In working with quantified expressions (those saying all or some or none) the one thing most likely to go wrong is to act as though we are talking about the same individuals when that is not justified. For example, in the argument Some teenagers are poor drivers and some poor drivers get into accidents, so some teenagers get into accidents we cannot assume that we are talking about the same individuals in the middle term poor drivers.

In order to work with a tree or with a derivation, we usually do instantiate expressions with existential quantifiers (W or E), but what we have to remember is that this is a hypothetical use of a name (as though saying, someone--call him Al--is such-and-such]. For that reason the letter used is not "free" in order to generalize on it (bring in a universal quantifier with V or D). When we repeat this process we need to use another name that has not already appeared (and, obviously, not one in the intended conclusion).

To avoid problems the best procedure is to instantiate existential quantifiers before instantiating universal ones. If we have both FGD and GHE to work with, we put down GaHaA (assuming no a already appears) before we put down FaGaC. If we have FGE and GHE then we would use FaGaA and GbHbA.

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