If climate-carbon feedbacks are positive, then warming causes changes in carbon dioxide (CO2) sources and sinks that increase CO2 concentrations and create further warming. Previous work using paleoclimatic reconstructions has not disentangled the causal effect of interest from the effects of reverse causality and autocorrelation. The response of CO2 to variations in orbital forcing over the past 800,000 years suggests that millennial-scale climate-carbon feedbacks are significantly positive and significantly greater than century-scale feedbacks. Feedbacks are also significantly greater on 100 year timescales than on 50 year timescales over the past 1,500 years. Posterior probability distributions implied by coupled models' predictions and by these paleoclimatic results give a mean of 0.03 for the non-dimensional climate-carbon feedback factor and a 90% chance of its being between -0.04 and 0.09. The 70% chance that climate-carbon feedbacks are positive implies that temperature change projections tend to underestimate an emission path's consequences if they do not allow the carbon cycle to respond to changing temperatures.