Replying to you, but really for bypel's benefit.
Definitions of truth are the wrong place to start here. Defining truth is hard, and you don't need to.
To use logic you have to start with some assumptions. What those assumptions are doesn't matter, only their relations to each other, which is why we can formalize logic. Given "A" and "A implies B", you know that B, no matter what A and B are replaced with. The inference rules of a logic preserve the truth of the statements they operate on, so you can use logic to find out what is implicit in a set of statements you have assumed the truth of for arbitrary reasons, but only what is implicit in a set of statements you have assumed the truth of for arbitrary reasons.
Now, a common method in math and philosophy is to provisionally assume some statement and see if it implies something contradictory or (for philosophy only) unacceptable. This can help you decide to reject a statement, and in this way logic can help you decide what to believe, but you still have to arbitrarily decide what statements to analyze, and failure to find a reason to reject something doesn't imply that it's true.
But you where the statements logic operates on come from isn't a problem logic helps you with. In science you can get them through observation and statistics, but even an individual scientist doesn't do every experiment themselves. For the most part we all (provisionally) accept or reject things others have told us for arbitrary reasons, and in order to share our knowledge and beliefs we need to convince others to (provisionally) accept the things we tell them. That is what rhetoric is for. Plato rightly distrusted it because you can use the tools of rhetoric to mislead people, but as we can't directly share our experiences it's the only tool there is.