To evoke, educe (emotions, feelings, responses, etc.); to generate, obtain, or provoke as a response or answer. (verb)
To draw out, bring out, bring forth (something latent); to obtain information from someone or something. (verb)
To use logic to arrive at truth; to derive by reason; deduce; construe. (verb)
Examples of word elicit
Of course, this answer is the one I suspect that Dawkins wishes to elicit from the reader of "Meet my cousin, the chimpanzee".
A similar problem unfolds in stanza five as the speaker seeks to elicit from the urn a transcendental message both aesthetic and ontological that will bring the poem to thematic and formal closure and that will confirm the urn's (and the poem's) status as a revelatory Romantic symbol.
The first step, however, was to elicit from the Germans a concrete statement of aims.
Meanwhile Dr Malan made an attempt to elicit from the Germans a more definite indication of their intentions towards South Africa.
And this is pretty much the standard crest-and-trough reaction I elicit from the Chinese.