Infinite is an undirect way to speak of the finite; more precisely infinity is about finite dynamical processes.
I second RobinZ's request for an elaboration. I know a little (a very little) about the technical topics of that paper, but I find Girard's philosophising here and elsewhere (for example) impenetrable.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).