Modern Square of Opposition

The classical square of opposition presupposes that the terms of any categorical proposition have referents. If we adopt the modern doctrine about existential import, then some of the relationships in the traditional square no longer hold.

## Subalternation and the Modern Square of Opposition

If theIproposition, "SomeSareP" implies the existence ofSs, while the correspondingAproposition does not, then the truth of theAproposition does not imply the truth of the correspondingI. The same is true forEandO. In other words, subalternation must be removed from the square.

## Subcontrary and the Modern Square of Opposition

Two statements are subcontraries if, by virtue of their logical form, they could both be true but could not both be false. However, if noSs exist, then both particular statements are false.IandOno longer fit the definition of subcontraries. Thus, subcontrary must be removed from the square.

## Contrary and the Modern Square of Opposition

Since neither of the universal statements have existential import, then they are both true in the case where there are noSs. Thus,AandEare no longer contraries. Contrary must, then, be removed from the square.

## Contradiction and the Modern Square of Opposition

The only relationship that survives in the modern square of opposition is that of contradictories. If there exists a single thing that is bothSandP, then theIproposition is true and theEfalse. However, if nothing is bothSandP, then theIproposition is false and theEis true--even if the absence of things that are bothSandPis due to the fact that there aren't anySs at all.The same reasoning applies to the

AandOpropositions. SoEis true if and only ifIis false, andAis true if and only ifOis false.