'If C is D, A may be B.'
But it is perhaps as well to retain the other, as it serves to emphasize the fact that formal logic is concerned only with the connection of ideas.
§ 713. A concrete instance will render the point under discussion clearer. The example we took before of an A proposition in the conjunctive form—
'If kings are ambitious, their subjects always suffer'
may be converted into
'If subjects suffer, it may be that their kings are ambitious,'
i.e. among the possible causes of suffering on the part of subjects is to be found the ambition of their rulers, even if every actual case should be referred to some other cause. It is in this sense only that the inference is a necessary one. But then this is the only sense which formal logic is competent to recognise. To judge of conformity to fact is no part of its province. From 'Every AB is a CD' it follows that ' Some CD's are AB's' with exactly the same necessity as that with which 'Some B is A' follows from 'All A is B.' In the latter case also neither proposition may at all conform to fact. From 'All centaurs are animals' it follows necessarily that 'Some animals are centaurs': but as a matter of fact this is not true at all.
§ 714. The E and the I proposition may be converted simply, as above.
§ 715. O cannot be converted at all. From the proposition
'If a man runs a race, he sometimes does not win it,'