alt Hacker NewsIn a constructive system, it’s often possible to refute a universal proposition without exhibiting a counterexample, by proving that the proposition implies falsehood.
The constructivist will still object that you can’t, from that, conclude that “…therefore a counterexample must exist,” without actually providing a counterexample. But the general principle I was describing still applies - a proof often gives you insight that an example by itself doesn’t.
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I think the constructive position is basically that people's entire issue with lack of excluded middle being absent is just that people like being able to say "P" instead of "~~P" because it sounds better, considering you can prove ~~P for all the classical propositions that use excluded middle.
To roughly repeat myself from a sibling comment: I may have been unclear. I didn't claim that the only way to disprove something in a constructive system is to produce a counterexample.
The part that I was referring to was the last statement from the OP: that "a proof of existence of a counterexample necessarily provides more insight than a counterexample". I can't imagine a constructivist would agree with that in general.