Possible And Impossible Universes

In philosophy, in physics and in science fiction, including some works by Poul Anderson, we contemplate multiple universes, including alternative versions of otherwise familiar human history. The proposition that the German lost World War II is true in our universe but not in every possible universe. What propositions would be true in every possible universe? Many, e.g.:

1+1=2;

if ((if p, then q) and p), then q;

all white men are men -

- in other words, any proposition that is true by virtue of the meanings of the terms used. We do not have to observe every white man to check whether one of them turns out not to be a man because one of them turning out not to be a man has already been ruled out by the phrase "white men." On other hand, "All white men are conceited" is empirically falsifiable.

I have heard it argued that a universe to which mathematics or logic did not apply would not be an impossibility but merely a universe that we would be unable to perceive or understand. I think that this argument misses the meaning of "logic." Logic is not a set of rules that happen to apply in some situations but might not apply in others. It is the kind of consistency without which we would be unable to describe any situation. Thus, if a man began a talk on Socrates by stating that Socrates was executed in 399 BC and ended the talk by stating that Socrates was executed in 299 BC and if, when questioned about this contradiction, he replied that he is free to contradict himself because logic is not applicable, then he would not succeed in telling us when Socrates was executed.

A geometrical figure cannot be triangular and square at the same time. A surface cannot be red all over and blue all over to a single observer at the same time.

Every narrative assumes two propositions: 

"There is a narrative"; 

"The narrative is (fill in the blank)."

Spatially distinct and temporally enduring subjects and objects of consciousness are part of the first proposition. not of the second.

However, that still leaves a lot of scope for other possible universe to differ from ours. Poul Anderson gives us the Romans losing the Second Punic War and worlds ruled by magic instead of physics.