Wolfgang Schwarz

Lewis 1969 on the probability of conditionals

I finally got around to adding the papers from Janssen-Lauret and Macbride 2023 to the search corpus at https://www.david-lewis.org. It's a wonderful collection with lots of treasures. I want to comment on an intriguing passage on pp.71f., from an abandoned 1969 textbook project on confirmation theory.

First, some context. At this point in the manuscript, Lewis has introduced \(\mathcal{M}\) as a probability measure on the propositions expressible in a language \(\mathcal{L}\) with classical boolean connectives; \(\mathcal{C}\) is the associated conditional probability measure, defined by the ratio formula. Lewis notes that conditional probabilities are often read as "the probability of C if A", which suggests that \(\mathcal{C}(C/A)\) might equal \(\mathcal{M}(C\textit{ if }A)\), where '\(C\textit{ if }A\)' is the material conditional. But that's obviously false. Lewis continues:

Time travel and sortal-relative predication

Here's an attractive picture. All there really is, at a fundamental level, are fields in spacetime (or something like that). The world as we know it, with its rocks and chairs and cats and people, somehow emerges from this basis: all truths about rocks and chairs etc. are made true by truths about fields in spacetime. But how? To explain this, it would help if we could locate the familiar objects – rocks and chairs etc. – in the physical description of reality. With the help of classical mereology, which is plausibly analytic, this seems possible: ordinary objects can be identified with aggregates of spacetime points. They are regions in spacetime. With this, we can explain how simple facts involving ordinary objects can emerge. For example, what makes it true that my chair has steel legs is that its region has a certain kind of subregion with high-amplitude excitations of quark and electron fields in a certain arrangement.