'versus' in this context simply mean ' in contrast to ' or 'as opposed to ' , as in ' he was able to think about which one is better rationally or irrationally'. Hope it helps:) That sentence didn't really make sense so I just interpreted it to what I thought it meant ^.^

In English versus means a contest or a conflict of one thing against another. In this context it is saying rationality as opposed to irrationality. Versus is commonly used in sporting contests, where one team is playing against another. For example, Detroit versus Chicago. It is usually written like this: Detroit vs. Chicago. Hope this helps.