There is no absolute truth in mathematics and logics. There are many consistent mathematical systems, consistent in the sense that they are not breaking the basic rules. But there is no absolute way of knowing that the basic rules are true. And there are limitless basic rules that can be chosen. Different basic rules gives different systems, like the intuitionist logic,predicate logic or fuzzy logic. So why then is mathematics/logic interesting and why are some systems studied instead of others? I would argue it is because mathematics is empirical. There are some logical and mathematical systems that are more true than others. Those systems that more closely follow the real world are more true than others. So truth in mathematics is ultimately derived from physics. Those mathematics that gives physicists more accurate models are more true.