Problem of multiple generality: Difference between revisions

Revision as of 13:03, 24 November 2007

Revision as of 13:06, 24 November 2007

Line 17:

:''For every mouse m, there exists a cat c, such that c is feared by m,''

:<math>\forall xm. \, \text{Mouse}(xm) \rightarrow \exists yc. \, \text{Cat}(yc) \land \text{Fears}(xm,yc)</math>

in which case the conclusion is trivial.

Line 24:

:''There exists a cat c, such that for every mouse m, c is feared by m.''

:<math>\exists yc. \, \text{Cat}(yc) \land \forall xm. \, \text{Mouse}(xm) \rightarrow \text{Fears}(xm,yc)</math>

This example illustrates the importance of specifying the scope of quantifiers as ''for all'' and ''there exists''.