Logical Consequence and Natural Language

Abstract

One of the great successes of the past fifty or so years of the study of language has been the application of formal methods. This has yielded a flood of results in many areas, both of linguistics and philosophy, and has spawned fruitful research programs with names like ‘formal semantics’ or ‘formal syntax’ or ‘formal pragmatics’. ‘Formal’ here often means the tools and methods of formal logic are used (though other areas of mathematics have played important roles as well). The success of applying logical methods to natural language has led some to see the connection between the two as extremely close. To put the idea somewhat roughly, logic studies various languages, and the only special feature of the study of natural language is its focus on the languages humans happen to speak. This idea, I shall argue, is too much of a good thing. To make my point, I shall focus on consequence relations. Though they hardly constitute the full range of issues, tools, or techniques studied in logic, a consequence relation is the core feature of a logic. Thus, seeing how consequence relations relate to natural language is a good way to measure how closely related logic and natural language are. I shall argue here that what we find in natural language is not really logical consequence. In particular, I shall argue that studying the semantics of a natural language is not to study a genuinely logical consequence relation. There is indeed a lot we can glean