The attitude towards approaches

Hello Rabbi,
There are many philosophical approaches – materialism, idealism, postmodernism, and more. It seems that in the end any approach can stand on its own once a person accepts it. For example, if I, as a fundamentalist, try to convince a postmodernist that my approach is more correct than his, I will never succeed (and he will never succeed in convincing me either).
It seems to me that the reason for this is because there are no philosophical principles that can determine which approach is more correct. It works the other way around. After we have chosen an approach, there can be philosophical principles that will underpin the method. But the choice between any method will always be up to each person themselves.
Since this is the case, I would like to ask – how can I know which approach is more correct? If each approach is the inclination of each person’s private heart, doesn’t that mean that my choice of approach should be questioned? What should be the attitude towards approaches?
Thanks in advance.