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This article offers an overview of inferential role semantics. We aim to provide a map of the terrain as well as challenging some of the inferentialist’s standard commitments. We begin by introducing inferentialism and placing it into the wider context of contemporary philosophy of language. §2 focuses on what is standardly considered both the most important test case for and the most natural application of inferential role semantics: the case of the logical constants. We discuss some of the (alleged) benefits (...) 

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two inﬂuential accounts of consequence, the modeltheoretic and the prooftheoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We brieﬂy discuss the main objections these accounts face, as well as Hartry Field’s contention that such objections (...) 

According to logical inferentialists, the meanings of logical expressions are fully determined by the rules for their correct use. Two key prooftheoretic requirements on admissible logical rules, harmony and separability, directly stem from this thesis—requirements, however, that standard singleconclusion and assertionbased formalizations of classical logic provably fail to satisfy :1035–1051, 2011). On the plausible assumption that our logical practice is both singleconclusion and assertionbased, it seemingly follows that classical logic, unlike intuitionistic logic, can’t be accounted for in inferentialist terms. In (...) 



Carnap in the 1930s discovered that there were nonnormal interpretations of classical logic  ones for which negation and conjunction are not truthfunctional so that a statement and its negation could have the same truth value, and a disjunction of two false sentences could be true. Church argued that this did not call for a revision of classical logic. More recent writers seem to disagree. We provide a definition of "nonnormal interpretation" and argue that Church was right, and in fact, (...) 

The paper suggests a revision of the notion of harmony, a major necessary condition in prooftheoretic semantics for a naturaldeduction proofsystem to qualify as meaning conferring, when moving to a bilateral proofsystem. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction and (...) 

The paper suggests a revision of the notion of harmony, a major necessary condition in prooftheoretic semantics for a naturaldeduction proofsystem to qualify as meaning conferring, when moving to a bilateral proofsystem. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between (positive) introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: (i) negative (...) 



Carnap’s result about classical prooftheories not ruling out nonnormal valuations of propositional logic formulae has seen renewed philosophical interest in recent years. In this note I contribute some considerations which may be helpful in its philosophical assessment. I suggest a vantage point from which to see the way in which classical prooftheories do, at least to a considerable extent, encode the meanings of the connectives (not by determining a range of admissible valuations, but in their own way), and I demonstrate (...) 

ABSTRACTLinguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and (...) 

Some bilateralists have suggested that some of our negative answers to yesorno questions are cases of rejection. Mark Textor (2011. Is ‘no’ a forceindicator? No! Analysis 71: 448–56) has recently argued that this suggestion falls prey to a version of the FregeGeach problem. This note reviews Textor's objection and shows why it fails. We conclude with some brief remarks concerning where we think that future attacks on bilateralism should be directed. 

It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic – logic is topic independent and does not derive from a general ‘logic’ of mental states – by adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and taking acceptance and rejection of sentences to be the common (...) 