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Potential Possibilities and the Limitations Involved in Formal Theories of Quantification for Natural Language - Essay Example

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Potential Possibilities and the Limitations Involved in Formal Theories of Quantification for Natural Language

Jon Barwise and John Etchemendy in Language Proof and Logic give a very understandable argument as to the reasons for quantifiers and the reasons they are not always accurate in their use. A very pertinent consideration for their argument starts out their ninth chapter in Language Proof and Logic by saying, "In English and other natural languages, basic sentences are made by combining noun phrases and verb phrases." (1. Chapter 9 page 227, Language Proof and Logic.) The consideration continues further in that Barwise and Etchemendy contend that, "Quantification takes us out of the realm of truth-functional connectives." (2. Chapter 9 page 227, Language Proof and Logic.) This gives us reason for the consideration that quantifiers are not always the most useful method for determining natural language tendencies. Quantifiers, according to Barwise and Etchemendy, have a tendency to dull the truthfulness of sentences giving them a generalisation that may not bear an ounce of truth within them.
In the case of first-order logic, the process assumes that there would be an infinite list of variables so there would be no possible way to run out of these variables, regardless of a sentence's complexity. Theorists like Fitch would understand all of these separate variables involved, of which there are many, but others like Tarski's World would not, in that Tarski's World uses six in place of infinite variables as Fitch would manage. This would in fact present a rather expressive limitation in Tarski's World of language use. Expanding the set of terms of language usually means adding variables to it. At this point, only individual consonants, also known as names would be considered the sole amount of basic terms. Obviously, first-order logic, in the eyes of Barwise and Etchemendy believe a complex series of quantifiers is necessary to describe natural language. They consider universal and existential quantifiers in their equations. Universal quantifiers are those that are all encompassing and ultimately considered unconditional. Existential quantifiers are more limiting in scope in giving a value but not a limitless value toward the quantification.

W. Tecumseh Fitch, from the University of St. Andrew's School of Psychology wrote a treatise titled The Evolution of Language: A Comparative Review. Fitch says in his work that the study of language evolution is often considered little more than speculative story-telling. Fitch further states that this has actually had little to do with the development of many fields which would touch upon it. Those fields include linguistics, evolutionary biology and neuroscience. Over the last fifteen years increasingly productive study of language evolution has occurred in various different quarters and there is far more collaboration and exchange in relation to this increasing study. There in fact would be three key innovations which should be explained in language evolution. The first critical step would be to distinguish among the various component abilities in languages. Mechanisms that are both ...Show more
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Summary

There are many potential possibilities and also equally as many limitations involved in the creation and execution of formal theories in the quantification of natural language. There would also be a great many who would willingly discuss the consideration of quantifiers and their positive and negative potential in the creation of formal theories of quantification in the world of natural language…
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