In previous chapters various procedures have been discussed for reducing semantic facts about public languages to facts about propositional attitudes, and facts about propositional attitudes to physical facts. In all cases there seemed a large amount of underdetermination. Some of those who advocated these reductions, David Lewis in particular, have acknowledged this and are prepared to live with it. While I have no conclusive arguments that the amount of underdetermination is too great to be acceptable I am impressed with the difference between how little these theories deliver and how definite we seem able to be about what a person's propositional attitudes are and about what the expressions mean in the language they speak. How can this be?

One feature of the views we have looked at is that they all seem to be reductive. Thus, for Lewis, an interpreted language ℒ is the language of a population P in w iff a convention of truthfulness and trust obtains in w in accordance with ℒ among members of P. And belief is defined in terms of a theory that explains behaviour. The question I want to raise is this. Suppose that there is a complex pattern of behaviour which constitutes a's believing that p. Why should we expect that there should be any theory in which ‘believes’ is a theoretical term whose meaning is defined by the physical consequences of the theory? Suppose the behaviour of a's and facts about a's environment, perhaps including facts about other people, is so complex that no theory can describe it. Maybe this is just a practical limitation, or maybe no physical language can provide a finite description of the behaviour.