Able to be clearly shown, proved, or made evident through examples or evidence.
From demonstrate (Latin demonstrare) + -able (capable of being). The root monstrare means 'to show,' so demonstrable literally means 'capable of being shown thoroughly.'
The word literally means 'showable'—from Latin monstrare (to show)—so when scientists talk about demonstrable facts, they're using a word that's 2,000 years old, proving that the idea of 'show me your work' is ancient.
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