Literally,
rigor means
stiffness. This is the
sense in which it is used in the
phrase "
rigor mortis".
Rigor also refers to formalism in logic or argument. A rigorous argument is one whose terms and steps are well-defined. It may or may not be valid and/or sound. However, if an argument is not rigorous, there is a good chance it is nonsense or at least no more than rhetoric.