>>38
In the first place, most mathematicians would say that the interesting or professional part of mathematics is not about 2 x 2 = 4, because 2 x 2 = 4 is a finite and small problem, and so the answer (and the consistency of mathematics at this level) can be ascertained by inspection. As we read in Recursive Aspects of Descriptive Set Theory, by Dick Mansfield and Galen Weitkamp, p. v, "The primary concern of mathematics has been to use the infinite to elucidate this world. ... The primary concern of mathematical logic[20] has been to explore the nature of infinity in order to classify and explain its mathematical applications." So, to elaborate, most mathematicians trust that the consistency of finite structures is ascertainable by inspection. Only infinite structures are problematic: the history of explicit controversy in mathematics is largely a history of notions of the infinitely large and infinitely small. Thus, 2 x 2 = 4 would become problematic only if there were a change in the whole of arithmetic, which is an endless or infinitary structure, such that a dispute about the infinitude of arithmetic reacted back on 2 x 2 = 4.