Hopeful Monsters : A Note on Multiple Conclusions

Arguments, the story goes, have one or more premises and only one conclusion. A contentious generalisation allows arguments with several disjunctively connected conclusions. Contentious as this generalisation may be, I will argue nevertheless that it is justified. My main claim is that multiple conclusions are epiphenomena of the logical connectives: some connectives determine, in a certain sense, multiple-conclusion derivations. Therefore, such derivations are completely natural and can safely be used in proof-theoretic semantics.info:eu-repo/semantics/publishedVersio

Ask not what bilateralist intuitionists can do for Cut, but what Cut can do for bilateralist intuitionism

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succe- dent. This interpretation goes against its own ecumenical ambitions, endow- ing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert.info:eu-repo/semantics/publishedVersio

Reflective equilibrium on the fringe : The tragic threefold story of a failed methodology for logical theorising

Reflective equilibrium, as a methodology for the ‘formation of log- ics’, fails on the fringe, where intricate details can make or break a logical the- ory. On the fringe, the process of theorification cannot be methodologically governed by anything like reflective equilibrium. When logical theorising gets tricky, there is nothing on the pre-theoretical side on which our theoretical claims can reflect of—at least not in any meaningful way. Indeed, the fringe is exclusively the domain of theoretical negotiations and the methodological power of reflective equilibrium is merely nominal.info:eu-repo/semantics/acceptedVersio

What is a Paraconsistent Logic?

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively

Ask not what bilateralist intuitionists can do for Cut, but what Cut can do for bilateralist intuitionism

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succe- dent. This interpretation goes against its own ecumenical ambitions, endow- ing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert.info:eu-repo/semantics/publishedVersio

Reflective Equilibrium on the Fringe

Reflective equilibrium, as a methodology for the "formation of logics," fails on the *fringe*, where intricate details can make or break a logical theory. On the fringe, the process of theorification cannot be methodologically governed by anything like reflective equilibrium. When logical theorising gets tricky, there is nothing on the pre-theoretical side on which our theoretical claims can reflect of---at least not in any meaningful way. Indeed, the fringe is exclusively the domain of theoretical negotiations and the methodological power of reflective equilibrium is merely nominal

Requiem for logical nihilism, or: Logical nihilism annihilated

Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.info:eu-repo/semantics/publishedVersio

WEAK DISHARMONY: SOME LESSONS FOR PROOF-THEORETIC SEMANTICS

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony

Variations on intra-theoretical logical pluralism : internal versus external consequence

Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland (Australas J Philos 91(2):355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form of intra-theoretical logical pluralism.info:eu-repo/semantics/publishedVersio