Logic, ancient

Western antiquity produced two great bodies of logical theory – those of Aristotle and the Stoics. Both aim to explain what distinguishes good arguments from bad. Both see that the best arguments are valid and that an argument’s validity depends on its form. For both, therefore, logic’s business is to identify the valid argument forms. Both theories do this by laying down a small number of basic argument forms – Aristotle’s ‘perfect syllogisms’, the Stoics’ ‘indemonstrables’ – and rigorously deriving other valid forms from them. Both theories also try – though in a less systematic manner – to classify the ways in which an argument can go wrong. Here the similarities between these two logics end. Their most significant differences can be illustrated by comparing basic argument forms from each. The argument ‘Every swan is an animal and every animal is moving, so every swan is moving’ has the same form as the argument ‘Every musician is human and every human is a substance, so every musician is a substance’. The Aristotelian expression of this form is ‘A belongs to all B and B belongs to all C, so A belongs to all C’. In this form the letters ‘A’, ‘B’ and ‘C’ stand for any terms whatever, and ‘A belongs to all B’ replaces ‘Every B is an A’. This represents the Aristotelian approach. Compare it with the following. The argument ‘If it is day then it is light, it is day, so it is light’ has the same form as the argument ‘If Dion walks then Dion moves, Dion walks, so Dion moves’. This form is expressed by the Stoics as ‘If the first then the second, the first, so the second’. Here the expressions ‘the first’ and ‘the second’ stand for any declarative sentences whatever. In both cases, the validity of the argument form is tantamount to the validity of all arguments having that form (though the Stoics, unlike Aristotle, require that the precise words used in an argument should recur in its form). But the Aristotelian argument form is different in kind from the Stoic one: while it abstracts from terms, the Stoic form abstracts from sentences. Aristotelian logic is a term logic, Stoic logic a sentential one.