Various Forms of the Disjunctive Proposition.
Disjunctive propositions may occur in a great variety of forms, of which the old logicians took insufficient notice. There may be any number of alternatives, each of which may be a combination of any number of simple terms. A proposition, again, may be disjunctive in one or both members. The proposition
Solids or liquids or gases are electrics or conductors of electricity
is an example of the doubly disjunctive form. The meaning of such a proposition is that whatever falls under any one or more alternatives on one side must fall under one or more alternatives on the other side. From what has been said before, it is apparent that the proposition
A ꖌ B = C ꖌ D
will correspond to
ab = cd,
each member of the latter being the negative of a member of the former proposition.
As an instance of a complex disjunctive proposition I may give Senior’s definition of wealth, which, briefly stated, amounts to the proposition “Wealth is what is transferable, limited in supply, and either productive of pleasure or preventive of pain.”[70]
| Let | A = wealth |
| B = transferable | |
| C = limited in supply | |
| D = productive of pleasure | |
| E = preventive of pain. |