The powerful arguments of the various philosophical schools

Hello Rabbi,
A few questions:
In your writings there are many references to different thinkers and different arguments that they raise, in some cases I understood from you that there are relatively weak arguments and some strong ones that can still be defined as standing today. I wanted to ask what, in the Rabbi's opinion, are the strong and enduring arguments of each school that cannot be refuted unequivocally. For example, I understood from the Rabbi's writings that Descartes' cogito and Anselm's ontological view are the strong arguments in the camp of the rationalist school, which still stand and have not yet been refuted unequivocally. Are they the only rationalist arguments that can be treated in this way? (As pure logical arguments that, beyond their specific claim, prove that pure logical arguments can be used as sources of information about the world). And what are the strong arguments that cannot be refuted unequivocally in the empiricist position?
Additionally, I wanted to ask, the Rabbi often divides the schools into rationalism and empiricism, are there other major philosophical schools at the "level" of these schools or are all the other schools simply classifications and innovations within the rationalist-empiricist continuum? (Are there other different approaches to gathering information about the world that are not rationalist/empiricist? The only examples that might come close to clarifying the matter are belief in an inner world, intuition (?), belief in tradition, or something like that?)
Thank you very much!