Able to be recognized as different or separate from something else; capable of being noticed or told apart.
From distinguish (from Latin distinguere, 'to separate') plus -able suffix meaning 'capable of.' The word evolved to describe anything that can be perceived as distinct or different.
This word reveals how language itself distinguishes—the suffix -able transforms any verb into a possibility, showing how English builds meaning like LEGO blocks. Interestingly, 'distinguishable' is one of the few words where we're literally describing our ability to use distinction itself.
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