The phrase "intellectual rigor" means being thorough and diligent in your thinking and analysis. It involves being disciplined in questioning and examining ideas or information critically. Full definition
Her arguments speak for themselves, and her utter lack of intellectual rigor. (judithcurry.com)
You do not need to approach them with intellectual rigor, they can simple be. (artprojects.com)
The problem is that, for intellectual rigor, this tradition requires a critique of the dominant formulation of evolutionary theory. (religion-online.org)