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I am interested in how little attention is paid to the limitations of the language when it is used to make statements that are supposedly logical. The consequences of this are particularly evident in mathematics, where there are theories that are based on the philosophy that numbers and other mathematical concepts are ‘actual’ things that exist independently of any physical reality. Such beliefs are commonly held on an almost subliminal level; most people have never taken the time to carefully examine the basis and the consequences of such beliefs. It is because of such beliefs that detailed considerations of language are ignored - the ‘actual’ non-physical reality is considered all-important - with the result that a detailed evaluation of the possibility of errors due to limitations of language is generally considered unnecessary.
Every statement has to be stated in some language. If assumptions are made that ignore some aspects of the language of the statement, then how can we be sure that the statement is entirely logical? In particular, when a statement refers in some way, either implicitly or explicitly, to some language, whether it is the language of the statement itself or some other language, there is a significant possibility of confusion.
Unless every aspect of such statements is very carefully analyzed, a statement that superficially appears to be logical may actually contain subtle errors of logic. In my work, I show how such errors can occur and how we can avoid such errors by careful analysis of language.