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Is the study of philosophy (particularly Greek philosophy including physics and metaphysics) forbidden, permitted, encouraged, or discouraged? Specifically what are the views of Geonim and Rishonim on this? (Based on direct evidence of their own writings; not based on secondary or tertiary sources.)

One possibly related source is the Gemara Menahot 99b, in which Ben Dama asks R. Yishmael if he may study hokhma yevanit; a possible reference to Greek philosophy, and R. Yishamel forbids this.

Do different subsets of philosophy have different statuses?

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