This particular idea seems straightforward, at least in non-technical sense: "infinity" should only appear from "traces" of finite dynamical processes, as a way of talking about their dynamics. Infinite objects are artifacts of objectifying time, and any infinite object can as well be regarded as a statement about a finite dynamical system. I liked this remark as a self-contained way of thinking about infinity (on informal level, apart from the specific axiomatizations).
(For example: think of the process of normalization as the dynamic on a term not in a normal form; whether it'll terminate is undecidable, and a priori the normal form can't be considered as another term (finitely encoded), yet we may reason about this output as another term, considering how it'll reduce in interactions with other terms, etc.)
Is there a way of describing it that doesn't require a computer science background? What are "traces" in this context? And what is a "finite dynamical process" that introduces infinities, and what is the "objectifying"? I can tell this is grammatical English, but the terminology is opaque.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).