Being right

After almost 400 years it turned out that Fermat’s last theorem was correct. However, the proof discovered by Andrew Wiles is a highly complex piece of modern mathematics, and almost certainly not what Fermat had in mind.

Did Fermat have another proof? Perhaps. But close to 400 years of searching hasn’t revealed any hints of it, and at this point it seems highly likely that Fermat was mistaken in his reasoning, but happened to be accidentally correct in his conclusion.

This leaves us with the question whether Fermat was was right or wrong. Are you still right when your conclusion is correct, but the reasoning that led you to arrive at the conclusion is flawed, or – even worse – you had simply guessed the correct conclusion?

I don’t think you are. Not outside of pub quizzes, anyway (everything is fair if free beer is at stake). Conclusions can be useful on their own in some – usually simple – cases, like which direction is the quickest. In almost all more complex arguments the reasoning is just as important, if not more important.

If I come to the conclusion that global warming is real because there isn’t enough classroom prayer then my conclusion is correct, but any attempts at actually solving this problem will be a waste of time and effort, as my reasoning is completely wrong. Just having the correct conclusion is often useless.

There are many examples where people might have a correct conclusion, but completely counter-productive reasoning:

Declassification of the Venona project in 1995 revealed that USSR spies had infiltrated the U.S. and U.K. governments, leading some to the conclusion that Joseph McCarthy’s frantic anti-Communist witch hunts were justified.
McCarthy had no knowledge of actual USSR spies, and there is zero overlap between actual spies identified by the Venona project and people identified by McCarthy.
Alex Jones’ famous THEY’RE TURNING THE FROGS GAY fragment is correct in its conclusion as chemicals are causing sexual changes in frogs and other animals. ^{(ref: 1,
2,
3)} Jones completely misidentifies the reason for this as ‘social engineering’ rather than urban and industrial waste (which is why he is crazy).
(…and many more; I’ll add examples as I find them…)