Capable of being convinced; able to be persuaded with evidence or argument.
From convince plus the suffix -ible (able to be), following the Latin pattern of formability. This suffix comes from Latin -ibilis.
The -ible suffix is actually rarer in modern English than -able, but both mean 'capable of being'—the difference is mostly historical and etymological rather than meaningful. Words ending in -ible tend to be older or more formal.
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