractionation of permeabilities and a permanent hierarchy of effabilities in language.

The grounds of discussion I am raking over here constellate a rather striking scene, especially for something intended as a neutral backdrop.  Unlike other concerns, the points I am making seem obvious to all reasonable people at the outset of discussion, and yet the difficulties that follow as inquiry develops get muddier and more grating the more one probes and stirs them up.  A large measure of the blame, I think, can be charged to a misleading directive that people derive from the epithet "meta", leading them to search for higher and higher levels of meaning and truth, on beyond language, on beyond any conceivable system of signs, and on beyond sense.  Prolonged use of the prefix "meta" leads people to act as if a meta-language were step outside of ordinary language, or an artificial platform constructed above and beyond natural language, and then they forget that formal models are developments internal to the informal context.  For this reason among others, I suggest replacing talk about rigidly stratified object languages and meta-languages with talk about contingent interpretive frameworks.

The grounds of discussion I am raking over here constellate a rather striking scene, especially for something intended as a neutral backdrop.  Unlike other concerns, the points I am making seem obvious to all reasonable people at the outset of discussion, and yet the difficulties that follow as inquiry develops get muddier and more grating the more one probes and stirs them up.  A large measure of the blame, I think, can be charged to a misleading directive that people derive from the epithet ''meta'', leading them to search for higher and higher levels of meaning and truth, on beyond language, on beyond any conceivable system of signs, and on beyond sense.  Prolonged use of the prefix ''meta'' leads people to act as if a meta-language were step outside of ordinary language, or an artificial platform constructed above and beyond natural language, and then they forget that formal models are developments internal to the informal context.  For this reason among others, I suggest replacing talk about rigidly stratified object languages and meta-languages with talk about contingent interpretive frameworks.

To avoid the types of cul-de-sac (cultist act) encountered above, I am taking some pains to ensure a reflective capacity for the interpretive frameworks I develop in this project.  This is a capacity that natural languages always assume for themselves, instituting specialized discourses as developments that take place within their frame and not as constructs that lie beyond their scope.  Any time the levels of recursive discussion become too involved to manage successfully, one needs to keep available the resource of "instant wisdom", the modest but indispensable quantum of ready understanding, that restores itself on each return to the ordinary universe (OU).

To avoid the types of cul-de-sac (cultist act) encountered above, I am taking some pains to ensure a reflective capacity for the interpretive frameworks I develop in this project.  This is a capacity that natural languages always assume for themselves, instituting specialized discourses as developments that take place within their frame and not as constructs that lie beyond their scope.  Any time the levels of recursive discussion become too involved to manage successfully, one needs to keep available the resource of ''instant wisdom'', the modest but indispensable quantum of ready understanding, that restores itself on each return to the ordinary universe (OU).

From this angle of approach, let us try to view afresh the manner of drawing distinctions between various levels of formalization in language.  Once again, I begin in the context of ordinary discussion, and if there is any distinction to be drawn between objective and instrumental languages then it must be possible to describe it within the frame of this informally discursive universe.

From this angle of approach, let us try to view afresh the manner of drawing distinctions between various levels of formalization in language.  Once again, I begin in the context of ordinary discussion, and if there is any distinction to be drawn between objective and instrumental languages then it must be possible to describe it within the frame of this informally discursive universe.

=====1.3.3.6.  A Formal Development=====

=====1.3.3.6.  A Formal Development=====

The point of view I take on the origin and development of formal models is that they arise with agents retracing structures that already exist in the context of informal activity, until gradually the most relevant and frequently reinforced patterns become emphasized and emboldened enough to continue their development as nearly autonomous styles, in brief, as "genres" growing out of a particular "paradigm".

The point of view I take on the origin and development of formal models is that they arise with agents retracing structures that already exist in the context of informal activity, until gradually the most relevant and frequently reinforced patterns become emphasized and emboldened enough to continue their development as nearly autonomous styles, in brief, as ''genres'' growing out of a particular ''paradigm''.

Taking the position that formal models develop within the framework of informal discussion, the questions that become important to ask of a prospective formal model are (1) whether it highlights the structure of its supporting context in a transparent form of emphasis and a relevant reinforcement of salient features, and (2) whether it reveals the active ingredients of its source materials in a critically reflective recapitulation or an analytically representative recipe, or (3) whether it insistently obscures what little fraction of its domain it manages to cover.

Taking the position that formal models develop within the framework of informal discussion, the questions that become important to ask of a prospective formal model are (1) whether it highlights the structure of its supporting context in a transparent form of emphasis and a relevant reinforcement of salient features, and (2) whether it reveals the active ingredients of its source materials in a critically reflective recapitulation or an analytically representative recipe, or (3) whether it insistently obscures what little fraction of its domain it manages to cover.

An interpretive system can be taken up with very little fanfare, since it does not enjoin one to declare undying allegiance to a particular point of view or to assign each piece of text in view to a sovereign territory, but only to entertain different points of view on the use of symbols.  The chief design consideration for an interpretive system is that it must never function as a virus or addiction.  Its suggestions must always be, initially and finally, purely optional adjunctions to whatever interpretive framework was already in place before it installed itself on the scene.  Interpretive systems are not constituted in the faith that anything nameable will always be dependable, nor articulated in fixed principles that determine what must be doubted and what must not, but rest only in a form of self-knowledge that recognizes the doubts and beliefs that one actually has at each given moment.

An interpretive system can be taken up with very little fanfare, since it does not enjoin one to declare undying allegiance to a particular point of view or to assign each piece of text in view to a sovereign territory, but only to entertain different points of view on the use of symbols.  The chief design consideration for an interpretive system is that it must never function as a virus or addiction.  Its suggestions must always be, initially and finally, purely optional adjunctions to whatever interpretive framework was already in place before it installed itself on the scene.  Interpretive systems are not constituted in the faith that anything nameable will always be dependable, nor articulated in fixed principles that determine what must be doubted and what must not, but rest only in a form of self-knowledge that recognizes the doubts and beliefs that one actually has at each given moment.

Before this project is done I will need to have developed an analytic and computational theory of interpreters and interpretive frameworks.  In the aspects of this theory that I can anticipate at this point, an interpreter or interpretive framework is exemplified by a collective activity of symbol-using practices like those that might be found embodied in a person, a community, or a culture.  Each one forms a moderately free and independent perspective, with no objective rankings of supremacy in practice that all interpretive frameworks are likely to support at any foreseeable moment in their fields of view.  Of course, each interpreter initially enters discussion operating as if its own perspective were "meta" in comparison to all the others, but a well-developed interpretive framework is likely to have acquired the notion and taken notice of the fact that this is not likely to be a universally shared opinion (USO).

 

Before this project is done I will need to have developed an analytic and computational theory of interpreters and interpretive frameworks.  In the aspects of this theory that I can anticipate at this point, an interpreter or interpretive framework is exemplified by a collective activity of symbol-using practices like those that might be found embodied in a person, a community, or a culture.  Each one forms a moderately free and independent perspective, with no objective rankings of supremacy in practice that all interpretive frameworks are likely to support at any foreseeable moment in their fields of view.  Of course, each interpreter initially enters discussion operating as if its own perspective were ''meta'' in comparison to all the others, but a well-developed interpretive framework is likely to have acquired the notion and taken notice of the fact that this is not likely to be a universally shared opinion (USO).

====1.3.4.  Discussion of Formalization : Concrete Examples====

====1.3.4.  Discussion of Formalization : Concrete Examples====

The POI's that define the intents and the purposes of this project are the closely related processes of inquiry and interpretation, so the MOI's that must be formulated are models of inquiry and interpretation, species of formal systems that are even more intimately bound up than usual with the IF's employed and the SOI's deployed in their ongoing development as models.

The POI's that define the intents and the purposes of this project are the closely related processes of inquiry and interpretation, so the MOI's that must be formulated are models of inquiry and interpretation, species of formal systems that are even more intimately bound up than usual with the IF's employed and the SOI's deployed in their ongoing development as models.

Since all of the interpretive systems and all of the process models that are being mentioned here come from the same broad family of mathematical objects, the different roles that they play in this investigation are mainly distinguished by variations in their manner and degree of formalization:

Since all of the interpretive systems and all of the process models that are being mentioned here come from the same broad family of mathematical objects, the different roles that they play in this investigation are mainly distinguished by variations in their manner and degree of formalization:

Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their interpretive practice that involves the use of the following nouns and pronouns:  "Ann", "Bob", "I", "you".

Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their interpretive practice that involves the use of the following nouns and pronouns:  "Ann", "Bob", "I", "you".

The "object domain" of this discussion fragment is the set of two people {Ann, Bob}.  The "syntactic domain" or the "sign system" of their discussion is limited to the set of four signs {"Ann", "Bob", "I", "You"}.

The ''object domain'' of this discussion fragment is the set of two people {Ann,&nbsp;Bob}.

In their discussion, Ann and Bob are not only the passive objects of nominative and accusative references but also the active interpreters of the language that they use.  The "system of interpretation" (SOI) associated with each language user can be represented in the form of an individual three-place relation called the "sign relation" of that interpreter.

 

In their discussion, Ann and Bob are not only the passive objects of nominative and accusative references but also the active interpreters of the language that they use.  The "system of interpretation" (SOI) associated with each language user can be represented in the form of an individual three-place relation called the ''[[sign relation]]'' of that interpreter.

 

Understood in terms of its set-theoretic extension, a sign relation ''L'' is a subset of a cartesian product ''O''&times;''S''&times;''I''.  Here, ''O, ''S'', and ''I'' are three sets that are known as the ''object domain'', the ''sign domain'', and the ''interpretant domain'', respectively, of the sign relation ''L''&nbsp;&sube;&nbsp;''O''&times;''S''&times;''I''.  In general, the three domains of a sign relation can be any sets whatsoever, but the kinds of sign relations that are contemplated in a computational framework are usually constrained to having ''I''&nbsp;&sube;&nbsp;''S''.  In this case, interpretants are just a special variety of signs, and this makes it convenient to lump signs and interpretants together into a ''syntactic domain''.  In the forthcoming examples, ''S'' and ''I'' are identical as sets, so the very same elements manifest themselves in two distinct roles of the sign relations in question.  When it is necessary to refer to the whole set of objects and signs in the union of the domains ''O'', ''S'', and ''I'' for a given sign relation ''L'', one may call this the "world of ''L''" and write ''W'' = ''W''(''L'') = ''O''&nbsp;&cup;&nbsp;''S''&nbsp;&cup;&nbsp;''I''.

To facilitate an interest in the abstract structures of sign relations, and to keep the notations as brief as possible when the examples become more complicated, I introduce the following abbreviations:

To facilitate an interest in the abstract structures of sign relations, and to keep the notations as brief as possible when the examples become more complicated, I introduce the following abbreviations:

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In the present examples, S = I = Syntactic Domain.

In the present examples, ''S'' = ''I'' = Syntactic Domain.

Tables 1 and 2 give the sign relations associated with the interpreters A and B, respectively, putting them in the form of relational databases.  Thus, the rows of each Table list the ordered triples of the form ‹o, s, i› that make up the corresponding sign relations:  A, B ?  O?S?I.  The issue of using the same names for objects and for relations involving these objects will be taken up later, after the less problematic features of these relations have been treated.

 

Tables 1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of relational databases.  Thus, the rows of each Table list the ordered triples of the form ‹''o'',&nbsp;''s'',&nbsp;''i''› that make up the corresponding sign relations:  ''A'',&nbsp;''B''&nbsp;&sube;&nbsp;''O''&times;''S''&times;''I''.  The issue of using the same names for objects and for relations involving these objects will be taken up later, after the less problematic features of these relations have been treated.

These Tables codify a rudimentary level of interpretive practice for the agents A and B, and provide a basis for formalizing the initial semantics that is appropriate to their common syntactic domain.  Each row of a Table names an object and two co-referent signs, making up an ordered triple of the form ‹o, s, i› that is called an "elementary relation", that is, one element of the relation's set-theoretic extension.

These Tables codify a rudimentary level of interpretive practice for the agents ''A'' and ''B'', and provide a basis for formalizing the initial semantics that is appropriate to their common syntactic domain.  Each row of a Table names an object and two co-referent signs, making up an ordered triple of the form ‹''o'',&nbsp;''s'',&nbsp;''i''› that is called an ''elementary relation'', that is, one element of the relation's set-theoretic extension.

Already in this elementary context, there are several different meanings that might attach to the project of a "formal semantics".  In the process of discussing these alternatives, I will introduce a few terms that are occasionally used in the philosophy of language to point out the needed distinctions.

Already in this elementary context, there are several different meanings that might attach to the project of a ''formal semantics''.  In the process of discussing these alternatives, I will introduce a few terms that are occasionally used in the philosophy of language to point out the needed distinctions.

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