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 vari ...Show more