Lanza quotes a famous experiment of a cat in a box to illustrate his argument: the cat is "both alive and dead," he writes: "both possibilities exist until you open the box and investigate."
Of course, they don't. If the cat is dead, it won't come alive when you open the box. The cat is dead or alive regardless of your perception. Existence is exists, even when you close you eyes. As Ayn Rand put it in Atlas Shrugged (1957):
Existence exists---and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists.
If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms. A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something. If that which you claim to perceive does not exist, what you possess is not consciousness.
Whatever the degree of your knowledge, these two---existence and consciousness---are axioms you cannot escape, these two are the irreducible primaries implied in any action you undertake, in any part of your knowledge and in its sum, from the first ray of light you perceive at the start of your life to the widest erudition you might acquire at its end. Whether you know the shape of a pebble or the structure of a solar system, the axioms remain the same: that it exists and that you know it.
To exist is to be something, as distinguished from the nothing of nonexistence, it is to be an entity of a specific nature made of specific attributes. Centuries ago [Aristotle] stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. [...] Existence is Identity, Consciousness is Identification.
(The rest of Lanza's article is useless mumbo jumbo meant to suggest that we're all helpless victims of a malevolent universe playing tricks on us, which is why I haven't bothered to quote from it more extensively.)