In this letter to Campbell, Lewis discusses the relationship between tropes and theories of space and time in the philosophy of physics.
What is a Trope?
Tropes are properties or relations which are not universal, but particular. For instance, the blackness of this cat, the height of this person, or the distance between these points. Campbell calls them ‘abstract particulars’. Lewis, unlike Campbell, was neutral between tropes and universals. He thought either option was compatible with his overall system.
Lewis vs. Campbell on Tropes, Space, and Time
Lewis responds to an objection Campbell had raised about space-time. Campbell has a worry about individuation conditions: where does one trope start and another end? Lewis answers by appealing to point-sized tropes which have space-time points as their locations. Point-sized things do not have start and end points. He compares this view to Russell’s.
Campbell holds the opposite view: he thinks each trope does not begin and end not because it is point-sized, but because it is universe-sized. He identifies that fields in physics with large tropes, because they are particulars, but also abstract.
Lewis replies that he does not object to Campbell’s trope-theoretic conception of fields. But he does not think that fields are identical with tropes, but rather wholes composed of them. In that case, it would be mysterious how they could differ from each other in spacetime. Lewis thinks that would mean that they would have to have different parts. But large abstract particulars do not have such parts in space and time. So Lewis prefers to think of a field as composed of point-sized tropes which are its parts.
Keith Campbell, Abstract Particulars. Oxford: Blackwell, 1990.