Lessons from Inferentialism and Invariantism

Abstract

In this chapter, I explain what is at issue in the debate on the meaning of the logical constants, exposing some weaknesses of the standard way in which logicians approach this subject. I present and discuss the two families of proposals that have been most successful: invariantism, which derives from (Tarski. History Philos Logic, 7, 143–154, 1986), and inferentialism, which derives from (Gentzen. Am Philosoph Quart 1(4), 288–306 1935/1964) and whose more philosophical aspects have been developed by Dummett, Hacking and Prawitz (Dummett M (1973) Frege. Philosophy of Language. New York, Harper and Row Publishers; Dummett M (1991) The logical basis of metaphysics. Cambridge, MA., Harvard University Press; Hacking. J Philos 76, 285–319 (1979); Prawitz. Synthese 148, 507–524 (2006)). I show that neither of these two approaches gets the set of logical constants right. Both have been accused of overgenerating, i.e. including notions that intuitively are not logical constants, and of undergenerating, i.e. leaving out of the picture some notions that clearly are logical constants. The constraints that their supporters have proposed to make them extensionally adequate point in the direction of taking on board the pragmatic roles that these notions play in communication. The last section of this chapter is devoted to explaining how a pragmatist account helps us to overcome the difficulties that more formalist approaches present, be they purely syntactic or semantically guided.