Changes of Mind: An Essay on Rational Belief Revision, by Neil Tennant

Abstract

In his recent book Changes of Mind, Neil Tennant develops a finitistic theory on rational belief revision. The book is divided into three parts. In the first part, Tennant introduces and motivates his theory and shows that it can be implemented on a computer. In the second part, Tennant argues that core logic is the minimal logic enabling an agent to revise her beliefs in accordance with this theory. Furthermore, he argues that the restriction to a finitistic theory constitutes no loss in generality. In the third part, Tennant compares his account to other views on rational belief change, both in formal as well as in mainstream epistemology. Theories on belief revision try to answer the following question. If an agent believes the sentences in a set B and then comes to believe a sentence S, what should she end up believing? If S is consistent with B, the answer seems easy enough. The agent should believe the closure of B and S, that is the sentences in B, as well as S and everything that follows from B and S. This procedure is called expansion of B by S. If S is not consistent with B, matters are more difficult. Before expanding B by S, everything needs to be erased from B which is inconsistent with S. This erasing process is known as contraction of B by ¬S. According to the Levi identity, a revision of B by S is the process of first contracting B by ¬S and then expanding the result by S (Isaac Levi, ‘Subjunctives, Dispositions and Chances’, Synthese, 34, 1977, pp. 423–55). The most uncontroversial requirements imposed on expansion and contraction are success and minimal mutilation. Success demands that after expanding B by S, S needs to be believed and after contracting B by ¬S, ¬S should no longer follow from the sentences believed. Minimal mutilation demands that a contraction should not erase more beliefs than necessary.