Skeptics of AmericaÂ’s engagements in Afghanistan and Iraq have frequently drawn comparisons to Vietnam as a reminder of the futility of far-flung military interventions. Rarely do they mention the Philippines, the site of one of our first forays into nation-building. A recent film, however, uses that mostly forgotten war as a backdrop for a meditation on the wisdom of sending Americans abroad in search of monsters to destroy. Written and directed by John Sayles, Amigo, which arrived in a handful of American cities last month, is set in 1900 amid the three-year Philippine-American War. In the spring of 1898, shortly...