'Existential Import' is a term so frequently bandied around (e.g. here and here) that it is worth explaining its correct meaning, and historical context. I have a complete discussion of it here, but it broadly amounts to this: In traditional logic, the sentence or categorial proposition consists of three parts: the predicate which is 'affirmed' or 'denied', the subject of the affirmation or denial, and the copula which signifies whether the predicate is affirmed or denied. The copula was thought to be signified by the verb 'is', (Latin: est). For example, in the proposition 'man is mortal', the verb 'is' signifies that the predicate 'mortal' is affirmed of the subject 'man'. Thus Mill writes
- Every proposition consists of three parts: the Subject, the Predicate, and the Copula. The predicate is the name [sic] denoting that which is affirmed or denied. The subject is the name denoting the person or thing which something is affirmed or denied of. The copula is the sign denoting that there an affirmation or denial (Mill, System of Logic).
What is now called a general existential proposition, such as 'some men are mortal' was then called a 'particular' proposition. It was not called 'existential', because it was not thought to be existential. A proposition of the form 'A exists' combines the subject 'A' with the verb 'exists'. Since (according to the traditional theory) every proposition consists of subject, predicate and copula, it follows that 'exists' must be a grammatical abbrevation of copula and predicate, and that it really stands for 'is existent' or something similar. If so, it is not the copula 'is' that signifies existence, but the adjective 'existent'.
The question of 'existential import' was traditionally whether a 'particular' proposition such as 'some mountains are golden' implies the corresponding 'existential' proposition 'golden mountains exist'. Mill argued that it does not.
- That the employment of [the word 'is'] as a copula does not necessarily include the affirmation of existence, appears from such a proposition as this: A centaur is a fiction of the poets; where it cannot be possibly implied that a centaur exists, since the proposition itself expressly asserts that the thing has no real existence. (System of Logic I.iv.1)
Note that this section is called 'Of the Import of Propositions', from which, perhaps, the term 'existential import' derives. There is another discussion of the question in Joyce's manual of traditional logic here.
Note also that the distinction between particular (Some A is B) and existential (Some A-B exists) also corresponds to the distinction made by Alexius Meinong in Chapter III of his master work 'On Assumptions', between being so or 'Sosein', and being or 'Sein'. This is not to be confused with his distinction between 'subsistence' and 'existence'.