Gentzen and Hacking on Structural and Operational Rules in the Definition of Logical Constants; Review and Critique

Gentzen divides rules of logical system into ‘operational rules’ and ‘structural rules’. By operational rules she means the rules of introduction and elimination of a logical constant. Structural rules represent the fundamental (structural) characteristics of an argument in such a way that any change in them causes changing in the whole system. In his works, Gentzen mentions that the meaning of logical constants can be achieved only through operational rules. This point is the infrastructure of inferentialism approach on meaningfulness of logical constants. Christopher Peacocke criticizes the basis of inferentialism approach. He believes that all structural and operational rules should be considered as the definition of logical constants. In response to this claim, Ian Hacking argued that accepting Peacock’s idea, will lead to a lack of conservation. Lack of conservation causes system incompatibility. In this paper, after careful examination of structural rules and expressing its difference with operational rules, Hacking argument will be evaluated and criticized and finally a solution to the problem will be presented.