## 4. 4 Reviewing Paradoxes

Probably all paradoxes (if there is no problem with the axiom) are born
from the form f(f). This is a special case like putting speakers and mikes
too close to eachother. The noise of the frequency can be cut with a circuit.
That is similar to the exclusion of the excluded middle in the previous
section 2. If we exclude the inference such as A and not A imp False, we
can probably avoid the paradoxes. That can be done easily by later adjusting
the program of the inference rule called LOGIC. However, there can be other
cases of noise made by something other than hauling, in those cases, bad
effects will come out as a result of the expandable area becoming narrow.
As a result of mathematics putting too much attention on the special phenomenons
like hauling, it will be getting things backwards to see the decline in
its expression ability. Of course, with the actual theorem that wasted
the exclusion middle (like the intuition theory) to see how far the various
theorems structurize is interesting and important.