Over the last four decades, (physical) cosmologists have developed startlingly precise ways of measuring our universe. This period has also seen the rise and widespread acceptance of a "standard model" of cosmology, which describes the large-scale structure and history of the universe since the big bang. According to this model, space is, and always has been, infinite. In this talk I will discuss the sense in which we (could) have evidence that space is infinite. After clarifying what we mean by "space" in the context of general relativity, I will emphasize the role that certain widely accepted assumptions play in the argument that space is infinite. I will then argue that rejecting these assumptions would amount to rejecting a certain conception of what it means to do "scientific" cosmology. The upshot will be that there is a deep relationship between cosmologists' understanding of the universe and background commitments to a particular philosophy of science.