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In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulas. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap in 1943 called categoricity. We show that categorical systems can be given for any finite many-valued logic using $n$-sided sequent calculus. These systems are understood as a further development (...) |
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Is linguistic understanding a form of knowledge? I clarify the question and then consider two natural forms a positive answer might take. I argue that, although some recent arguments fail to decide the issue, neither positive answer should be accepted. The aim is not yet to foreclose on the view that linguistic understanding is a form of knowledge, but to develop desiderata on a satisfactory successor to the two natural views rejected here. |
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We present an inferentialist account of the epistemic modal operator might. Our starting point is the bilateralist programme. A bilateralist explains the operator not in terms of the speech act of rejection ; we explain the operator might in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of might provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. (...) |
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This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings of (...) |
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Rumfitt has given two arguments that in unilateralist verificationist theories of meaning, truth collapses into correct assertibility. In the present paper I give similar arguments that show that in unilateral falsificationist theories of meaning, falsehood collapses into correct deniability. According to bilateralism, meanings are determined by assertion and denial conditions, so the question arises whether it succumbs to similar arguments. I show that this is not the case. The final section considers the question whether a principle central to Rumfitt's first (...) |
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In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant log... |
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Does (affirmative) judgement have a logical dual, negative judgement? Whether there is such a logical dualism was hotly debated at the beginning of the twentieth century. Frege argued in ?Negation? (1918/9) that logic can dispense with negative judgement. Frege's arguments shaped the views of later generations of analytic philosophers, but they will not have convinced such opponents as Brentano or Windelband. These philosophers believed in negative judgement for psychological, not logical, reasons. Reinach's ?On the Theory of Negative Judgement? (1911) spoke (...) |
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Even though the strong relationship between proof-theoretic and model-theoretic notions in one’s logical theory can be shown by soundness and completeness proofs, whether we can define the model-theoretic notions by means of the inferences in a proof system is not at all trivial. For instance, provable inferences in a proof system of classical logic in the logical framework do not determine its intended models as shown by Carnap (Formalization of logic, Harvard University Press, Cambridge, 1943), i.e., there are non-Boolean models (...) |
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