There are two ways that we might respond to the underdetermination of theory by data. One response, which we can call the agnostic response, is to suspend judgment: “Where scientific standards cannot guide us, we should believe nothing”. Another response, which we can call the fideist response, is to believe whatever we would like to believe: “If science cannot speak to the question, then we may believe anything without science ever contradicting us”. C.S. Peirce recognized these options and suggested evading the dilemma. It is a Logical Maxim, he suggests, that there could be no genuine underdetermination. This is no longer a viable option in the wake of developments in modern physics, so we must face the dilemma head on. The agnostic and fideist responses to underdetermination represent fundamentally different epistemic viewpoints. Nevertheless, the choice between them is not an unresolvable struggle between incommensurable worldviews. There are legitimate considerations tugging in each direction. Given the balance of these considerations, there should be a modest presumption of agnosticism. This may conflict with Peirce's Logical Maxim, but it preserves all that we can preserve of the Peircean motivation.