You know, many textbooks on mathematical logic look more like textbooks on scholasticism and metaphysics. On one hand, they promise to show you the strictest foundation of thought — and on the other, they tell you: "Well, but if things get even slightly more complex than arithmetic, contradictions arise, proofs become impossible, incompleteness shows up, here are your paradoxes." If a system is just a bit more complex than arithmetic, it's already somehow defective — and to explain all of this, you need an even more complex system, which is itself, naturally, also "defective," incomplete, contradictory… In the end, any ordinary student drowns in all this like in some set of riddles the human mind is simply not equipped to solve.
So what comes next? Essentially nothing — you're calmly taught logic, told to use it, everything is fine, it shows things clearly and precisely, the most complex algorithms work, calculations come out right. So what was the point of that digression in the course about contradictions and paradoxes? In this article, I try to briefly and precisely explain to the student — at a basic level — and resolve these non-constructive pseudo-problems.
This applies not only to students. Specialists who were put through this scholastic mis-education in their university years would also do well to spend 10–15 minutes to quickly and simply sort this out — and regain confidence in their own logic. After all, you've noticed throughout your life that logic is sound and works just fine, haven't you?
https://zenodo.org/records/19220604