You may have left out the most important machlokus related to the topic, which is whether the first of the Ten Commandments is a foundational prelude or a commandment in and of itself. If the former, God is a fact and you're either in or out, no point in paskening belief. If the latter, then there's no need to pasken, since the imperative to believe is right there at the beginning. Perhaps you could even say (and you wouldn't be the first commentator to do so) that given this and many other examples there is no difference between doing and believing, between ritual and spiritual law. That's a distinction for the non-Jewish world, particularly the modern world. Yes, there may be a commandment to believe, but it's no different from a commandment to wear tefillin -- we do both because we are recipients of a tradition that argues quite persuasively for itself, including that we personally heard God say believe in him, and to do what we're told.
Good point, that's an important discussion. I would just add that according to Gil Student's opinion mentioned in the piece--dfferentiating between "foundational belief" and other beliefs--belief in God would be a “foundational belief". So it wouldn't necessarily follow that since there's a requirement to believe in God (either as a foundational prelude or a commandment in and of itself), there would be no difference between doing and believing in *all cases* of hashkafa
You may have left out the most important machlokus related to the topic, which is whether the first of the Ten Commandments is a foundational prelude or a commandment in and of itself. If the former, God is a fact and you're either in or out, no point in paskening belief. If the latter, then there's no need to pasken, since the imperative to believe is right there at the beginning. Perhaps you could even say (and you wouldn't be the first commentator to do so) that given this and many other examples there is no difference between doing and believing, between ritual and spiritual law. That's a distinction for the non-Jewish world, particularly the modern world. Yes, there may be a commandment to believe, but it's no different from a commandment to wear tefillin -- we do both because we are recipients of a tradition that argues quite persuasively for itself, including that we personally heard God say believe in him, and to do what we're told.
Good point, that's an important discussion. I would just add that according to Gil Student's opinion mentioned in the piece--dfferentiating between "foundational belief" and other beliefs--belief in God would be a “foundational belief". So it wouldn't necessarily follow that since there's a requirement to believe in God (either as a foundational prelude or a commandment in and of itself), there would be no difference between doing and believing in *all cases* of hashkafa