ABSTRACT
The following is a famous1 argument: (1) All men are mortal. (2) Socrates is a man. (3) ∴ Socrates is mortal. Here (1) and (2) are the assumptions and (3) is the conclusion. If you agree to the truth of (1) and (2) then you are obliged to accept the truth of (3). This is therefore a valid argument, and not a very complex one, but it cannot be shown to be valid using propositional logic. Thus propositional logic, whilst very useful, is not up to the job of analysing even quite simple arguments. The goal of this last chapter is to add features to propositional logic that will make it more powerful and more useful; in particular, we shall see that in this richer logic we can prove that the above argument is valid. There will be a price to pay in that the resulting system will be intrinsically harder to work with.
