Question

Hello Rabbi,
A few questions:
In your writings there is a lot of discussion of different thinkers and the various arguments they raise. In some cases I understood from you that there are relatively weak arguments, and some strong ones that can still be described as holding their ground even today. I wanted to ask what, in the Rabbi's opinion, are the strong and durable arguments of each school that cannot be refuted unequivocally. For example, I understood from your writings that Descartes' cogito and Anselm's ontological proof are the strong arguments in the rationalist camp, which still stand and still have not been decisively refuted. Are these the only rationalist arguments that can be treated this way? (That is, as purely logical arguments which, beyond their specific claim, prove that one can use purely logical arguments to add information about the world.) And what are the strong arguments in the empiricist position that cannot be decisively refuted?
In addition, I wanted to ask: the Rabbi usually divides the schools into rationalism and empiricism. Are there other major philosophical schools on the same "level" as these schools, or are all the other schools simply qualifications and innovations within the rationalist-empiricist continuum? (Are there other different approaches to gathering information about the world that are neither rationalist nor empiricist? The only examples that perhaps come close, for the sake of clarifying the issue, are belief in an inner world, intuition (?), belief in tradition, or something like that?)
Thank you very much!