Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

ABSTRACT In ‘Properties, Propositions, and Conditionals’ Field [2021] advances further on our understanding of the logic and meaning of naive theories – theories that maintain, in the face of paradox, basic assumptions about properties and propositions. His work follows in a tradition going back over 40 years now, of using Kripke fixed-point model constructions to show how naive schemas can be (Post) consistent, as long as one embeds in a non-classical logic. A main issue in all this research is the (...) question of finding a suitable conditional for the naive schemas, an implication connective that is well-behaved enough to be useful but weak enough to maintain coherence when there are paradoxes in the surrounding aether. Field takes several cues from the exemplary work of Ross Brady. Brady's work is predominantly concerned with models for naive theories in relevant logic. Field's considered view is that ‘relevant conditionals are just the wrong tool for naive theories’ [ibid.: 140]. In this note, I reply that a relevant conditional is an indispensable tool for at least one very important job: giving identity conditions for properties. (shrink)

The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads (...) to triviality. (shrink)

There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...) this paper, I explore the limits of what a relevant connective is, showing how some basic criteria motivated by the ideology of relevant logicians provide robust limits on potential connectives. These criteria provide some plausible necessary conditions on being a relevant connective. (shrink)

Mares and Goldblatt, 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the relevant logic R. In this paper, I show how to extend the Mares-Goldblatt frames to accommodate identity. Simpler frames are provided for two zero-order logics en route to the full logic in order to clarify what is needed for identity and substitution, as opposed to quantification. I close with a comparison of this work with the Fine-Mares models for relevant logics with identity and a (...) discussion of constant and variable domains. (shrink)

In two early papers, Max Cresswell constructed two formal logics of propositional identity, pcr and fcr, which he observed to be respectively deductively equivalent to modal logics s4 and s5. Cresswell argued informally that these equivalences respectively “give . . . evidence” for the correctness of s4 and s5 as logics of broadly logical necessity. In this paper, I describe weaker propositional identity logics than pcr that accommodate core intuitions about identity and I argue that Cresswell’s informal arguments do not (...) firmly and without epistemic circularity justify accepting s4 or s5. I also describe how to formulate standard modal logics (k, s2, and their extensions) with strict equivalence as the only modal primitive. (shrink)

In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.

The semantic characterization of the (syllogistic) relations of contrariety and subcontrariety is problematic, as the present discussion illustrates here by attending to some suggestions of D. H. Sanford.

This essay discusses rules and semantic clauses relating to Substitution—Leibniz’s law in the conjunctive-implicational form s=t ∧ A(s) → A(t)—as these are put forward in Priest’s books "In Contradiction" and "An Introduction to Non-Classical Logic: From If to Is." The stated rules and clauses are shown to be too weak in some cases and too strong in others. New ones are presented and shown to be correct. Justification for the various rules are probed and it is argued that Substitution ought (...) to fail. (shrink)

Sedlár and Vigiani [18] have developed an approach to propositional epistemic logics wherein (i) an agent’s beliefs are closed under relevant implication and (ii) the agent is located in a classical possible world (i.e., the non-modal fragment is classical). Here I construct first-order extensions of these logics using the non-Tarskian interpretation of the quantifiers introduced by Mares and Goldblatt [12], and later extended to quantified modal relevant logics by Ferenz [6]. Modular soundness and completeness are proved for constant domain semantics, (...) using non-general frames with Mares–Goldblatt truth conditions. I further detail the relation between the demand that classical possible worlds have Tarskian truth conditions and incompleteness results in quantified relevant logics. (shrink)

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".