Over the last decade, I have published some research articles within philosophical logic and theoretical philosophy, mainly on the topics of substructural logics, proof theory for non-classical logics and logico-semantic paradoxes. In addition, I have touched upon the issues of logical nihilism and logical inferentialism. 

Nowadays I am also working on the philosophy of proof theory, trying to get a better understanding of the nature and purpose of deductive systems through a perspective informed by contemporary philosophy of science. In that regard, I primarily interested in how deductive systems can be used in explanations and in making sense of deductive systems with infinitary inference rules. Finally, I am also increasingly interested in modal logic, decidability and interpolation. 

Below you will find titles and abstracts of my published and unpublished academic writing. 

Journal articles

2025

Dialetheism and the countermodel problem (Co-authored with with Ben Martin) Philosophy and Phenomenological Research 110 (2): 709-733 (link)

According to some dialetheists, we ought to reject the distinction between object and meta‐languages. Given that dialetheists advocate truth‐value gluts within their object‐language, whether in order to solve the liar paradox or for some other reason, this rejection of the object‐/meta‐language distinction comes with the commitment to use a glutty metatheory. While it has been pointed out that a glutty metatheory brings with it expressive deficiencies, we highlight here another complication arising from the use of a glutty metatheory, this time evidential in nature. According to this countermodel problem, while the thoroughgoing dialetheist who embraces a glutty metatheory can justify their acceptance of a rule of inference's invalidity using countermodels, to justify their renunciation of an unwanted rule they actually require the means to warrant their rejection of the rule's validity—which cannot be supplied by countermodels based on a standard dialetheic semantics. We end by sketching out a possible solution for the thoroughgoing dialetheist using a bilaterialist semantics.

A multiplicative ingredient for omega-inconsistency Australasian Journal of Logic 22 (3): 289-307 (link).

This paper presents a distinctively multiplicative quantificational principle that arguably captures the problematic aspects of Zardini's infinitary rules for a multiplicative quantifier within the context of the semantic paradoxes and the theoretical goal to obtain a (omega)-consistent theory of transparent truth. After showing that the principle is derivable with Zardini's rules and that one obtains through vacuous quantification an inconsistent theory of truth if truth is transparent, the paper presents two results regarding the principle and omega-inconsistency. First, the principle is used to obtain a non-classical variant of McGee's omega-inconsistency result for certain classical theories of truth. Second, it is demonstrated that the conditions for a truth-theoretic variant of Bacon's omega-inconsistency result for certain non-classical theories of transparent truth implies that the principle holds for the paradoxical formula. Finally, the paper argues that the paradoxical reasoning that the principle enables is structurally similar to the kind of infinitary reasoning popularised by Hilbert's Grand Hotel.

2022

Expressing logical disagreement from within Synthese 200 (2):1-33 (link)

Against the backdrop of the frequent comparison of theories of truth in the literature on semantic paradoxes with regard to which inferences and metainferences are deemed valid, this paper develops a novel approach to defining a binary predicate for representing the valid inferences and metainferences of a theory within the theory itself under the assumption that the theory is defined with a classical meta-theory. The aim with the approach is to obtain a tool which facilitates the comparison between a theory and its competitors within the theory itself, thereby expressing the disagreement between the theories within the theories. After discussing what we can and should require of an object-linguistic representation of a theory for that purpose, this paper proposes to restrict the representation of valid metainferences to locally valid metainferences, a requirement which turns out to be -consistent and conservative over classical first-order arithmetic. This approach is then applied to four theories definable on strong Kleene models using a labelled nested sequent calculus.

2021

Metainferential Reasoning on Strong Kleene Models Journal of Philosophical Logic 51 (6):1327-1344 (link)

Barrio et al. (Journal of Philosophical Logic, 49(1), 93–120, 2020) and Pailos (Review of Symbolic Logic, 2020(2), 249–268, 2020) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where each subsequent metainferential logic ‘says’ about the former logic that it is transitive. While Barrio et al. (2020) suggests that this hierarchy is such that each subsequent level ‘in some intuitive sense, more classical than’ the previous level, Pailos (2020) proposes an extension of the hierarchy through which a ‘fully classical’ metainferential logic can be defined. Both Barrio et al. (2020) and Pailos (2020) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the -hierarchy is non-classical to an equal extent and that the ‘fully classical’ metainferential logic is actually just the original non-transitive logic ST ‘in disguise’. The paper concludes with some remarks about how the various results about the -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive.

IKTω and Lukasiewicz-models. (co-authored with Jan-Fredrik Olsen)  Notre Dame J. Formal Logic 62 (2) 247 - 256 (link)

In this note we show first that the first-order logic IKω is sound with regard to the models obtained continuum-valued Lukasiewicz-models for first-order  languages by treating the quantifiers as infinitary strong disjunction/conjunction  rather  than  infinitary weak disjunction/conjunction. We then proceed to show that these models cannot be used to provide a new consistency proof for the theory of truth IKTω obtained by expanding IKω with transparent truth since the models are incompatible with transparent truth. Moreover, we also show that whether or not this inconsistency can be repro-duced in the sequent calculus for IKTωdepends on how vacuous quantification is treated.

Logical Nihilism and the Logic of ‘prem'. Logic and Logical Philosophy Vol. 30(2)  311-325 (link)

As the final component of a chain of reasoning intended to take us all the way to logical nihilism, Russell (2018) presents the atomic sentence ‘prem’ which is supposed to be true when featuring as premise in an argument and false when featuring as conclusion in an argument. Such a sentence requires a non-reflexive logic and an endnote by Russell (2018) could easily leave the reader with the impression that going non-reflexive suffices for logical nihilism. This paper shows how one can obtain non-reflexive logics in which ‘prem’ behaves as stipulated by Russell (2018) but which nonetheless has valid inferences supporting uniform substitution of any formula for propositional variables such as modus tollens and modus ponens.

2020

Structural proof theory for first-order weak Kleene logics. Journal of Applied Non-Classical Logics 30 (3): 272-289  (link)

This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.

A note on the cut-elimination proof in "truth without contra(di)ction". The Review of Symbolic Logic 13 (4):882-886. (link)

This note shows that the permutation instructions presented by Zardini in "Truth without contra(di)ction" (RSL, 2011) for eliminating cuts on universally quantified formulas in the sequent calculus for the non-contractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counter-example is of the kind that leaves open the question whether cut can be shown to be eliminable in the sequent calculus for IKTω with an alternative strategy.

Herzberger's limit rule in labelled sequent calculus. Studia Logica 108 (4): 815-855.  (link) 

Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger's limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two semantics, we show that the theory of truth obtained with the labelled sequent calculus based on Herzberger's limit rule is equivalent to PosFS.

2018

Infinitary Contraction-free Revenge. Thought 7(3): 179-189. (link) 

How robust is a contraction-free approach to the semantic paradoxes? This paper aims to show some limitations with the approach based on multiplicative rules by presenting and discussing the significance of a revenge paradox using a predicate representing an alethic modality defined with infinitary rules.

2017

Non-Classical Elegance for Sequent Calculus Enthusiasts. Studia Logica 105(1):93-119. (link)

In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth LP, K3, STT and a non-reflexive logic TS which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley (2012) for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between derivable sequents and validity in comparison to the calculus developed by Ripley (2012).

2016

Omega-Inconsistency Without Cuts and Nonstandard Models. Australasian Journal of Logic 13(5) (link)

This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee (1985) for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on Robinson Arithmetic where the deontic modality is treated as a predicate, proves omega-inconsistency and shows thus, pace Cobreros et al.(2013), that the result in McGee (1985) does not rely on transitivity. Finally, it also explains why the omega-inconsistent logics of truth in question do not require nonstandard models of arithmetic.

Naïve modus ponens and failure of transitivity. Journal of Philosophical Logic 45(1):65-72 (link)

In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I respond on behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation.

2015

How a Semantics for Tonk Should Be. The Review of Symbolic Logic, 8(3):488-505: (link)

This paper explores how a semantics for Prior’s infamous connective tonk should be, a connective defined by inference rules that trivialize the logic of a deductive system if that logic is supposed to be transitive. To avoid triviality, one must reject transitivity and in a relatively recent paper, Roy Cook develops a semantics for tonk with non-transitive entailment. However, I show in this paper that a cut-free sequent calculus for tonk - the arguably most natural and simplest deductive system for a non-transitive logic - can neither be complete with respect to Cook’s semantics nor with respect to a semantics with non-transitive entailment based on a semantics for vagueness and transparent truth developed by Cobreros et al. It is argued that the failure to adequately represent tonk is connected with the fact that tonk is not uniquely defined in a cut-free sequent calculus system unless the logic is in addition non-reflexive. To remedy this, the paper develops a semantics with non-transitive and non-reflexive entailment based on the idea that complex formulae are true or false relative to them being assessed as premise or as conclusion.

2011

Har katter mistet kjærligheten til visdom? Filosofisk Supplement: 04/2011 (link)

This essay was my submission to an essay competition in connection to Filosofisk Supplement's 25th issue with the question "Har vitenskapene mistet kjærligheten til visdom?" which in English amounts to asking whether the sciences have lost the love of wisdom? The English title of my submission is "Have cats lost the love of wisdom?" and I argue, using Carnap's notion of analyticity from Meaning and Necessity and Wittgenstein's notion of grammatical propositions, that the statement corresponding to their question is analytically false as opposed to the statement corresponding to my question. I then reformulate their question to concern scientists rather than science, and observe that we must ask the scientists to figure out the answer to this new question. However, I conclude by observing that we cannot exclude that their statement is true even if we accept my framework and analysis since it follows that I've only spoken about the definition, not the thing in itself. Somehow I won the competition.

Manuscripts

Transparency, Transitivity or Reflexivity. PhD Dissertation at the University of Aberdeen

This thesis investigates logico-philosophical aspects of using either a non-transitive or a non-reflexive logic to obtain a logic of truth in which truth is transparent. It enquires into and rejects the claim that restricting transitivity of entailment to accommodate transparent truth suffices to make the connective tonk acceptable by arguing that tonk as defined in a cut-free sequent calculus requires in addition that the logic is non-reflexive to be uniquely defined, and develops a semantics for tonk based on models with two valuations which delivers a non-transitive and non-reflexive logic. It develops a cut-free sequent calculus and two kinds of semantics for a non-reflexive logic of truth in which truth is transparent, one based on trivalent models and one based on models with two valuations. It shows how to define a non-transitive, a paraconsistent and a paracomplete logic of truth on the models with two valuations and develops a cut-free sequent calculus that captures all four logics. It investigates to which extent the non-reflexive and the non-transitive logic of truth can express their own meta-inferences, and shows among other things how one can employ the paraconsistent and the paracomplete logic to express the meta-inferences of the non-transitive and the non-reflexive logic respectively. Finally, it proves that the non-transitive logic of truth is omegainconsistent and furthermore that transitivity is not required as assumption to establish that a logic in which truth satisfies the conditions of quantified standard deontic logic is omega-inconsistent.