Changes

In practice, this question has little consequence for the present study, on account of the extremely simple and artificial kinds of languages that are needed to carry out its aims.  If some reason develops to emulate the properties of interesting natural languages in this microcosm, then a decision about which strategy to use can be made at that time.  For now it seems worthwhile to keep exploring all of the above options.

In practice, this question has little consequence for the present study, on account of the extremely simple and artificial kinds of languages that are needed to carry out its aims.  If some reason develops to emulate the properties of interesting natural languages in this microcosm, then a decision about which strategy to use can be made at that time.  For now it seems worthwhile to keep exploring all of the above options.

In a formal language context one begins with the imposition of general inhibition against the notion that a specific class of signs has any meaning at all, or at least, that its elements have the meanings one is accustomed to think they do.  It is significant that one does not proscribe all signs from having meaning, or else there is no point in having a discussion, and no point from which to carry on a discussion of anything at all.  Therefore, the arena of formal discussion is a limited one and, except for the occasional resonance that its action induces in the surrounding discursive universe, most of the signs outside its bounds continue to be used in the habitual ways.

In a FL context one begins with the imposition of general inhibition against the notion that a specific class of signs has any meaning at all, or at least, that its elements have the meanings one is accustomed to think they do.  It is significant that one does not proscribe all signs from having meaning, or else there is no point in having a discussion, and no point from which to carry on a discussion of anything at all.  Therefore, the arena of formal discussion is a limited one and, except for the occasional resonance that its action induces in the surrounding discursive universe, most of the signs outside its bounds continue to be used in the habitual ways.

What can be done with the signs in question?  Apparently, signs viewed as objects in the formal arena, temporarily cut off from their usual associations, treated as terminal values in themselves, and put under review to suggest explanations for themselves, can still be discussed.  Doing this involves the use of other signs for denoting the signs in question.  These extra signs, whose sense and use are not in question at the moment in question, are called into play as "higher order" (HO) signs, and it is their very meaningfulness and effectiveness that one must rely on to carry out the investigation of the "lower order" (LO) signs that are in question.

What can be done with the signs in question?  Apparently, signs viewed as objects in the formal arena, temporarily cut off from their usual associations, treated as terminal values in themselves, and put under review to suggest explanations for themselves, can still be discussed.  Doing this involves the use of other signs for denoting the signs in question.  These extra signs, whose sense and use are not in question at the moment in question, are called into play as ''higher order signs'', and it is their very meaningfulness and effectiveness that one must rely on to carry out the investigation of the ''lower order signs'' that are in question.

An apt and proper discussion of a set of signs in question requires the ability to classify the tokens of these signs according to their types.  Doing this calls on the use of other HO signs to denote these "tokens", the transient instances of signs, and their "types", the propertied classes of tokens that correspond to what is typically valued as a sign.  The invocation of HO signs can be iterated in a succession of HOs that extends as far as one pleases, but no matter how much of this order is progressively formalized one eventually must resort to signs of such a high order that they are taken for granted as resting, for the moment, in an informal context of interpretation.

Detailed discussion of a set of signs in question requires the ability to classify the tokens of these signs according to their types.  Doing this calls on the use of other higher order signs to denote these ''tokens'', the transient instances of signs, and their ''types'', the propertied classes of tokens that correspond to what is typically valued as a sign.  The invocation of higher order signs can be iterated in a succession of higher orders that extends as far as one pleases, but no matter how much of this order is progressively formalized one eventually must resort to signs of such a high order that they are taken for granted as resting, for the moment, in an informal context of interpretation.

What is the sense and use of such a proceeding?  Evidently, the signs in question, as a class, must present the inquirer with phenomena that are somehow simpler than, and yet convey instructive information about, the phenomenon known as the "whole objective world" (WOW).  If their orders of complexity and perplexity are just as great as the world at large, then their investigation affords no advantage over the general empirical problem of trying to account for the WOW.  If they enjoy no informative connection with the greater wonders of why the world is the way it is, and therefore fail to present a significant representation of the original question, then their isolated inquiry can serve no larger purpose in the world.

What is the sense and use of such a proceeding?  Evidently, the signs in question, as a class, must present the inquirer with phenomena that are somehow simpler than, and yet convey instructive information about, the phenomenon known as the ''whole objective world'' (WOW).  If their orders of complexity and perplexity are just as great as the world at large, then their investigation affords no advantage over the general empirical problem of trying to account for the WOW.  If they enjoy no informative connection with the greater wonders of why the world is the way it is, and therefore fail to present a significant representation of the original question, then their isolated inquiry can serve no larger purpose in the world.

In situations like the one just described, where functions and relations on one order of arguments are clarified, defined, or explained in terms of functions and relations on another order of arguments, it is natural to understand the effort at clarification, definition, or explanation as a recursive process.  What raises the potential for confusion in the given arrangement of formal and casual contexts is the circumstance that what seems natural to call the LO arguments are being discussed in terms of what seems natural to call the HO arguments.  What is going on here?  As it happens, the ordering of signs from LO to HO that seems obvious from the standpoint of their typical construction and their order of appearance on the stage of discussion does not reflect the measure of complexity that is relevant to the effort at recursive exposition.

In situations like the one just described, where functions and relations on one order of arguments are clarified, defined, or explained in terms of functions and relations on another order of arguments, it is natural to understand the effort at clarification, definition, or explanation as a recursive process.  What raises the potential for confusion in the given arrangement of formal and casual contexts is the circumstance that what seems natural to call the lower order arguments are being discussed in terms of what seems natural to call the higher order arguments.  What is going on here?  As it happens, the ordering of signs from lower order to higher order that seems obvious from the standpoint of their typical construction and their order of appearance on the stage of discussion does not reflect the measure of complexity that is relevant to the effort at recursive exposition.

The measure of complexity that is relevant to the formal exposition is the measure of doubt, uncertainty, or perplexity that one entertains about the sense and use of a sign beset by questions, whether this occurs by force of a voluntary effort to bracket its habitual senses or by dint of a puzzling event that brings its automatic uses to a halt.

The measure of complexity that is relevant to the formal exposition is the measure of doubt, uncertainty, or perplexity that one entertains about the sense and use of a sign beset by questions, whether this occurs by force of a voluntary effort to bracket its habitual senses or by dint of a puzzling event that brings its automatic uses to a halt.

It is the language being discussed that is the formal one, to be treated initially as an object, while the language that is used to carry out the discussion tries to maintain its informal viability, expecting in effect to be taken on faith as not undermining or vitiating the effort at inquiry due to unexamined flaws of its own.  Nevertheless, if inquiry in general is expected to be self correcting, then a continuing series of failures to conclude inquiries by means of a given arrangement, that is, an inability to resolve uncertainties through a particular division of labor between FL and IL contexts, must lead to the grounds of attack being shifted.

It is the language being discussed that is the formal one, to be treated initially as an object, while the language that is used to carry out the discussion tries to maintain its informal viability, expecting in effect to be taken on faith as not undermining or vitiating the effort at inquiry due to unexamined flaws of its own.  Nevertheless, if inquiry in general is expected to be self correcting, then a continuing series of failures to conclude inquiries by means of a given arrangement, that is, an inability to resolve uncertainties through a particular division of labor between FL and IL contexts, must lead to the grounds of attack being shifted.