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  1. Metainferences from a Proof-Theoretic Perspective, and a Hierarchy of Validity Predicates.Rea Golan - 2022 - Journal of Philosophical Logic 51 (6):1295–1325.
    I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. Then, (...)
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  2.  84
    On the Metainferential Solution to the Semantic Paradoxes.Rea Golan - 2023 - Journal of Philosophical Logic 52 (3):797-820.
    Substructural solutions to the semantic paradoxes have been broadly discussed in recent years. In particular, according to the non-transitive solution, we have to give up the metarule of Cut, whose role is to guarantee that the consequence relation is transitive. This concession—giving up a meta rule—allows us to maintain the entire consequence relation of classical logic. The non-transitive solution has been generalized in recent works into a hierarchy of logics where classicality is maintained at more and more metainferential levels. All (...)
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  3.  38
    A Unified Interpretation of the Semantics of Relevance Logic.Rea Golan - 2023 - Mind 132 (528).
    I introduce a novel and quite intuitive interpretation of the ternary relation that figures in the relational semantics of many relevance logics. Conceptually, my interpretation makes use only of incompatibility and parthood relations, defined over a set of states. In this way, the proposed interpretation—of the ternary relation and the conditional—extends Dunn’s and Restall’s works on negation and the Routley star operator. Therefore, the interpretation is unified, and hence not only intuitive but also parsimonious. Additionally, the interpretation provides us with (...)
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  4.  85
    There is no tenable notion of global metainferential validity.Rea Golan - 2021 - Analysis 81 (3):411-420.
    The use of models to assign truth values to sentences and to counterexemplify invalid inferences is a basic feature of model theory. Yet sentences and inferences are not the only phenomena that model theory has to take care of. In particular, the development of sequent calculi raises the question of how metainferences are to be accounted for from a model-theoretic perspective. Unfortunately there is no agreement on this matter. Rather, one can find in the literature two competing model-theoretic notions of (...)
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  5. Why inconsistent intentional states underlie our grasp of objects.Rea Golan - forthcoming - Southern Journal of Philosophy.
    Several authors maintain that we are capable of having inconsistent intentional states, either in cases of illusion, in certain cases of imagination, or because the observable world is (partly) inconsistent and we perceive it as such. These views are all premised on the assumption that inconsistent intentional states—even if acknowledged—are peculiar and have nothing essential to do with our perceptual capacities. In the present article, I would like to present, and argue for, a much stronger thesis: that inconsistent intentional states (...)
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  6. A simple sequent system for minimally inconsisteny LP.Rea Golan - 2023 - Review of Symbolic Logic 16 (4):1296-1311.
    Minimally inconsistent LP (MiLP) is a nonmonotonic paraconsistent logic based on Graham Priest's logic of paradox (LP). Unlike LP, MiLP purports to recover, in consistent situations, all of classical reasoning. The present paper conducts a proof-theoretic analysis of MiLP. I highlight certain properties of this logic, introduce a simple sequent system for it, and establish soundness and completeness results. In addition, I show how to use my proof system in response to a criticism of this logic put forward by JC (...)
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  7.  94
    An Argument from Proof Theory against Implicit Conventionalism.Rea Golan - 2023 - Philosophical Quarterly 74 (1):273-290.
    Conventionalism about logic is the view that logical principles hold in virtue of some linguistic conventions. According to explicit conventionalism, these conventions have to be stipulated explicitly. Explicit conventionalism is subject to a famous criticism by Quine, who accused it of leading to an infinite regress. In response to the criticism, several authors have suggested reconstructing conventionalism as implicit in our linguistic behaviour. In this paper, drawing on a distinction from proof theory between derivable and admissible rules, I argue that (...)
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  8. Minimally Nonstandard K3 and FDE.Rea Golan & Ulf Hlobil - 2022 - Australasian Journal of Logic 19 (5):182-213.
    Graham Priest has formulated the minimally inconsistent logic of paradox (MiLP), which is paraconsistent like Priest’s logic of paradox (LP), while staying closer to classical logic. We present logics that stand to (the propositional fragments of) strong Kleene logic (K3) and the logic of first-degree entailment (FDE) as MiLP stands to LP. That is, our logics share the paracomplete and the paraconsistent-cum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to (...)
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  9.  75
    Reasoning and grasping objects.Rea Golan - 2021 - European Journal of Philosophy 29 (4):699-711.
    There is a pervasive view that inference—as opposed, notably, to a grasp of objects—is an intralinguistic process that does not draw on extralinguistic resources. The present paper aims to show that this dichotomy between inferring and grasping objects can be resisted. Specifically, I offer an alternative view: a phenomenological account according to which our most basic inferences draw on our grasp of objects. I motivate this account on the grounds that, although it is restricted to such basic inferences, it has (...)
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  10.  96
    Is there a neutral metalanguage?Rea Golan - 2019 - Synthese 198 (Suppl 20):4831-4858.
    Logical pluralists are committed to the idea of a neutral metalanguage, which serves as a framework for debates in logic. Two versions of this neutrality can be found in the literature: an agreed upon collection of inferences, and a metalanguage that is neutral as such. I discuss both versions and show that they are not immune to Quinean criticism, which builds on the notion of meaning. In particular, I show that the first version of neutrality is sub-optimal, and hard to (...)
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