A mental event is a particular occurrence of something going on in the mind.
For example, if Mary is walking through a park and she sees City Hall, that instance of seeing City Hall is an instance of perception—something that is supposed to be going on in Mary's mind. That instance of seeing is a mental event. It is an event because it is something that happens, and it is mental because it happens in someone's mind. If Mary thinks to herself, "I am a human being," that thought is a mental event; if she feels happy after doing well on an exam, that is a mental event. And so on.
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