Secondly, take “no x are y”.  Here we only understand “are” to mean “are, as an actual fact”—­which does not at all imply that no x can be y.  But they understand the Proposition to mean, not only that none are y, but that none can possibly be y.  So they mean more than we do:  their meaning includes ours (for of course “no x can be y” includes “no x are y"), but ours does not include theirs.  For example, “no Policemen are eight feet high” would be true in our Game (since, as an actual fact, no such splendid specimens are ever found), but it would be false, according to these writers (since the Attributes “belonging to the Police Force” and “eight feet high” are quite compatible:  there is nothing to prevent a Policeman from growing to that height, if sufficiently rubbed with Rowland’s Macassar Oil—­which said to make hair grow, when rubbed on hair, and so of course will make a policeman grow, when rubbed on a Policeman).

Thirdly, take “all x are y”, which consists of the two partial Propositions “some x are y” and “no x are y’”.  Here, of course, the treatises mean less than we do in the first part, and more than we do in the second.  But the two operations don’t balance each other—­any more than you can console a man, for having knocked down one of his chimneys, by giving him an extra door-step.

If you meet with Syllogisms of this kind, you may work them, quite easily, by the system I have given you:  you have only to make ‘are’ mean ‘are capable of being’, and all will go smoothly.  For “some x are y” will become “some x are capable of being y”, that is, “the Attributes x, y are compatible”.  And “no x are y” will become “no x are capable of being y”, that is, “the Attributes x, y are incompatible”.  And, of course, “all x are y” will become “some x are capable of being y, and none are capable of being y’”, that is, “the Attributes x, y are compatible, and the Attributes x, y’ are incompatible.”  In using the Diagrams for this system, you must understand a red counter to mean “there may possibly be something in this compartment,” and a grey one to mean “there cannot possibly be anything in this compartment.”

3.  Fallacies.

And so you think, do you, that the chief use of Logic, in real life, is to deduce Conclusions from workable Premisses, and to satisfy yourself that the Conclusions, deduced by other people, are correct?  I only wish it were!  Society would be much less liable to panics and other delusions, and political life, especially, would be a totally different thing, if even a majority of the arguments, that scattered broadcast over the world, were correct!  But it is all the other way, I fear.  For one workable Pair of Premisses (I mean a Pair that lead to a logical Conclusion) that you meet with in reading your newspaper or magazine, you will probably find five that lead to no Conclusion at all:  and, even when the Premisses are workable, for one instance, where the writer draws a correct Conclusion, there are probably ten where he draws an incorrect one.