Arthur's recent article
Arthur, Richard T. W. Leibniz's actual infinite in relation to his analysis of matter. G. W. Leibniz, interrelations between mathematics and philosophy, 137–156, Archimedes, 41, Springer, Dordrecht, 2015
was recently reviewed by Knobloch, who wrote in part:
Despite his rejection of an infinite number and infinite collections, he admitted an actual, but syncategorematic, infinite. There is an infinity of things; that is, there are always more of them than can be specified. Secondly, Arthur refutes Rescher's two-tiered ontology and Russell's pseudo-dilemma. One has to distinguish between division and resolution, between composable, resolvable, and divisible. Arthur essentially bases his deductions on Leibniz's correspondence with Arnauld and de Volder. A body is actually divided into parts by its different motions, but resolved into unities. There are actually infinitely many monads. This infinite is understood syncategorematically. "There are actually infinite aggregates but—in contrast to Cantor—there are no infinite numbers" (p. 155).
This seems surprising to me since Leibniz on many occasions spoke precisely of infinite numbers (while rejecting infinite collections). Have Arthur and Knobloch gotten it right?
They don't fully address the distiction between infinite multitudes/wholes/collections, on the one hand, and infinite numbers, on the other. I haven't seen anything in Leibniz that would suggest that he thought that infinite numbers led to contradiction, and on the contrary Leibniz often exploits them as "useful fictions".
In a recent article in HOPOS: History of Philosophy of Science we defend the thesis that Leibniz used infinite numbers galore. We also argue against the so-called syncategorematic interpretation first developed by Ishiguro allegedly following Russell (according to which Leibniz did nothing of the sort). See here.