- $\forall x(P(x)) \vee \forall x(Q(x))$
I am currently reading a logic book by Patrick J. Hurley, and in the book the author says that we can't universally instantiate a statement like statement 1. Specifically, he says that universal instantiation must be applied only to whole lines but he never defines what he means by whole lines and he never explains why universal instantiation is applicable only to whole lines.
I don't know why it might be wrong to instantiate statement 1 at just one step. For example, what is wrong with using John as our instance and then saying that either John has the property P or John has the property Q?