It's interesting that in the Warhammer 40k universe, the Tech-Priests have a special class of "Rune Priests" who happen to both specialise in the ritualistic and religious part of their cult, and are capable of intuitive speculation and innovation. Probably the only ones capable of it since Cult Mechanicus is notorious for being utterly incapable of any technological development and innovation, all they do is to accumulate past construction templates and guard it like relics.
But this actually fit the actual history of scientific development in Europe. Most historians of the Middle Ages would speak of the struggle between faith and reason as the works of Aristotle and the pagan philosophers percolated through Western Europe, clashing with Church authorities until the final triumph of Thomism and the "successful" reconciliation of faith and reason.
Edward Grant in his work The Foundations of Modern Science in the Middle Ages however advances an ironic twist to this common tale. He argues that the Catholic Church's reactionary backlash against Aristotelianism, cumulating in the Condemnation of 1277 where over 200 Aristotelian propositions were singled out, actually provided the conceptual toolsets for transcending the limits of Aristotelian science, paving the way for modern physics. The Catholic Church insisted that God's absolute power was not bound to so-called natural laws prescribed by Aristotelian cosmology and could create universes with radically different laws. Here is Grant's detailed explanation:
The widespread assumption of "natural impossibilities," or counterfactuals, or, as they are sometimes called, "thought experiments," as described in chapters 5 and 7, was a significant aspect of medieval methodology. A hypothetical occurrence would have been considered "naturally impossible" if it were thought inconceivable within the accepted framework of Aristotelian physics and cosmology. Natural impossibilities were derived largely from the concept of God's absolute power as embodied in the Condemnation of 1277. Counterfactuals allowed the imagination to soar. In the Middle Ages, such thinking resulted in conclusions that challenged aspects of Aristotle's physics. Whereas Aristotle had shown that other worlds were impossible, medieval scholastics showed not only that other worlds were possible but that they would be compatible with our world. The novel replies that emerged from the physics and cosmology of counterfactuals did not cause the overthrow of the Aristotelian world view, but they did challenge some of its fundamental principles. They created an awareness that things could be quite different than was dreamt of in Aristotle's philosophy. But they accomplished more than that. Besides influencing scholastic authors in the sixteenth and seventeenth centuries, this characteristically medieval approach also influenced important nonscholastics, who were aware of the topics debated by scholastics.
One of the most fruitful ideas that passed from the Middle Ages to the seventeenth century was that God could annihilate matter and leave behind a vacuum. For example, John Locke based his argument for the existence of a three-dimensional void space on the assumption that God could annihilate any part of matter. If God did destroy a body, a vacuum would remain, "for it is evident that the space that was filled by the parts of the annihilated body will still remain, and be a space without a body."
[...]
A significant natural impossibility that derived from the Condemnation of 1277 involved article 49/ which made it mandatory after 1277 to concede that God could move the world rectilinearly, despite the vacuum that might be left behind. More than an echo of this imaginary manifestation of God's absolute power reverberated through the seventeenth century. When Gassendi declared that "it is not the case that if God were to move the World from its present location, that space would follow accordingly and move along with it," he was using the supernatural motion of the world as a convenient support for his belief in the absolute immobility of infinite space.33 As spokesman for Isaac Newton, Samuel Clarke (1675-1729)/ in his dispute with Leibniz, also defended the existence of absolute space when he argued that "if space was nothing but the order of things coexisting [as Leibniz maintained]; it would follow that if God should remove the whole material world entire, with any swiftness whatsoever; yet it would still always continue in the same place." Finally, the power of counterfactuals is nowhere more impressively illustrated than in the principle of inertia, which Newton proclaimed as the first law of motion in The Mathematical Principles of Natural Philosophy (1687): "Every body continues [or perseveres] in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it." In medieval intellectual culture, where observation and experiment played negligible roles, counterfactuals were a powerful tool, because they emphasized metaphysics, logic, and theology, the very subjects in which medieval natural philosophers excelled.
The Church as such played a vital role in not only putting natural philosophy and physics firmly under the thumb of an omnipotent God who is not bound to their prescriptions and laws, but vitally enabled medieval philosophers and later Early Modern scientists literally imagine all kinds of other hypothetical models and ways in which God could have made the universe transcending the limits imposed by Aristotelian physics and even what our own eyes perceive. Where would Newton be without the ability to imagine an object in perpetual motion in space? An omnipotent God opened up infinite imaginative space for the medieval man, to borrow God's infinite power and dream of all the ways in which He could have made the universe in their mind's eye.