Studies and Exercises in Formal Logic

by John Neville Keynes

where A₁, B₁, P₁, Q₁, &c. are all simple terms.[501]

[⁵⁰¹] So that both subject and predicate consist of a series of alternants which themselves contain only simple determinants; that is, there is no alternant of the form (A or B)(C or D).

As shewn in section [446], this may be resolved into the independent propositions:—

All A₁A₂ … is P₁P₂ … or Q₁Q₂ … or &c. ;
All B₁B₂ … is P₁P₂ … or Q₁Q₂ … or &c. ;
&c.   &c.   &c.;

in none of which is there any alternation in the subject.

These propositions may be dealt with separately, and if any one of them affords information with regard to X, then the original proposition does so.

We have then to consider a proposition of the form

All A₁A₂ … A_n is P₁P₂ … or Q₁Q₂ … or &c. ;

and this proposition may by contraposition be reduced to the form 505

Everything is a₁ or a₂ … or a_n or P₁P₂ … or Q₁Q₂ … or &c. ;