"then religious institutions are diametrically opposed due to their "turtles all the way down" reliance on irrationality"
That's a pretty broad statement.
"no matter how deep you go eventually you have to make a leap of faith off of the rationality train."
The same is true of mathematics. Eventually you need to make certain assumptions that cannot be proved, or else you would have circular logic (among other issues).
The real mark of irrationality is an unwillingness to resolve or even acknowledge inconsistencies. Some religions have this feature, usually dressed up in a "this tests your faith" argument. Other religions demand that inconsistencies be resolved by religious authorities or by practitioners willing to devote time and effort.
In the past century, a large number of religious leaders from various religious have adjusted their doctrines and teachings in the face of scientific results. Not every religion is based on denying reality or condemning people who question core beliefs. I know an ultra-Orthodox rabbi who acknowledges that it is possible to be an observant, orthodox Jew who does not believe in God.
1) Yes, it is a broad statement about institutions devoted to religion.
2) Mathematics is based on logic, which doesn't need phenomenal "facts", just logical consistency. Physics, which uses mathematics needs both phenomenal facts and logical consistency, and since the more phenomenal facts can be discovered, the physical models can change. Mathematics is a tool of rationality, not a replacement for it.
3) Somewhat agreed that irrationality is an unwillingness to accept models rationally created. If the model of a system isn't created by phenomenal facts and logical consistency, then it is irrational.
That's a pretty broad statement.
"no matter how deep you go eventually you have to make a leap of faith off of the rationality train."
The same is true of mathematics. Eventually you need to make certain assumptions that cannot be proved, or else you would have circular logic (among other issues).
The real mark of irrationality is an unwillingness to resolve or even acknowledge inconsistencies. Some religions have this feature, usually dressed up in a "this tests your faith" argument. Other religions demand that inconsistencies be resolved by religious authorities or by practitioners willing to devote time and effort.
In the past century, a large number of religious leaders from various religious have adjusted their doctrines and teachings in the face of scientific results. Not every religion is based on denying reality or condemning people who question core beliefs. I know an ultra-Orthodox rabbi who acknowledges that it is possible to be an observant, orthodox Jew who does not believe in God.