The phrase "substantial disagreement" means a strong or significant difference of opinion or disagreement about something important or meaningful. Full definition
We found two substantial disagreements between the proxy - based and the thermometer - based estimates. (globalwarmingsolved.com)
«There's substantial disagreement on possible future yields of energy crops,» he said, as well as questions on the consequences of growing biofuels on water supply. (scientificamerican.com)
There is substantial disagreement in the terms used to distinguish the different Christian traditions. (religion-online.org)