Discussions about reductionism are often assumed to be primarily of interest to philosophers. Often, however, the question of whether multi-scale systems can be understood “bottom-up” has important practical implications for scientific inquiry. Cancer research, I argue, is one such example. While the focus on genetic factors has intensified with recent investments in cancer genomics, the importance of biomechanical factors within the tumor microenvironment is increasingly acknowledged. I suggest that role of solid-state tissue properties in tumor progression can be interpreted as a form of downward causation, understood as constraining relations between tissue-scale variables and micro-scale behaviors. Experimental demonstrations of these sort of influences reveal limitations of reductionist accounts and expose the dangers of what Wimsatt calls functional localization fallacies. These relate to the common bias of downgrading factors that – as a practical necessity – are left out of scientific analysis. Any heuristic, experimental or theoretical, involves foregrounding some aspects while ignoring others. In cancer research, different strategies produce different partial perspectives. These perspectives are not reducible to one another, but neither do they seem to make up a neatly integrated “causal mosaic” of different influences. At present, the picture looks more like a fragmented cubist painting in need of a more balanced attention to difference-making factors at different levels or scales.