The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural (...) rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.

While most theoreticians of meaning in the first half of the twentieth century subscribed to a representational theory (viewing meanings as entities stood for by the expressions), the second half of the century was marked by the rise of various versions of use-theories of meaning. The roots of this ‘pragmatist turn’ are detectable in the writings of the later Wittgenstein, the Oxford speech act theorists (Austin, Grice) and the American neopragmatists (Quine, Sellars). Though it is now rather popular (and sometimes (...) even fashionable) to invoke the use-theory of meaning, it is by far not so popular to inquire what such a theory really is. In this paper we try to give at least a part of the answer, whereby we find out that the usual conception of such a theory is unsatisfactory. We propose that for an improvement we must, together with Wittgenstein and Sellars, conceive language as a (tool of a) rule-based activity, which enables us to replace the concept of disposition, usually constituting the backbone of the use-theory, by the concept of propriety. The resulting normative version of the use-theory then becomes the investigation of the rules which expressions acquire vis-`a-vis the rules of the relevant language games – especially of the rules of inference. (shrink)

I present an account of truth values for classical logic, intuitionistic logic, and the modal logic s5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.