Logic And Timelines

When I studied logic at University, I learned:

if p, then not not-p;
not (p and not-p);
either p or not-p.

For example, if it is the case that Socrates was executed in 399 BC, then it is not the case that Socrates was not executed in 399 BC - unless there are alternative timelines, in which case logical consistency is maintained by making our propositions, p and not-p, more specific. Thus, if it is the case that Socrates was executed in 399 BC in timeline 1, then it is not the case that Socrates was not executed in 399 BC in timeline 1.

This may seem obvious but I meet people who get their idea of logic not from Aristotle or his successors but from Mr Spock. "Logic" means something like thinking rigidly and unemotionally instead of just thinking and speaking consistently which everyone tries to do. No one openly contradicts himself on a matter of fact, then says, "I am free to contradict myself because I am not bound by logic like Mr Spock." And anyone who did say that would not succeed in telling us anything. "Socrates both was and was not executed in 399 BC in timeline 1 and I am free to contradict myself..."

It might be imagined that a rigidly "logical" thinker, having denied that Socrates could both be executed and not be executed in 399 BC, would then compound his rigidity by denying that there can be alternative timelines. Merely to reply that Mr Spock experiences alternative timelines is to confuse a conceptual question with an empirical question.

A conceptual question: Are alternative timelines possible?
Answer: Yes. There is no reason why not. No contradiction is involved.

An empirical question: Do alternative timelines in fact exist?
Answer, within the framework of the Star Trek narrative: Yes. They have been discovered and entered.

Not only Star Trek. We are grateful for the alternative timelines of Poul Anderson, SM Stirling and Harry Turtledove.