"That one believes the cat is alive and also believes the cat is not alive"
Explain how both of these can happen simultaneously, please.
Lol you are the one that said this was Impossible, you have the burden of proof.
With the belief that you actually are interested in understanding-
Take any two mutually exclusive positions. Let us use the flip of a coin.
The coin is flipped and covered.
I ask two questions.
Is it true that the coin is heads?
Is it true that the coin is tails?
Now given that the coin has equal chance, we would likely hear the answer "I don't know"
But we don't get to ask questions. We have to make propositions.
Heads is facing up.
Tails is facing up.
Now most people are influenced by skepticism. They reject both propositions until further evidence is discovered.
They are not accepting that neither proposition is true. This is because they believe one of the two propositions that they did not accept as true, is actually true.
Similarly, we can accept both of the propositions as true. I can look at that flipped coin and believe it is heads and believe it is tails, knowing that one of those beliefs will be wrong. But until further evidence is discovered that allows me to conclude it is not heads or tails I can believe both.
Perhaps a different scenario will help. One with justice in mind. Imagine two people. One of these two people committed mass murder and torture. But you do not know which one is guilty. With law we approach from the skeptic angle. Both are innocent until proven guilty.
However, in a clue type situation, where we find ourselves trapped in a mansion with these two, we act differently. Instead of treating these two as if neither one or the other is guilty, we treat them both as guilty, lest we become the next victim.
So while the answer to your question is simply one can believe the cat is alive, one can believe the cat is dead, and one can believe that one of the aforementioned beliefs will eventually prove wrong is enough to establish that one need not believe both the state of being alive and the state of being not alive are occurring simultaneously.
I should add that there is now a quantum piece of the puzzle wherein some do believe that both occur simultaneously until observation occurs. That people believe such should in itself indicate that belief in both is possible.