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One of the main impulses for the development of theories of objects were the problems that arose in connection with intentionality. Mally's teacher Meinong followed Brentano in concluding that the distinctive and defining feature of intentional mental acts is that they are always directed towards something. That is, thinking, believing, intending, etc., all involved thinking, believing, or intending something. Meinong took this a step further by believing that we have to be ontologically generous when analyzing intentional mental acts: every such act is directed towards an object, even if sometimes that object does not or cannot exist. So, when we search for the fountain of youth or think about the round square (and conclude that the latter is impossible), Meinong required that there be such objects like the fountain of youth and the round square. According to Meinong, the former is an object (the waters of which confer everlasting life but) which doesn't exist, while the latter is an object which is round, square, and which couldn't exist.
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