The theories and theorems that are involved in quantifying language fail to provide us a limitless and potentially useable formula for quantification regardless of their complexity and their rationale supporting it.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 a 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 generalization 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.
Commonsense Reasoning in and over Natural Language