I don’t understand logic in proofs

Question

I just had a general question about proofs. For “If A, then B” statements, we prove them by assuming the if statement is true and then find a way to get the consequent to be true. But for example the statement, “if 1=2, then 1+1=4” here the hypothesis is false, but assuming it to be true, we can prove that 1+1 does equal 4. From a logic standpoint, F—>T is True. But taking a step back from logic, proving that statement above to be true just seems ridiculous since 1+1 doesnt equal 4.

Answer 1

The statement : "If A , then B" does not tell anything about the case "not A". This is often formulated as "We can derive everything from a false statement" Of course, we can derive also every false statement, but this is no contradiction to the If-statement.

Answer 2

It’s not generally about understanding the logic in a proof, but the idea in a proof. I can’t count the number of times I’ve run through a proof line by line, yet still failed to understand the proof.

It shows that there is more to a proof than it’s logic. In the same way a house is more than just the bricks that go up to make it.

This does not mean you can forgo rigour, but the right attitude is to find the right level of rigour, and that will depend on your own background.