"Pragmatism" and "practicality" aren't the same things. When a person says, "I'm just being practical," he's probably being highly impractical.
It normally means he's just thinking rationally: with the certitude of his left hemisphere, which excludes everything that the right hemisphere can teach him, which includes a massive and mysterious mound of truth that is filled with holes and quicksand, like subtlety and paradox.
"Being practical," therefore, is just "taking a mental shortcut to get the solution sought by the left hemisphere to deal with the project in front of it."
As I've repeatedly emphasized (because McGilchrist repeatedly emphasizes), it's not a bad thing. But it is an incomplete thing. An untruthful thing. It's like flying from Detroit to Los Angeles and telling people that your trip took you through Illinois, Iowa, Nebraska, Colorado, and Nevada. It's complete bulls***. It's perfectly fine to travel to Los Angeles and might be a very good thing indeed, but it doesn't mean you hit all points in between.
Such it is with the left hemisphere and its efforts to be practical. It gets us to L.A., which is great, but when it turns around and congratulates us on traversing the United States, we must scoff. When a person says, "I'm just being practical," we can likewise scoff if, by "practical," he means he has taken into account everything that needs to be taken account of.
Pragmatism, on the other hand, tries to take into account everything that needs to be taken account of. And what "needs to be taken account of"? Everything that affects what we're trying to figure out.
This includes modes of consciousness that exist in the vast bulk of mankind. This is the approach of William James, whose classic, The Varieties of Religious Experience, says, "Look, I'm not saying the claimed metaphysics underlying religion are accurate or true, but the fact is, the religious experience is widespread and has a tremendous impact. We can't ignore it or, worse, ridicule it. We need to accept it as a fact and see how it affects our approach to the world, even if it means that approach cannot be governed solely by the practical concerns of the hard sciences."
It's an approach that the left hemisphere doesn't appreciate. It muddies the practical waters of hard science.
It also muddies the practical waters of every academic discipline. When it comes to history, there are a large number of facts that are inconvenient to the "Whig interpretation of history," which sees history as a relentless march of progress informed by the designs of the left hemisphere.
Exhibit A: The Resurrection. It is a historical fact. If, for instance, we had empirical evidence that, once every couple hundred years, a person rose from the dead and it has happened about ten times in recorded history, no historian would doubt that Christ rose from the dead. The historical evidence is pretty solid that he rose from the dead, but it's rejected by most historians because it is also a metaphysical truth that muddies the historian's presumptions (narrative) and thereby hinders his progress on whatever projects he's working on.
Exhibit B: Miracles attributed to the saints, like levitation. They did fly, and it baffles historians who prefer to reject that fact because it doesn't fit their narrative. It is an "inconvenient" truth . . . an "impractical truth" that hinders the left hemisphere's mental historical shortcuts.
Such a rejection is practical, but it's not pragmatic. The most excellent and pragmatic historian, Carlos Eire, has apparently attempted to redress it.