Existential Assumption

Perhaps in most ordinary conversation we employ categories that we assume have members; for example, when we use the terms "dogs" we believe that there exist real dogs. However, if the category is "pet owners in New York City over 100 years old" we may not be absolutely sure that it has real members, and if "New York City" were replaced by a much smaller town we might really doubt that the category has any members. In fact, it is really not all that rare to think about classes without any membership. For example, when the property owner posts "All trespassers will be prosecuted" the attempt is to ensure that "trespassers" will remain an empty category and, likewise, with the announcement, "All students who do not study will fail," the teacher is trying to keep "students who do not study" an empty category. And the distinction as to whether membership is or isn't assumed for the categories makes a difference as to what can be validly concluded in some cases. For example, from the premises, "All Dogs are Mammals" and "All Mammals are Animals," it follows that "All Dogs are Animals," and this is clearly displayed on the schematics.

Premises

Conclusion

But, together with our knowledge that dogs exist, it also follows that "Some dogs are animals," although this is not displayed. To get this on the schematic we must add "Some dogs exist" as a premise and—employing the method advanced by Sommers and Englebretsen—this can be done by entering "Some Dogs are Dogs," as follows:

Premises

Conclusion

This "presupposition" can be made for any term whatever. For example, the following premises yield no conclusion at all without a membership presupposition:

Premises

Conclusion

but upon presupposing that some Bats exist it follows that some nonAardvarks are nonCats. That is:

Premises

Conclusion

Although this way of handling existential presupposition may seem a bit contrived, it works perfectly with the schematics and its legitimacy is established by Sommers and Englebretsen.