Do the Amish allow swimming

Yes, they do swim. I am not Amish, but know an Amish family in Penn. who have a pond on their farm with a dock and diving board that they swim in in the summertime.

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I am currently staying at a Comfort Inn in Goshen, IN (near Shipshewana). Just saw an Amish family swimming in the hotel's pool. They wore regular bathing suits, although the colors were black and subdued.