> it implies checking is only possible with a complete specification of the program No, it doesn't. If exploratory testing has any value at all, that implies

> it implies checking is only possible with a complete specification of the program No, it doesn't. If exploratory testing has any value at all, that implies that there cannot be complete test coverage with checks, thus there cannot be checks matching a complete specification. > incomplete specifications, both positive and negative There's more to testing than positive and negative test cases. > execute far more test cases than any manual exploration ever could Exploratory testing does not "execute test cases," so you have a tautology here. > testing is about sheer volume of tests The purpose of testing is open to wildly contradictory opinions. I usually claim that it's to find user-impacting bugs before users do. Maybe that can happen with lots of checks and maybe those can be automated. Maybe you're dealing with a system with lots of hidden interdependencies and some "I'm not gonna touch that" dev code and even if you want to check everything you just can't. Maybe the user experience matters more and that goes far beyond positive/negative test cases. There's no simple one-size-fits-all solution.