The great early sociologist, Max Weber, wrote, "With Newton we became disenchanted and entered Modernity". I believe Weber was right, we remain disenchanted, and are inarticulately lost in Modernity. Many of us seem to sense the end of something, perhaps a futile meaninglessness in our Modernity.
Was Weber right? And how is it based on Science? Yes, Weber was right, and our disenchantment remains because, at least in part, we remain Newton's children.
Before Newton in the previous two centuries in Europe, we had the black and white magi. Kepler was the last of the white magi hoping the Platonic solids would state the orbits of the planets only to surpass that, and Aristotle's certainty that orbits were perfect, thus were circles, when Kepler discovered orbits were ellipses.
But the black magi sought occult knowledge to stand nature on her head and wrest their due, a misguided use of God's promise to Adam in Genesis. In those centuries we lived with magic and were enchanted.
Newton changed everything with his three laws of motion, universal gravitation, and his invention of differential and integral calculus. Consider seven billiard balls rolling on a billiard table. What will they do? Newton taught us to measure initial conditions of positions and momenta of the balls, the boundary conditions of the table, then write the forces between the balls (and walls) using differential equation forms of his laws of motion. Then, said Newton, we were to integrate his equations of motion to obtain the forever trajectories of the balls - ignoring friction for the moment. But integration is deduction of the consequences of the differential equations, and deduction is logical entailment. So Newton, in what I'll call the Newtonian Paradigm, gave us both classical physics and an entirely entailed becoming of physical systems.
With Laplace a bit more than a century later, we obtain his view that, were all the positions and momenta of all the particles in the universe known, a giant computer in the sky, the Laplacian Demon, could, using Newton's laws, calculate the entire entailed future and past of the universe. This is the birth of modern reductionism in physics, Weinberg's Dream of a Final Theory that will entail all that becomes in the universe.
Quantum mechanics does not change this fundamental view. In place of deterministic entailed trajectories, we have from the Schrodinger equation the entailed trajectory of a probability distribution, obtained as the squares of the amplitudes of the Schrodinger linear wave equation. In modern physics, General Relativity and Quantum Mechanics, all that becomes in the universe is entailed. Nothing novel can arise. And, profoundly, we remain disenchanted. There can be no natural magic.
From Newton we get the Enlightenment, our Age of Reason, thence the Industrial Revolution, and then the rise of Modernity. We remain disenchanted.
Beyond the Newtonian Paradigm
I claim that at least for the living evolving world, the evolving biosphere, human economy, legal systems, culture and history, no laws at all entail the becoming of these worlds into their forever newly emerging, but unpre-statable "adjacent possible opportunities" which, in evolution are not achieved by the "action" of natural selection, nor in human life are these adjacent possible opportunities typically "achieved" by human intent.
Because these evolutionary processes typically cannot be pre-stated, the very phase space of biological, economic, cultural, legal evolution keeps changing in unpre-statable ways. In physics we can always pre-state the phase space, hence can write laws of motion, hence can integrate them to obtain the entailed becoming of the physical system. Because in the evolution of life, and human life, the very phase space changes in unpre-statable ways, we can write no laws of motion. Nor can we noncircularly pre-state the boundary conditions on this evolution, so we neither have laws of motion, nor their boundary conditions so cannot integrate the entailed trajectories of the laws of motion we do not have anyway.
To show why we cannot pre-state the evolution of the biosphere I start in a strange place: Please list for me ALL the uses of a screw driver. Well, screw in a screw, open a can of paint, wedge a door open, or shut, stab an assailant, tie to a stick to make a fish spear, rent the spear to locals for 5% of the catch....
Here seem to be the new and essential issues: 1) The uses of a screw driver are indefinite in number. 2) These uses, unlike the integers, are in no way naturally orderable, that is the uses are unorderable.
But these two premises imply that no effective procedure, or algorithm, can list all the uses of a screw driver. This is the famous frame problem in algorithmic Computer Science, unsolved since Turing and his machine.
But all that has to happen in the evolution of a bacterium in, say, some new environment, is that a molecular screw driver "finds a use" that enhances the fitness of the bacterium, that there be heritable variance for that "use", then Natural Selection will "pull out" this new use by selecting at the level of the bacterium, not the molecular screw driver.
The profound implication of the newly selected bacterium with the molecular screw driver is that this evolutionary step changes the very phase space of evolution in an unpre-statable way. Hence we can write no laws of motion for this evolution, nor can we pre-state the niche boundary conditions non-circularly, so we could not even integrate the laws of motion we cannot write in the first place. Since we cannot list all the uses of the molecular screw-driver we do not know the sample space of evolution.
Evolution of the biosphere and, a fortiori, of the human economy, legal systems, culture and history, are entailed by no laws at all. True novelty can arise, beyond the Newtonian Paradigm broken beyond the watershed of life.
Re-enchantment, a path beyond Modernity, is open to us.