Wednesday, 6 July 2011

A need for another class of nouns?

In linguistics, I've seen only one reference to this phenomenon (a passing remark, actually) that I want to talk about, and try and shed some light on because I think it goes into the heart of logical and linguistic anomalies found in metaphysics, set theory and other (in)famous paradoxes.


In talking about the weather we often use the word "it" as in, "it is sunny outside" - the passing remark in linguistics - without really referring to something particular. The explanation I read  somewhere was unmemorable because I thought it wrong-headed and circular. But having come across the same problem in set theory - a highly abstract branch of mathematics having to do with arithmetic of the infinite - and the "barber of seville" paradox that Bertrand Russell found in its axioms, and in various metaphysical problems and infinite regress constructs, I think the problem has mostly to do with linguistics - at least in the technical sense.


In the human language, we may treat a verb as a noun and vice versa without missing our stride. In fact, the Inuit Language structure builds this capacity right into the grammar where the intervening morphemes may change the stem from verbal to nominal and vice versa. But an apparently "deep" problem arises when the grammatical elements become metaphysical problems, or more precisely are treated as such.


For eg, the word "truth" is treated as a noun when in fact it really is a state of being and the word "truth" is really just a grammatical function and not something with a unique status as a nominal being like the other "real" nouns in which it is classified. It really is a linguistic "function" required by the grammar much like the famous ƒ(x) of calculus.


Seen in this way, the problem of infinite regression in the statement: "everything that exists has a location... the location has a location, has a location..." ad infinitum... can be resolved by stating that the location of that which exists is a function of that which exists, ƒ(x). The barber of seville problem can likewise be resolved by stating that the barber who shaves only the men who do not shave themselves has a unique status of being a function, ƒ(x) (or more precisely, S(x)) that defines a set and is not a member of the set by virtue of its function. The set of all (possible) sets then has a value of infinity itself - which closes the function (or arithmetic) in set theory rather neatly.


The problem of clearly demarcating classification rules that determine a lexeme class (or set) is a profound one in mathematics, linguistics and metaphysics because it affects or facilitates a precise formulation of problems of substance in these fields of study. But I think some of these problems can be resolved by cross-disciplinary collaboration where insights from one can be used to resolve problems in another.


Jay

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