From postclassical Latin inclūsīvus (= the participial stem of inclūdĕre "to include" plus an adjectival ending). (Oxford English Dictionary)
In the sense of inclusive disjunction, as standardly understood nowadays, the earliest attestation I have found is surprising late: Quine (1940):
We must decide whether 'or' is to be construed in an exclusive sense, corresponding to the Latin 'aut', or in an inclusive sense, corresponding to the Latin 'vel'.... When 'or' is used in the inclusive sense,... the compound is regarded as true if at least one of the components is true; joint truth of the components verifies the compound. (p. 12)
However, at least some earlier logicians had used the term inclusive disjunction in a different sense — namely, for a disjunction of predicates in which all the disjuncts are understood as subcategories of the subject, as in Angles are acute, right, or obtuse. Here is Baldwin (1908):
The third case is that called inclusive disjunction, in which the members of a class are assigned to one or other of certain sub-classes or terms,... for example "coins are either gold, or silver, or copper." (p. 51)
What we would now call inclusive disjunction, Baldwin instead called "indefinite" disjunction:
[T]he meaning of the disjunctive judgment...is not always exclusive, but may be indefinite as to inclusion. For example, when I say, "The apple or the orange fell off the table," I do not mean to assert that they did not both fall off. In this case, to be called indefinite disjunction, the range of indeterminateness is wider. The whole meaning is not so shut in by a circle of belief, nor narrowed down to so contracted a content. I may not have the subject-matter so fixed that it is a question of one of the alternatives only, in my growing experience. On the contrary, it may be a meaning of a more indefinite character to which the alternation gives a tentative filling. By the sentence given above I may mean, ''something fell off the table — apple, orange, or what ? ” The result may show that both things fell, and possibly more. (pp. 50–51)
In the sense of inclusive first-person pronouns, inclusive appears to have been introduced in Humboldt (1828):
Several American languages have two plural forms in the first person, an exclusive and an inclusive form, according as we would include or exclude the person addressed. It has been thought that this peculiarity belonged exclusively to the American languages; but it is also found in the Mantchu, the Tamul, and in all the dialects of the South Sea Islands. All these languages have indeed this grammatical form in common; but it is only in the abstract. Each of them expresses it by a different sound: the identity of this form, therefore, does not furnish any proof of the affinity of these languages. (p. 7)
- Baldwin, James Mark (1908) Thought and Things: A Study of the Development and Meaning of Thought, or Genetic Logic, vol. II: Experimental Logic, or Genetic Theory of Thought. Swan Sonnenschein & Co.
- von Humboldt, Wilhem (1828) An Essay on the Best Means of Ascertaining the Affinities of Oriental Languages. J.L. Cox.
- Quine, Willard Van Orman (1940) Mathematical Logic. W.W. Norton & Co.