Barbara. Celarent.
Darii. Ferio.
The first mood Barbara is formed by placing the cards on top of each other, so that B is within the margin of A, and C within the margin of B. This is the syllogism, 'All B is A, all C is B, therefore all C is A.'
Next let B and C be as above, but let A be wholly apart from both. This is Celarent: 'No B is A, all C is B, therefore no C is A.'
In Darii the whole of B is in A, but only a part of C coincides with B. The syllogism is: 'All B is A, some C is B, therefore some C is A.'
In Ferio A is again wholly separated from the others, and C is only partially in B. Argument: 'No B is A, some C is B, therefore some C is not A.'
It is to be remembered that all the other figures and moods are reducible to the above figure of four moods, so that the reduction applicable to the latter is equally applicable to the former.
To reduce Darii to Barbara all that is necessary is to ignore the dotted part of C. That is suggested by the use of the word 'some,' which has a correlative 'all' or 'others.' But the correlative quantity does not enter into the syllogism, and we know nothing about it. It may not even exist. We are therefore at liberty to substitute for 'some C' the name D, and consider it an integer instead of a fraction. Then we have the Barbara syllogism: 'All B is A, all D (= some C) is B, therefore all D is A.' The phrase 'all of some' is quite allowable: 'I met some firemen, all of whom wore brass helmets.'