Conciliatory reasoning, self-defeat, and abstract argumentation

in Review of Symbolic Logic (2021), First View

According to conciliatory views on the significance of disagreement, it’s rational for you to become less confident in your take on an issue in case your epistemic peer’s take on it is different. These ... [more ▼]

According to conciliatory views on the significance of disagreement, it’s rational for you to become less confident in your take on an issue in case your epistemic peer’s take on it is different. These views are intuitively appealing, but they also face a powerful objection: in scenarios that involve disagreements over their own correctness, conciliatory views appear to self-defeat and, thereby, issue inconsistent recommendations. This paper provides a response to this objection. Drawing on the work from defeasible logics paradigm and abstract argumentation, it develops a formal model of conciliatory reasoning and explores its behavior in the troubling scenarios. The model suggests that the recommendations that conciliatory views issue in such scenarios are perfectly reasonable---even if outwardly they may look odd. [less ▲]

Mechanizing Principia Logico-Metaphysica in Functional Type Theory

in Review of Symbolic Logic (2019)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical ... [more ▼]

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory (inspired by ideas of Ernst Mally, formalized by Zalta) that distinguishes between ordinary and abstract objects. This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics. Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. [less ▲]

Reactive Preferential Structures and Nonmonotonic consequence

in Review of Symbolic Logic (2009), 2(2), 414450

We introduce Information Bearing Relation Systems (IBRS) a s an abstraction of many logical systems. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very ... [more ▼]

We introduce Information Bearing Relation Systems (IBRS) a s an abstraction of many logical systems. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can ”break” the strong coher ence properties of preferential structures by higher arrows, i.e. arrows, which do not go to points, but t o arrows themselves [less ▲]

Cumulativity without closure of the domain under finite unions

in Review of Symbolic Logic (2008), 1(03), 267304

For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.