There are many valid arguments which cannot be shown to be valid using propositional logic alone. For example,
Beryl is a philosopher.
All philosophers are wise.
Beryl is wise.
is valid. Yet if we try to analyse this at a propositional level we find that 'Beryl is a philosopher' is an atomic proposition (which might be symbolized by A) and 'All philosophers are wise' is also an atomic proposition, different from the first one (and so might be symbolized by B), and the conclusion 'Beryl is wise' is an atomic proposition different from the other two (and could be symbolized by C); so the apparent logical form of the argument, as judged by propositional logic, is
A, B ∴ C
which is an invalid form.
Obviously what is needed here is a more careful look at the structure of the propositions which make up the argument. And predicate logic is the tool for this.
The task of this second part of the course is to learn the symbolization techniques, the semantics, and the new rules of inference, for predicate logic. Then we will be in a position to make informed judgements about a wider range of arguments.
In predicate logic, 'atomic' propositions are analysed at a finer level. A proposition like 'Beryl is wise' is not just something which is true or is false; rather it is something with a structure... there is a thing, Beryl, which has the property of being wise.