Invariably, I am rejoined with: "But we know 2+2=4! That is irrefutable and unassailable, and requires no assumptions."

This disturbed me, because it seemed to violate my previously stated ideology, so I thought deeply on it, and I came to the conclusion that mathematical statements like that are actually tautologies -- that four is

*defined*as the sum of two and two, and that the idea of four -- the actual, abstract idea, consists in and of itself of a sum of two and two.

Further, in another thread (one about perpetual motion), a cracked pot declared that "anything is possible if you believe that it is", to which (I believe it was iNow) replied "Unfortunately, there is no way to find a rational square root of two, no matter if you believe contrariwise".

Extending the conceptual basis I just introduced, this additional mathematical "truth" can just as well be reduced to tautology, however complex, in that the square root of two is just the number which, multiplied by itself results in two, which hearkens back to the statement 2+2=4. But

*that*the square root of two squared equals two is not being questioned here, rather its identity as rational. However, rationality is again

*defined*to be the quality of ability of representation by the quotient of two integers.

In conclusion, it seems to me that the whole body of math does not include any actual knowledge, just an infrastructure of definition based entirely on the abstract idea of quantity.