THE LOGIC NOTES

4   Expressing Generality


We now turn from the logic of sentential connectives to a more comprehensive system allowing us to analyse logical inferences which turn on the internal structure of atoms and on the behaviour of locutions like 'all' and 'some' which express generality. Consider the following for example:

Example 14 All logicians are rational
Some philosophers are not rational
Therefore not all philosophers are logicians.

Plainly this is valid in virtue of its form, but to demonstrate and explain its validity we need a richer language and more formal machinery than are available in the logic we have studied so far