Probability without a Process: Three Foundational Concerns about "Sets and Probability"

Horsten and Brickhill (2024) propose two methods for constructing non-Archimedean probability functions on the set-theoretic universe V: the finite snapshot approach and the bootstrapping approach. The mathematical execution is competent and the results within their framework are correct. This note raises three foundational concerns that the paper does not adequately address. First, the proposed sample space — the entire set-theoretic universe V — lacks the probabilistic motivation that real-valued sample spaces possess; the authors' analogical defense ("if random graphs are meaningful, why not random sets?") does not answer the structural objection. Second, the constructions depend on existence assumptions that exceed ZFC, most importantly the existence of strongly inaccessible cardinals; this dependence is acknowledged in a single sentence and not treated as the substantive foundational commitment that it is. Third, the bootstrapping approach in Section 4 is presented as conceptually superior to the finite snapshot method but generates no independent results, and is shown by the authors themselves (Propositions 8 and 9) to be incompatible with rather than complementary to the snapshot method. The combined effect is that "probability on V" is not a unified mathematical object but a family of mutually incompatible technical constructions whose philosophical motivation remains underdetermined.