For a long time I have found some of the pronouncements of modern mathematics difficult to believe, and I believe that I am not alone in this. For that reason I decided to study and analyse these pronouncements in real depth – and found them wanting in many respects, relying on intuition rather than logic, and often contradictory.
Where modern mathematics appears to trip over itself is when there are different levels of languages involved. Mathematicians appear to have a blind spot in such cases - little attention is paid to what constraints there might be on such statements that are consequent on the language used to express the statement. But every logical statement has to be stated in some language. In many cases, assumptions are made that ignore the need for a full consideration of all aspects of the language of the statement. In particular, some statements refer either implicitly or explicitly to either another language, or the language of the statement itself.
In such cases, unless every aspect of the statement is very carefully analyzed, a statement that superficially appears to be logical may actually contain subtle errors of logic. My work explains how and where such errors occur.