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If logic applies in all possible worlds, does that mean that that which is logic in our world stays the same in all of them, since we define those worlds as possible through it, meaning that the proposition by which we define logic in our world is true in all possible worlds? Wouldn't that mean that the definition of logic should be a tautology, and thus uninformative? This has been on my mind for quite some time and I'd really appreciate some insight, since I haven't seen an uninformative definition of logic, but don't understand the fault of my reasoning. Thanks.

Edit: A possible world is a taken to be a consistent and complete description of how things might have been or might in fact be.

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Logic only deals with structures that preserve the validity of propositions independently of their content. Because of this independence from content, logic doesn't serve to be informative about anything. It simply shows how propositions can be restructured while maintaining their truth value.

Bertrand Russell summarized this idea well:

"Propositions which form part of logic, or can be proved by logic, are all tautologies—i.e. they show that certain different sets of symbols are different ways of saying the same thing, or that one set says part of what the other says. Suppose I say: 'If p implies q, then not-q implies not-p.' Wittgenstein asserts that 'p implies q' and not 'not-q implies not-p' are merely different symbols for one proposition: the fact which makes one true (or false) is the same as the fact which makes the other true (or false). Such propositions, therefore, are really concerned with symbols." (Bertrand Russell, Analysis of Matter, p. 171)

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