PUBLICATIONS
WHY INCONSISTENT INTENTIONAL STATES UNDERLIE OUR GRASP OF OBJECTS
Southern Journal of Philosophy, forthcoming. Link
Several authors maintain that we are capable of having inconsistent intentional states, either in cases of illusion, or 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 paper, I would like to present, and argue for, a much stronger thesis: that inconsistent intentional states underlie the possibility of having intentional content in mind. I argue for this thesis on the basis of a Husserlian phenomenological analysis of our grasp of objects, which I formulate in terms of incompatibility semantics.
A UNIFIED INTERPRETATION OF THE SEMANTICS OF RELEVANCE LOGIC
Mind, 132 (528): 1105–1125. 2023. Link
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 a cogent argument to the effect that a ternary relation is indispensable, and we cannot do merely with a binary relation.
AN ARGUMENT FROM PROOF THEORY AGAINST IMPLICIT CONVENTIONALISM
The Philosophical Quarterly, 74 (1): 273-290. 2023. Link
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 implicit conventionalism has not been stated in a sufficiently precise way, as it leaves open what one needs to say about admissible yet underivable rules. Moreover, it turns out that this challenge cannot be easily met, and that any attempt to meet the challenge makes conventionalism much less attractive a thesis.
ON THE METAINFERENTIAL SOLUTION TO THE SEMANTIC PARADOXES
Journal of Philosophical Logic, 52 (3): 797-820. 2023. Link
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 metarule—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 the logics in this hierarchy can accommodate a truth predicate, including the logic at the top of the hierarchy—known as C M ω —which presumably maintains classicality at all levels. C M ω has so far been accounted for exclusively in model-theoretic terms. Therefore, there remains an open question: how do we account for this logic in proof-theoretic terms? Can there be found a proof system that admits each and every classical principle—at all inferential levels—but nevertheless blocks the derivation of the liar? In the present paper, I solve this problem by providing such a proof system and establishing soundness and completeness results. Yet, I also argue that the outcome is philosophically unsatisfactory. In fact, I'm afraid that in light of my results this metainferential solution to the paradoxes can hardly be called a “solution,” let alone a good one.
A SIMPLE SEQUENT SYSTEM FOR MINIMALLY INCONSISTENT LP
Review of Symbolic Logic, 16(4):1296-1311. 2023. Link
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 Beall.
MINIMALLY NONSTANDARD K3 AND FDE
(with Ulf Hlobil)
Australasian Journal of Logic, 19(5): 182-213. 2022. Link
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 paraconsistentcum-paracomplete nature of K3 and FDE, respectively, while keeping these features to a minimum in order to stay closer to classical logic. We give semantic and sequent-calculus formulations of these logics, and we highlight some reasons why these logics may be interesting in their own right.
METAINFERENCES FROM A PROOF-THEORETIC PERSPECTIVE, AND A HIERARCHY OF VALIDITY PREDICATES
Journal of Philosophical Logic, 51: 1295–1325. 2022. Link
I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics recently introduced by Barrio, Pailos and Szmuc. 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, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given in a recent paper by Dicher and Paoli). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis that the validity predicate introduced by Beall and Murzi has to express facts not only about what follows from what, but also about the metarules, etc.
THERE IS NO TENABLE NOTION OF GLOBAL METAINFERENTIAL VALIDITY
Analysis, 81(3): 411-420. 2021. Link
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 aren't the only phenomena 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 metainferential validity, known as the “global” notion and the “local” notion. In this article, I argue that given certain plausible considerations about metainferential validity, the global notion collapses into the local notion.
REASONING AND GRASPING OBJECTS
European Journal of Philosophy, 29 (4): 699-711. 2021. Link
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 significant implications for the general question of whether inference involves taking one's premises to support one's conclusion. The proposed account implies that basic inferences need not involve corresponding “takings,” (even though such inferences involve conceptual content), but it leaves open the possibility that non-basic inferences do involve corresponding “takings,” while relying on basic inferences. It will turn out that such a disjunctive view, according to which non-basic reasoning is somewhat parasitic on basic reasoning, manages to avoid many of the problems with which the literature on the “taking condition” deals.
IS THERE A NEUTRAL METALANGUAGE?
Synthese 198, 4831–4858, 2021. Link
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 (i) the first version of neutrality is sub-optimal, and hard to reconcile with the theories of meaning for logical constants, and (ii) the second version collapses mathematically, if rival logics, as object languages, are treated with charity in the metalanguage. I substantiate (ii) by proving a collapse theorem that generalizes familiar results. Thus, the existence of a neutral metalanguage cannot be taken for granted, and meaning-invariant logical pluralism might turn out to be dubious.