This is not a trick question, nor a nonsense one either, unless you mean perfect nonsense, which is what immortality is. So yes, it is perfectly nonsensical to posit an immortal soul, but mere nonsense to deny it. I will explain what I mean. At some point in this post.
Take, for example, universals, which uniquely characterize human intelligence. They are a necessary condition for abstract thought, being that they form the basis of abstraction. Frankly, one cannot say anything without deploying universals, since words are already universals.
Augros makes the point that universals cannot possibly exist in the physical structure of our brains, any more than they could on a sheet of paper. You cannot draw a universal -- say, a tree -- without particularizing it. But the fact that you can particularize it means you possess implicit knowledge of the universal.
Indeed, the drawing is proof of this pre- or trans- or foreknowledge -- a three-way knowledge between the idea, the drawing, and the third party who can see that the drawing is of a tree, and thereby retrieve the universal from the particular.
No universal could fit into the brain, since the brain is finite, while the universal is infinite: "every universal enables its possessor to know things about an infinity of individuals." Thus, our minds differ from the minds of animals "as the nonmaterial from the material." Critically, "this is no mere difference of degree," but rather, of kind.
Again, man is not a new animal, but a new reality -- very similar to how life is not just a new kind of matter, but a new world, the biosphere. Imagine reducing life to matter and calling yourself a biologist. Now, imagine reducing mind to brain and calling yourself a psychologist. Congratulations! You're tenured.
The next step is to realize that, not only can universals not be stored in the brain, they cannot be a product of the brain:
Your intellect is not a power in your brain or in any bodily organ. It is incorporeal. Accordingly, it does not depend on your brain or on any part of your body as a power depends on an organ to host it.
your intellect is to your brain as your sense of sight is to visible objects. Without visible objects, your sense of sight can exist, but it will have nothing to do. Without your brain, your intellect can exist, but it will have nothing to do.
Bottom line: your intellect "depends on your brain only for its objects, not for its power." It is in, but not of, matter. To understand the material world is to have transcended it.
Clearly, the Incarnation emphasizes this reality. In Genesis, there is the general creation, followed by the special creation of man in the course of day six. Just as Jesus is two natures in one person, so too, in a sense, are we all. In our case, clearly, we have bodies and intellects, and yet, we are one person. But Genesis 3 suggests that we have become divided -- against the world, against, ourselves, against others, and against the Creator.
"You are part body and part spirit, a mammal with a nonmaterial mind capable of knowing eternal truths. Where in the world can a being like you have come from?" Is it even possible that we came from "within" the world, a la natural selection? How can the world transcend the world? Or, how could finitude give rise to infinitude?
This infinitude of the soul converges on the Absolute, for "Cosmic evolution cannot surpass intellectual souls. They represent a destination more than a middle of the journey. They are evolution's end." And as we know, the end is chronologically last but ontologically first, i.e., the telos of material and efficient causation.
Eh. I just go back to Schuon, since he's so concise and pointed. The whole shocking Doctrine in a sharpshorting paragraph:
All the knowledge the brain can hold is nothing in the light of Truth even if it is immeasurably rich from a human point of view. Metaphysical knowledge is like a divine seed in the heart; thoughts represent only faint glimmers of it.
The imprint of the divine Light in human darkness, the passage from the Infinite to the finite, the contact between the Absolute and the contingent -- this is the whole mystery of intellection. --Spiritual Perspectives and Human Facts