35. How shall we reduce the following syllogism
to the first figure ?

All birds are vertebrates ;

Some winged animals are not vertebrates ;

Some winged animals are not birds.
The premises are A O in the second figure, and the
conclusion being O, the argument is a valid syllogism in
Baroko.
The letter k directs us to employ the Redudio aa
impossibiUy as explained in the Elementary Lessons, p. 149.
Or we may convert the major by contraposition, getting —

All not-vertebrates are not birds ;
Some winged .animals are not-vertebrates ;
Therefore, Some winged animals are not birds.
Taking the negative terai nbt-vertebrates as the middle
term, this is valid in Barbara.
36. Can we reduce the mood Camestres per
impossibile ?

Taking the symbolic example —

All X% are Fs ;
No Zs are Fs ;
Therefore, No Zs are A''s,

and assuming for sake of argument that the conclusion is
false, the contradictory * some Zs are X% ' will be true, which
put as minor premise with the original as major, gives the
valid syllogism in Darii —



VIII.] QUESTIONS AND ANSWERS. 93

AUJTsare Vs;
Some Zs are A's ;
Therefore, Some Zs are Vs.
But this conclusion is the contradictory of the original
minor premise ' no Zs are Fs,' so that we cannot contradict
the conclusion of Camestres without producing a syllogism
in Datii to contradict one of our original premises. Thus
we prove the conclusion of Camestres indirectly by a mood
of the first figure. It will be found on trial that all the
moods of the imperfect figures may be similarly proved
indirectly by one or other of the moods of the first or
so-called f^iffct figttre.
CHAPTER IX.
QUESTIONS AND EXERCISES ON THE SYLLOGISM.
