[The reasons why the synthesis is needed between Faith and Reason is clear to anyone who has observed communities that are based on faith alone, and reject reason. Religious fanaticism leads to anything except good character. Why this should be so is an open question, but a hint can be gained from the Rambam in his showing the intermediate step of Natural Law was necessary between the "ravings of the Sabians" and the Giving of Torah. Also it is possible to suggest that Torah in its pure form is on the level of the Platonic forms that the hit the ground of being --the individual. דרך ארץ קדמה לתורה. Another suggestion is it is a kind of Hegelian dialectical process. [I mean to say that being things need a ground of being to exist. Being itself. Platonic forms hit that ground and become individual things]
The goal would be to make full use of the Rambam and the Ari, the Gra, and Kant and Hegel.
I mentioned this a few times about 6 years ago. But today it seems all the more necessary.
I admit most of the work in this direction was already done by Dr Kelley Ross. However he does ignore important ideas of Hegel. But the main ideas are already in place. That is you would have to equate what is called immediate non-intuitive knowledge with faith.
Falsification is not how new ideas are discovered. It is an important part of the Kant Friesian system but does not explain the processes of reason. But neither does Dr Michael Huemer where reason simply recognizes universals. However Dr Huemer does have a kind of dialectical process in his system in which things that are recognize by reason can be defeated by other concepts that turn out to have more intuitively clear consequences. So in any case Hegel's dialectical process in fact seem to be at the root of all new advances in reason
But furthermore the dialectical process the way most understand it is confined to reason but there does not seem to be any reason to limit it in that range. It could easily work between conflicting areas of value as per the Kant-Friesian system
Even if I am not the man for this job clearly the job in need to be done. It is perfectly possible to get a good synthesis of Reason and Revelation and to base it on the labors of predecessors like the Rambam -and also to have the sense of what to reject. [I think people are right for taking the Guide of the Rambam as the best guide to how to go about this. The purpose of this is that without it, authentic Torah is not possible. People go into a whole array of delusions they image are real Torah and you end up with the nightmare world of the religious.