A Valid Argument with Schrödinger's Paradox

In deductive logic, an argument is valid if and only if it is necessary that if all its premises are true, its conclusion is true. By this loophole in the definition, any argument with a contradiction in its premises is valid. As long as there can't exist a world where the contradiction is possible due to logic, then it is valid.

After being aware of the premises above, Schrödinger's Paradox, in which a cat is both alive and dead simultaneously, immediately popped up in my head. I figured I didn't know enough about the Nobel prize winning paradox to determine the accuracy of this definition so I decided to do some research. This is what I summarized from National Geographic:

In the Schrödinger experiment, a cat, poison, a geiger counter, radioactive material and a hammer are sealed inside a container. The amount of radioactive material is minuscule enough that it only had a 50/50 shot of being detected over the course of an hour. If the geiger counter detects the radiation, the hammer would smash the poison and kill the cat. Until someone opens the container and observes the system, it is impossible to predict whether the cat is alive or dead. Therefore, until the system collapses into one configuration, the cat would exist in the superposition state of being both alive and dead.

Schrödinger's Cat Paradox is actually an analogy to illustrate the dual nature of a wave function. A wave function describes all of the possible states that such particles can have.

"If you put the cat in the box, and if there's no way of saying what the cat is doing, you have to treat it as if it's doing all of the possible things—being living and dead—at the same time," explains Eric Martell, an associate professor of physics and astronomy at Millikin University. "If you try to make predictions and you assume you know the status of the cat, you're probably going to be wrong. If, on the other hand, you assume it's in a combination of all of the possible states that it can be, you'll be correct." Immediately upon looking at the cat, an observer would immediately know if the cat was alive or dead and the "superposition" of the cat—the idea that it was in both states—would collapse into either the knowledge that "the cat is alive" or "the cat is dead," but not both.

After reading, I know for a fact that a cat can not be both simultaneously alive and dead, but I still wondered if an electron in the micro atomic world can. The answer I got was that even though really, really tiny things don't obey Newton's Laws, an atom or electron still can not be at both places at the same time, therefore the valid definition is correct in all possible worlds.