Any social cost of carbon (SCC) calculated from an integrated assessment model of global climate-economy interactions will always be disputed. This is because a key model input-namely the valuation of centennial climate damage-is highly unknowable for fundamental reasons discussed here. Problems with damage valuation are highlighted by the implicit implausibility to climate scientists of a leading model's (centennial) damage function, and by strong criticisms of damage functions by many climate economists. The claim that statistical analyses of past weather impacts on local economies, combined with structural modeling of sectoral impacts, can significantly improve centennial damage valuation rests on untestable, far-out-of-sample extrapolation. Testing centennial climate (natural) science projections is generally harder than testing predictions in astronomy, geology and other earth sciences, because of Earth's uniqueness, and the unprecedented degree of likely climate change; but stable underlying laws make climate modeling based on past observations meaningful. By contrast, the added complexity of human behavior means there are no quantitatively stable laws for modeling the value of centennial climate damage. I suggest that any carbon prices used to inform climate policies, be they carbon prices used as policy instruments, or complementary, non-carbon-price policies, should instead be based on marginal abatement costs, found by modeling low-cost pathways to socially agreed, physical climate targets. A pathway approach to estimating carbon prices poses challenges to many economists, and is no panacea, but it avoids any illusion of optimality, and facilitates detailed analysis of sectoral policies. This article is categorized under: Climate Economics > Aggregation Techniques for Impacts and Mitigation Costs Assessing Impacts of Climate Change > Evaluating Future Impacts of Climate Change