Imagine building a bridge without a specification. It would be criminally irresponsible. It has been known for decades now that proper specification is absolutely necessary to produce correct software. This is practically a tautology, because there isn't a formally meaningful way to define "correct" besides "satisfies some specified behaviors." Good unit testing does this in an ad hoc way, because the tests serve as a (usually incomplete) specification of the desired behavior. That said we must remember that testing can never prove the absence of bugs, only their presence. The only practicable ways to prove the absence of bugs in nontrivial programs are automatic formal verification or constructive proof using formally defined semantics.

Of course for most commercial software correctness is so irrelevant that it's left undefined. All that matters is pleasantness, that is to say does it generally please the user, perhaps by attracting customers or investors.