Given the subjective nature of the statement I do not find it particularly disturbing to consider it may not be objectively true. Additionally, I disagree with the implication that because a conclusion is not reached through logic it is not objectively true. For one, there may still exist a logical argument whether I have made that argument or not. For another there is no guarantee that logic leads always to truth or that truth can only be found with logic. (Although I do find those two ideas rather disturbing...)