If something is possible, then its truth exists in a possible world. Thus, although in a possible world, its truth does exist. So it's true. Thus, anything possible is also true. In other words, if a proposition is possible, then it's true.

Another argument supporting this conclusion is that all possible truths are truths. They're truths, truths that are possible. The set of all possible truths is a subset of the set of all truths.

It's also self-evident that if a proposition is true, then it's possible. So we get the following argument.

(1) If a proposition is true, then it's possible.

(2) If a proposition is possible, then it's true.

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Therefore by Biconditional Introduction, (3) **A proposition is true if and only if it's possible.**

So, truth and possibility are logically equivalent. Therefore, we can validly define each as the other. Truth is possibility and possibility is truth.