Several philosophical ideas have had a direct influence on the course of physics. Maupertuis invented the principle of least action under the influence of Leibniz's philosophy that this is "the best of all possible worlds", and that God takes the best way to accomplish His ends.
The principle of least action was taken up by Euler and developed into the calculus of variations. Lagrange then adopted that and in his Mechanique Analytique introduced his Action- Lagrangean method based on it. Hamilton modified Lagrange's method into his own Hamiltonian method, and these two methods are everywhere in modern physics.
Emmy Noether proved that every symmetry of the Lagrangean induces a conserved quantity in the equations of motion. Maupertuis would have been delighted by that, and seen it as a confirmation of God's benevolence.