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Synonyms for Wonder (same or very similar meaning)

WordNet sense 1 (the feeling aroused by something strange and surprising):
admiration, wonderment

WordNet sense 2 (something that causes feelings of wonder):

WordNet sense 3 (a state in which you want to learn more about something):

WordNet sense 4 (place in doubt or express doubtful speculation):

WordNet sense 5 (have a wish or desire to know something):
enquire, inquire

From the ODE community, based on WordNetadd/edit