The phrase "faith within the bounds of reason" refers to Immanuel Kant's radical notion that religion (or faith) could be deduced by logic alone. In 1793, Kant published the treatise "Religion within the Bounds of Reason Alone" (variously translated). In it, he defined religion as personal acceptance of divine law and ethical obligations. He argued that any historically specific iteration of religion could not contain the entire truth. He claimed that true religion supersedes the specifics of place and time. Moreover, he argued, individuals can deduce moral law by exercising their powers of perception and reason.
This doctrine put Kant at odds with the common thought of his day, which presumed the unique truth of Christian dogma. For many of Kant's contemporaries, faith and reason were strictly at odds. The idea that religious devotion need not involve a rejection of scientific reasoning was therefore quite controversial.