The paradoxes

Conclusion The paradoxes act as restraints on undisciplined or erroneous reasoning and so perform a valuable role. The fact that they have resisted solution for so long suggests that the current systems of logic are defective. The paradoxes of set theory, in my opinion, completely condemn all the current forms of set theory and their associated definitions of the natural numbers. Nothing short of a complete review of the whole area seems capable of remedying the situation.