This paper investigates the polysemous nature of the English auxiliary should and argues that its core function is to show the discrepancy between the speaker's observation of a fact and his/her expectation. The literature on this issue has traditionally supposed a dichotomy in auxiliaries, i.e., the root and the epistemic use, and has argued that should expresses the speaker's strong feelings, as in "the emotive should" (cf. Aijmer 1972). However, this line of thought falls short in that few studies have treated the phenomena holistically. In addition, being an auxiliary, should might naturally express the subject's feelings, however no satisfactory analysis has explained why should is apt to express the speaker's "strong" feelings. We will see that the core meaning of should is to show that the speaker's observation is inconsistent with his or her expectation, and hence, should expresses a strong desire and functions as a suggestion.