Tense in Formal and Informal Arguments :: Tense Arguments Logic Essays

Tense is one of the most significant disparities between formal arguments in classical first-order logic and informal arguments. Tense is a vital grammatical tool for expressing both actions and states of objects. Yet the syntax of classical first-order logic is not designed to accommodate tense. In this paper I shall evaluate several attempts to address the issue of the formal treatment of tense. I will seek to determine how tense is important to the consequence relations among sentences. First, I will examine Quine's approach, which tries to represent temporal discourse without extending the syntax of classical logic. Then I will look at Prior's approach, which introduces tense operators. Finally, I will outline two approaches of my own, which require second-order calculus, and will try to show why the second one best captures the aspects of tense that are appropriate for formal treatment in logic, while minimising uncomfortable ontological commitments. Tense logics, as the name suggests, seek to formalise the logically relevant aspects of tense in arguments. The traditional treatment of tense is to require that the tense of informal arguments remain the same throughout. However, this requirement is inadequate because in some cases it is vital to represent tense in order to evaluate the validity of an argument. For example, consider the following: Eve marries Adam Eve is faithful to Adam Eve gives birth to a child Adam is the father of the child This argument seems valid, but notice how that intuition changes if the order of the premises is changed: Eve gives birth a child Eve marries Adam Eve is faithful to Adam Adam is the father of the child It is not nearly as clear whether this version of the argument is valid. This is because tense matters. Our natural tendency in informal arguments is to assume that premises like these are presented in chronological order, but such an assumption will not do for formal arguments. Therefore, we need to incorporate tense to clarify the temporal relations among the sentences. When this is done, the argument looks like the following: Eve has married Adam Eve has been faithful to Adam Eve gives birth to a child Adam will be the father of the child This argument is clearly valid, because the temporal sequence of the sentences is explicitly indicated. Now, how should we formally represent tensed sentences?