Indefinite Extensibility in Natural Language

Abstract

The Monist's call for papers for this issue ended: "if formalism is true, then it must be possible in principle to mechanize meaning in a conscious thinking and language-using machine; if intentionalism is true, no such project is intelligible". We use the GrellingNelson paradox to show that natural language is indefinitely extensible, which has two important consequences: it cannot be formalized and model theoretic semantics, standard for formal languages, is not suitable for it. We also point out that object-object mapping theories of semantics, the usual account for the possibility of non intentional semantics, doesn't seem able to account for the indefinitely extensible productivity of natural language. Keywords: natural language; formalization; indefinite extensibility; universe of discourse; semantics. Introduction.There exist at least three published papers (Cook 2007(Cook , 2009Schlenker 2010), arguing that natural language is indefinitely extensible in some sense. More concretely, all the three papers start from the Liar paradox and by means of Strengthened and Strengthened Strengthened Liars construct a hierarchy of truth values with as many of them as there are ordinal numbers. Both authors renounce the principle of Bivalence in order to solve the Liar and its revenge forms.Bivalence is, however, a fundamental law of classical logic with a considerable intuitive appeal; it is the logical counterpart of the ontological principle that any well-defined situation either obtains or does not obtain. As we see it, trading such a fundamental principle for a solution of the Liar is no bargain. The price could be too high for many people. So, we offer a path to the indefinite extensibility of natural language that is compatible with all principles commonly held as laws of logic. Instead of the Liar, we will use the Grelling-Nelson paradox.We will first address the issue of formalizability, just to show that natural language is not formalizable. Then we will interpret the result in terms of indefinite extensibility as defined in due time. Vagueness.Some readers may contemplate natural language as trivially non formalizable because of its inherent vagueness. We do not wish to go into the discussion whether vagueness can be formalized or not. We just wish to show that, leaving vagueness aside, natural language turns out to be non formalizable on quite another account, namely, indefinite extensibility.So we ask the reader to assume we are dealing with a definite segment of Englishwhich we will call -English-so that all metalinguistic predicates here used are definite and that the corresponding sets, when they exist, are ordinary nonfuzzy sets. The reader may well not believe such a crisp core of English to exist but this should not prevent him from following us: we only purport to show that on the assumption that -English exists we can all the same prove that it cannot be formalized; this will reveal at least that

Identifying Authorship from Linguistic Text Patterns

“…Natural language is indefinitely extensible [11] [12][41] [33], so it can be continually extended, and changed, existing in a state of impermanence. No true form of permanent modeling for language studies can ever really exist [33].…”

“…Natural language is indefinitely extensible [11] [12][41] [33], so it can be continually extended, and changed, existing in a state of impermanence. No true form of permanent modeling for language studies can ever really exist [33]. A similar concept, relative indefinite extensibility, can be explained through several examples (e.g., [33]), including, most notably, the fact that there is no complete, written set of all possible existing numbers (due to the infinite number of possible and valid combinations).…”

“…No true form of permanent modeling for language studies can ever really exist [33]. A similar concept, relative indefinite extensibility, can be explained through several examples (e.g., [33]), including, most notably, the fact that there is no complete, written set of all possible existing numbers (due to the infinite number of possible and valid combinations). Therefore, any information system artifact that attempts to model language must also be indefinitely extensible.…”