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Andrews, Scotland, UK. Both work within the linguis- tic approach called Axiomatic Functionalism henceforth AF.

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Hervey, Michael A. Hervey for the beginnings of AF see Mulder Martinet had a great impact on Mulder, so that AF is often regarded as a formalized branch of Martinetian functionalism cf. Akamatsu , but there are many considerable differences and dis- agreements between these two functional linguistic schools. On the other hand, they are closely related as to the basic tenets, the most important of which is the principle of func- tional relevance. This society is also connected to the renewed Prague Linguistic Circle, as can be witnessed from a joint colloquium held in Prague in In spite of being treated here as a linguistic approach, AF is in fact better described as a paradigm in semiotics cf.

Hervey First of all, it is not a purely linguistic approach, but a semiotic one. It is not limited to treatment of natural languages only but is, at least in principle, designed to account for different semiotic systems.

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On the other hand, AF is mostly focused on core-linguistic theory and description and so will it be presented here except for one illustrating semiotic example. Another person to have had a great impact on AF was the philosopher Karl Popper. As such, AF explicitly rejects all forms of speculativism, opera- tionalism and inductivism in linguistics.

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In AF the hypothetico-deductivism of Popper is enriched by a distinction between theories and descriptions. Such a distinction is not usu- ally recognized in natural sciences, because there is usually one world to describe but in linguistics this is a necessary dichotomy, as there are hundreds of different worlds, i. Now, under the hypothetico- deductivism of AF, it is theories which should be deductive, but not hypothetical, while it is in descriptions where we launch hypotheses that as Popper says should be in principle refutable.

The core of the theory of AF is formed by six axioms therefore axiomatic functional- ism which are basic—arbitrary but appropriate—propositions the whole theory rests on. They are given below taken from Mulder As AF is a semiotic approach, the termi- nology in the axioms is generally semiotic, though in natural languages terms like cenotac- tic, cenological, cenetic, plerological could be replaced by phonotactic, phonological, phonetic and grammatical, respectively. Axiom A: All features in semiotic sets are functional.

This axiom sets the scope of the theory: it deals with only those features that are rele- vant to the purport of semiotic systems, which is communication. This axiom establishes two basic systems, phonology and grammar, for dealing, re- spectively, with figurae semiotic entities which have only form and signa semiotic entities with both form and information-value. Also, it sets an important dichotomy: ordering vs. Semiotic entities may be either ordered e. Axiom C: Cenological entities may have para-cenotactic features and plerological entities may have para-syntactic features.

Roughly speaking, this is an axiom of suprasegmental or prosodic or para-tactic fea- tures.

In AF this includes accent, juncture, tones para-phonotactic features and in- tonation para-syntactic features. Axiom D: All semiotic systems contain sentences, constituted by a base and para- syntactic features. This axiom sets the sentential level as a level distinct from the syntactic one. Axiom E: There may be a many-to-one relation between cenetic form and figura al- lophony , and between cenological form and signum allomorphy , and vice versa homophony and homonymy respectively.

This could be called an axiom of realization: it states that both figurae and signa may have formal variants allophones and allomorphs respectively and that there may be formal coincidence between variants of different figurae i. Axiom F: Signa may be realized an unlimited number of times in actual communica- tion , each resulting utterance denoting a denotatum which may belong to a poten- tially infinite denotation class. The axiom introduces semantics dealing with the denotational aspect of signa. Let it be noted that AF explicitly operates with denotation rather than connotation of signa, through the treatment of the latter was suggested by Hervey Hervey , see also Dickins ff.

The axioms are interpreted by a network of accompanying definitions. It is no coincidence that I have described the axioms as basic propositions that are arbi- trary but appropriate. The basic meta-theoretical assumptions of glossemat- ics are in many respects relevant to AF.

Both the glossematicians and axiomatic functional- ists hold that a linguistic theory should be arbitrary, which means it could be different if necessary, but it must be appropriate to its purpose. The third common feature to mention is the denial of any existential postulate for the lin- guistic theory, a point discussed in detail in Ontological Questions in Linguistics.

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The mentioned book deals with problems connected with the nature of linguistic objects. Mulder and Rastall argue for a reduced ontological commitment in linguistics. It is a view strongly opposed to many prevailing contemporary ones. One of the ontological questions that is discussed in the book is the ontological status of speech events and their connection or correspondence to reality.

The aim of a linguistic theory, by establishment of certain entities and their classes, is to provide adequate tools for allow- ing us to account for speech events, but the theory cannot make any claim about the outer existence of the entities it has established. It operates with constructs only! For instance, a linguistic theory can set up the notion phoneme. We cannot even claim it is once and for all the pho- neme of Czech, because once again the interpretation of the Czech phonological system is dependent on the governing theory.

This may strike as strange to many linguists at the first sight. See Figure 1.

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There is therefore no a priori linguistic reality of the speech event [let] that is to be discovered by a linguist. Its interpretation is wholly dependent on the theory through which it is created. Something similar is true for a color picture: a person who is color-blind will perceive and describe it differently than the one without the defect of seeing.

Let me also quote de Saussure , going back to the beginning of 20th century : Let us remember in fact that the object in linguistics does not exist to start with, is not predeter- mined in its own right. Hence to speak of an object, to name an object, is nothing more than to invoke a particular point of view, A. It is merely a way by which, in phonetics, we account for specific speech phenomena by means of a phonetic theory.

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It is a common mistake to assume that sounds are the real things, real events, and phonemes are certain abstract and generalized models of the sounds. Even the sounds are abstract and generalized models, because actual pronuncia- tions at any given time and space are directly inaccessible. They are immediately gone and can never be repeated; they exist only in passing.

Before moving to the discussion of signum-theory in AF, I will sketch the overall struc- ture of the theory of AF and of another of its components: systemology. The theory of AF—by which I mean the tool for description of languages—has three basic components or sub-theories: systemology, semantics, and signum-theory. Mulder 70 likens it to a stool with three legs where the seat of the stool can be seen as be- ing the all-pervading point of view of the theory, the functional principle.

The most impor- tant leg of the theory is nevertheless the signum-theory because it sets the ontological na- ture of linguistic objects. Systemology then deals with internal deployment of linguistic objects, that is, the ways they are used in the system, covering mainly classical phonology and grammar. Seman- tics—which is an autonomous sub-theory of AF, not an extension of grammar—deals with external deployment of linguistic object, that is, with regard to the purpose of denoting things.

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In mathematical logic , a formal theory is a set of sentences expressed in a formal language. A formal system also called a logical calculus , or a logical system consists of a formal language together with a deductive apparatus also called a deductive system. The deductive apparatus may consist of a set of transformation rules , which may be interpreted as valid rules of inference, or a set of axioms , or have both.

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A formal system is used to derive one expression from one or more other expressions. Although a formal language can be identified with its formulas, a formal system cannot be likewise identified by its theorems. A formal proof or derivation is a finite sequence of well-formed formulas which may be interpreted as sentences, or propositions each of which is an axiom or follows from the preceding formulas in the sequence by a rule of inference.

The last sentence in the sequence is a theorem of a formal system.