arXiv subjects

Yale Weiss

Publications and source records attributed to Yale Weiss.

3 recordsLinked to original sources

arXiv2026

Stalnaker's logical problem of conditionals is unsolvable

The logical problem of conditionals, as conceived by Stalnaker, amounts to axiomatizing a particular semantics for conditionals which utilizes selection functions that take propositions (i.e., sets of worlds) as arguments. While the sentential form of this semantics is recursively axiomatizable, we prove that its enrichment with first-order quantifiers is not---that is, we show that Stalnaker's logical problem of conditionals is unsolvable in the language with first-order quantifiers. We demonstrate this by showing how to interpret arithmetic in the logic. In the conclusion, we discuss the implications of this result for the study of conditional logic.

math.LO↗

arXiv2026

Post Completeness in Conditional Logic

A logic is Post complete if it is consistent but has no consistent proper extensions. In this article, we systematically investigate the Post complete extensions of certain basic conditional logics. We identify all of the finitely many regular and normal Post complete conditional logics, and prove analogues of Makinson's embedding theorems. We also show that certain basic conditional logics have uncountably many Post complete extensions for which closure under some, but not necessarily all, rules peculiar to the conditional are relaxed. We reflect on what our results tell us about the structure of certain lattices of conditional logics and also draw some morals for multimodal logic.

math.LO↗

arXiv2026

Incompleteness in Quantified Conditional Logic

Stalnaker and Thomason famously proved that the conditional logic \textsf{C2} with first-order quantifiers is complete with respect to a selection function semantics. However, the selection functions used in this completeness result take formulas, rather than propositions (i.e., sets of worlds), as arguments. Yet Stalnaker has repeatedly emphasized the philosophical importance of viewing selection functions as functions on propositions, and many of the applications of his theory require this. Can their completeness result be extended to a selection function semantics in which the functions take propositions as arguments? We prove the answer is negative: Their logic is frame incomplete. Moreover, this result is invariant with respect to many choice points regarding the semantics, such as variable vs.~constant domains or whether to include an identity or existence predicate. We conclude by discussing some of the important and difficult questions for the philosophical and logical study of conditionals that our results raise.

math.LO↗