Integrated assessment models (IAMs) play a major role in the science and policy of climate change. Similarly to other widely used computational tools for addressing socially relevant problems, IAMs need to account for the key uncertainties characterizing processes and socio-economic responses. In the case of climate change, these are particularly complex given the very long-term nature of climate and the deep uncertainty characterizing technological and human systems. Here we draw from philosophical discussion of mathematical modeling of social problems and review the role of uncertainty in climate-economic modeling. In agreement with the literature, we highlight the crucial role of epistemic uncertainty in IAMs. We posit that the normative components of models, more than the physical and socio-techno-economic ones, are the most fraught by uncertainty and yet the least understood. We suggest a research agenda to explore uncertainties of evaluation frameworks, transcending the current implicit normativity of IAMs.