Proving a positive requires nothing more than an example.
> Blue cars exist.
> *Oh really? Prove it.*
> Look to your left.
> *Oh.*
On the other hand, proving a negative requires you to demonstrate the impossibility of the corresponding positive. Proving negatives is generally only possible in conceptual contexts such as mathematics, strictly controlled systems or limited size data sets.
The most famous example of the unprovable negative is “God doesn’t exist”. Anyone can just define the nature of God around your argument.
A provable negative would be something like “It didn’t rain in Washington this week” because you are limiting your dataset to a manageable size.
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