Changes

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.

Depending on one's school of thought, the syntactic bit of computation for interesting cases of natural languages is thought to be either (1) formally independent of all the more properly semantic features, or (2) heavily reliant on the construal of further bits of meaning to make its decision.  Accordingly, the semantics proper for such a language ought to begin either (1) serially after or (2) concurrently while the syntactic bit is done.  The first standpoint is usually described as a "declaration of syntactic independence", while the second opinion is often called a "semantic bootstrapping hypothesis".

Depending on one's school of thought, the syntactic bit of computation for interesting cases of natural languages is thought to be either (1) formally independent of all the more properly semantic features, or (2) heavily reliant on the construal of further bits of meaning to make its decision.  Accordingly, the semantics proper for such a language ought to begin either (1) serially after or (2) concurrently while the syntactic bit is done.  The first standpoint is usually described as a “declaration of syntactic independence”, while the second opinion is often called a “semantic bootstrapping hypothesis”.

Over and above both of these positions the pragmatic theory of signs poses a stronger thesis of irreducibility or non independence that one might call a "pragmatic bootstrapping hypothesis".  Even though it is a more complex task initially to work with triadic relations themselves instead of their dyadic projections, this hypothesis suggests that the structural integrity of interesting natural languages, when taken over the long haul, may well depend on them.  One part of this thesis is not a hypothesis but a fact.  There do indeed exist triadic relations that cannot be reconstructed uniquely from their dyadic projections, and thus are called "irreducibly triadic" (IT).  The parts of the thesis that are hypothetical, and that need to be cleared up by empirical inquiry, suggest that many of the most important sign relations are IT, and that interesting cases of natural languages depend heavily on these kinds of sign relations for their salient properties, for example, their relevance and adaptability to the objective world, their structural integrity and internal coherence, and their learnability by human agents and other species of finitely informed creatures.

Over and above both of these positions the pragmatic theory of signs poses a stronger thesis of irreducibility or non-independence that one might call a “pragmatic bootstrapping hypothesis”.  Even though it is a more complex task initially to work with triadic relations themselves instead of their dyadic projections, this hypothesis suggests that the structural integrity of interesting natural languages, when taken over the long haul, may well depend on them.  One part of this thesis is not a hypothesis but a fact.  There do indeed exist triadic relations that cannot be reconstructed uniquely from their dyadic projections, and thus are called ''irreducibly triadic''.  The parts of the thesis that are hypothetical, and that need to be cleared up by empirical inquiry, suggest that many of the most important sign relations are irreducibly triadic, and that interesting cases of natural languages depend heavily on these kinds of sign relations for their salient properties, for example, their relevance and adaptability to the objective world, their structural integrity and internal coherence, and their learnability by human agents and other species of finitely informed creatures.

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 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.

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.