By Bryant D. E., Lindner C. C.

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So properly speaking, the extensional connectives are primitive: the supposed definitions of them given above are characterisations in terms of our natural meanings. The nominal meanings of the sentential connectives are familiar enough, but a little must be said about the intensional sentential connectives, and, in the next chapter, about extensional implication. Intensional negation occurs only with intensional complements, such as inside and outside, true and false, and similar and dissimilar.

For example, if R stands for polygon, T for trilateral, and U for quadrilateral, then TnR, or Q, stands for triangle, and UnR, or P, for quadrangle, and S does not exist; the intensional disjunction of these is ((TnR)m(UnR))tR, which is any polygon — and it is possible for something to be neither a triangle nor a quadrangle, yet still be a polygon. The three truth tables for equivalence are similar with respect to their truth values, but otherwise the nominal truth table differs from the other two.

As relations, these connectives do not exist when one or more of their terms are null sets, 25 Relation Philosophy since null sets do not exist and a relation cannot exist unless all of its terms exist. In such cases they are purely nominal connectives (see page 35). Also, the word every may be used to define a null set, as with the set of every even prime number greater than two, but in such cases the function every does not exist: the every is a purely nominal relation. *** We can now distinguish three distinct set theories.