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Persuade or convince?
Persuade: verb - using a person as the object – be successful in urging someone to do, or not to do, something; lure, attract, or entice to something or in a specific direction; lead, cause, or make to believe a statement, doctrine, or the truth of it; try to lead to do, urge or advise strongly: using an idea as the object - recommend the acceptance of a statement or opinion; inculcate, advocate or recommend an action; prove, demonstrate; talk earnestly with someone to gain agreement or compliance; expostulate with, plead with.
Convince: verb - master in argument, confute; persuade someone to believe firmly in the truth of something; satisfy by evidence or argument; persuade someone to do something; bring someone to awareness of their sins or error; prove; expose the true character; disprove or refute some idea or doctrine.
Another example of the subtlety of the English language, and an illustration of why it is easier to say something precisely in this widely understood tongue.
In general terms, you motivate someone using persuasion, but you change their minds by convincing them.
'In spite of her natural modesty and a certain prudery, inherited through her father's career as a minister, Prudence was persuaded by Gerald to indulge in moonlight skinny-dipping, and discovered the joy and freedom of swimming without the encumbrance of a costume.'
'You'll never convince any man of reason that the myths of religion are anything more than stories unless you're able to provide some hard evidence that they're more than the words of mere men.'