Changes

===6.12. Issue 1. The Status of Signs===

===6.12. Issue 1. The Status of Signs===

This Section considers an issue that affects the status of signs and their mode of significance, as it appears under each of the three norms of significance.  The concerns that arise with respect to this issue can be divided into two sets of questions.  The first type of question has to do with the default assumptions that are made about the meanings of signs and the strategies that are used to deal with signs that fail to have meanings.  The second type of question has to do with higher order signs, or signs that involve signs among their objects.

This section considers an issue that affects the status of signs and their mode of significance, as it appears under each of the three NOSs.  The concerns that arise with respect to this issue can be divided into two sets of questions.  The first type of question has to do with the default assumptions that are made about the meanings of signs and the strategies that are used to deal with signs that fail to have meanings.  The second type of question has to do with higher order signs, or signs that involve signs among their objects.

Only certain types of signs are able to make their appearance in a given medium or a particular style of text, while many others are not.  But a sign is a sign by virtue of the fact that it is interpreted as a sign, and thus plays the role of a sign in a sign relation, and not of necessity because it has any special construction other than that of being construed as a sign.

Only certain types of signs are able to make their appearance in a given medium or a particular style of text, while many others are not.  But a sign is a sign by virtue of the fact that it is interpreted as a sign, and thus plays the role of a sign in a sign relation, and not of necessity because it has any special construction other than that of being construed as a sign.

The theory of formal languages, as pursued under the FL perspective, is closely related to the theory of semigroups, as pursued under the IL perspective, in the sense that arbitrary formal languages can be studied as subsets of the semigroups that embody the primitive concatenation of linguistic symbols within their algebraic laws of composition.  Thus, in staging any discussion of formal languages, the theory of semigroups is often taken for a neutral, indifferent, or undifferentiated background, but the wisdom of using this setting is contingent on understanding the distinct outlooks of the casual and formal NOSs.  What divides the two styles and their favorite subjects in practice is a certain difference in attitude toward the status and role of their subject materials.  Namely, it turns on the question of whether their primitive and derived elements are valued as terminal objects in and of themselves or whether these syntactic objects and constructions are interpreted as mere signs and sundry expressions whose true value lies elsewhere.

The theory of formal languages, as pursued under the formal language perspective, is closely related to the theory of semigroups, as pursued under the IL perspective, in the sense that arbitrary formal languages can be studied as subsets of the semigroups that embody the primitive concatenation of linguistic symbols within their algebraic laws of composition.  Thus, in staging any discussion of formal languages, the theory of semigroups is often taken for a neutral, indifferent, or undifferentiated background, but the wisdom of using this setting is contingent on understanding the distinct outlooks of the casual and formal norms of significance.  What divides the two styles and their favorite subjects in practice is a certain difference in attitude toward the status and role of their subject materials.  Namely, it turns on the question of whether their primitive and derived elements are valued as terminal objects in and of themselves or whether these syntactic objects and constructions are interpreted as mere signs and sundry expressions whose true value lies elsewhere.

In taking up the IL attitude toward any mathematical system, semigroups in particular, one assumes that signs are available for denoting a class of formal objects, but the issue of how these notational matters come to be constellated is considered to be peripheral, lacking in a substantive weight of concern and enjoying a purely marginal interest.

In taking up the informal language attitude toward any mathematical system, semigroups in particular, one assumes that signs are available for denoting a class of formal objects, but the issue of how these notational matters come to be constellated is considered to be peripheral, lacking in a substantive weight of concern and enjoying a purely marginal interest.

In the discussion of formal languages the presumption of significance is shifted in the opposite direction.  Signs are presumed to be innocent of meaning until it can be demonstrated otherwise.  One begins with a set of primitive objects, formally called "signs", but treated as meaningless tokens or as objects that are bare of all extraneous semantic trappings.  From these simplest signs, a law of composition allows the construction of complex expressions in regular ways, but other than that anything goes, at least, at first.

In the discussion of formal languages the presumption of significance is shifted in the opposite direction.  Signs are presumed to be innocent of meaning until it can be demonstrated otherwise.  One begins with a set of primitive objects, formally called “signs”, but treated as meaningless tokens or as objects that are bare of all extraneous semantic trappings.  From these simplest signs, a law of composition allows the construction of complex expressions in regular ways, but other than that anything goes, at least, at first.

A first cut taken in the space of expressions divides them into two classes:  (a) the "grammatical", "well formed" or "meaningful, maybe", versus (b) the "ungrammatical", "ill formed" or "meaningless, for sure".  This first bit of semantic information is usually regarded as marking a purely syntactic distinction.  Typically one seeks a recursive function that computes this bit of meaningfulness as a property of its argument and thereby decides (or semi decides) whether an arbitrary expression ("string", "strand", "sequence") constitutes an expressive expression ("word", "sentence", "message"), or not.  The means of computation is often presented in the form of various "grammars" or "automata" that can serve as "acceptors or "generators" for the language.

A first cut taken in the space of expressions divides them into two classes:  (a) the "grammatical", "well formed" or "meaningful, maybe", versus (b) the "ungrammatical", "ill formed" or "meaningless, for sure".  This first bit of semantic information is usually regarded as marking a purely syntactic distinction.  Typically one seeks a recursive function that computes this bit of meaningfulness as a property of its argument and thereby decides (or semi decides) whether an arbitrary expression ("string", "strand", "sequence") constitutes an expressive expression ("word", "sentence", "message"), or not.  The means of computation is often presented in the form of various "grammars" or "automata" that can serve as "acceptors or "generators" for the language.