Could evoke possibly mean just 'to register something in your mind (for the first time)' and not 'to summon up what has registered in your memory'? I just couldn't make sense out of this explanation below if it only meant the latter. Or, I say it should include both calling up memories, or better yet bringing up what has registered in your mind to a conscious level, and registering new information to make this sentence coherent.
(1) a. In her talk, Baldwin introduced the notion that syntactic structure is derivable from pragmatic principles.
A Heim-style approach to definiteness, where use of a definite noun phrase is felicitous just in case its referent has been previously evoked (...), provides neither necessary nor sufficient conditions for the felicitous use of the definite article.
For instance, in the example given above in (1a), the notion that syntactic structure is derivable from pragmatic principles is felicitous even when the claim in question represents brand-new information (...). Crucially, however, it also represents information that is uniquely identifiable, in that there is exactly one notion that is denoted by the noun phrase. Thus, the noun phrase itself uniquely specifies the claim in question. (Uniqueness, Familiarity, and the Definite Article in English by Betty Birner and Gregory Ward)
The thing is you don't have to have previously evoked something to say 'the something' the second time or later. Granted unless you are aware of it at the time of citing it, or so the speaker thinks, he/she cannot use 'the.' But it doesn't have to be 'summoned up' before it is mentioned with 'the.' Someone just says it and it stays in your conscious mind, and the speaker refers to it with 'the.' This is not evoking it, isn't it?