Seeking ever better valuations of the centurial impacts of global environmental change (GEC) can sometimes amount to denying inherent limits to the knowability of such impacts, thus misallocating scarce scientific resources needed for finding better ways to slow such change. The limits to knowability, compared here for large, future changes in global climate and biodiversity, stem from the Earth's uniqueness, and the persistence and irreversibility of much GEC, which together make timely hypothesis testing impossible. Special attention is given to climate damage functions that global climate-economy models need to complete a cost-benefit analysis and thus derive a social cost of carbon as a carbon price to inform climate policies. The high unknowability of damage functions has led to much guesswork, albeit sometimes veiled by probabilistic methodologies. The "new climate-economy literature" is improving damage functions by analysing past weather events, but underlying high unknowability will still limit progress. This, and similar limits to valuing biodiversity, suggest putting more effort into cost-effectiveness analyses of policies to achieve biophysical GEC targets chosen on precautionary grounds. Applied to climate policy, this yields carbon prices without using damage functions; and moreover can highlight gaps between national policies and global aspirations, the costs of nations not participating, and the needs to improve technology and infrastructure policies and to avoid perverse incentives to increase emissions. Choosing appropriate discount rates will remain problematic, though, as GEC policies inevitably require ethical choices under irreducible uncertainty.