In this chapter we summarize our main conclusions: that Leibniz treated the infinite and infinitely small as fictions beginning with his work on infinite series in Paris in the mid-1670s, and not as a result of later criticisms; that this did not in itself commit him to the existence of such fictions, and instead relied only on the Principle of Unassignable Difference; that he justified this principle in the DQA by arguments he continued to value, and which formed the basis of his later strategies for justifying the use of infinitesimals and infinities; that he applied himself to the question of the existence of infinitesimals after devising the differential algorithm, and decided it in the negative; that the notion of comparability underlying his “lemmas on incomparables” is a relational notion, and that taking incomparables as actual elements in the continuum is incompatible with Leibniz’s definitions of quantity and number; that Leibniz provided three different strategies for defending his calculus from criticism in the early 1700s, one depending on the Lemmas on Incomparables supported by a reductio argument, a second strategy appealing to the Law of Continuity that is assumed in the ordinary algebraic calculus; and a third that shows that even in these cases where one appeals to the fiction of infinitely small quantities, one can give a justification where these infinitely small quantities are understood syncategorematically: that is as standing for quantities that may be made as small as is needed for the error to be proven null.