Extending the logical analysis

In the chapter about propositional logic, it was shown that we could decide whether inferences and sentences were correct or true (tautological) by using such techniques as the truth-table method.

However, we can express many inferences in natural language which are intuitively felt to be correct but which cannot be shown to be correct in propositional logic, e.g. (1).

1. (1) If all moose are clever and Bruce is a moose, then Bruce is clever

The reasoning in these sentences seems sound to everyone, yet it cannot be shown to be correct in propositional logic. (1) would be analysed as (p & q) → r in propositional logic, which can be shown to be anything but tautological by a truth table. Predicate logic, on the other hand, gives us an instrument with which we can show that the inference in (1) is correct. In general, it can be said that predicate logic takes us from those logical relations that hold between sentences to those that hold within a sentence.

We will now examine in more detail how this is done. Let us start with a simple sentence.

1. (2) Bruce is a moose

This sentence says something about an individual. The individual is Bruce and it is said of him that he has the property of being a moose. Such sentences are called predications – one predicates something (e.g. a property) of an individual.