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.