Chaos theory is the study of systems that are highly sensitive to initial conditions.

It is important to stress that there is nothing random or undetermined about chaos theory. It involves no quantum indeterminacy, which is the basis for ontological chance. Although it exhibits behaviors that resemble some phenomena in the real world, they are metaphors for behaviors, not physical explanations.

Chaos should not be confused with unpredictability, just as determinism should not be confused with predictability. The fundamental importance of chaos theory is its application to systems that are extremely sensitive to initial conditions. Chaotic systems are deterministic, but not predictable. Their unpredictability does not mean that they are random or indeterministic, as many philosophers and a few scientists who dislike quantum mechanics have mistakenly believed (e.g., Ilya Prigogine).

Some philosophers appear to believe that chaos theory can provide all the randomness need to prevent free will from being deterministic (e.g., Daniel Dennett). Some think that non-linear chaotic behavior disproves the determinism of Laplace's super-intelligent demon. Laplace probably knew that the information required by the demon was unobtainable. Isaac Newton certainly knew that his observations could not confirm his theory to arbitrary accuracy needed to prove perfect determinism.

Ludwig Boltzmann, his admirer and contemporary Franz Exner, and Exner's student Erwin Schrödinger, often pointed out that deterministic theories go beyond the available evidence. Popularization of physical theories has often confused not just the public, but even philosophers of science.

On the three hundredth anniversary of Newton’s Principia, Sir James Lighthill gave a lecture to the Royal Society, lamenting the confusion between Newton's classical mechanical determinism and the apparent claim of perfect predictability:

”We are all deeply conscious today that the enthusiasm of our forebears for the marvellous achievements of Newtonian mechanics led them to make generalizations in this area of predictability which, indeed, we may have generally tended to believe before 1960, but which we now recognize were false. We collectively wish to apologize for having misled the general educated public by spreading ideas about determinism of systems satisfying Newton’s laws of motion that, after 1960, were to be proved incorrect...”

(J. Lighthill, Proc. Roy. Soc. (London) A 407, 35 (1986))

Sensitivity to initial conditions was in fact known long before modern chaos theory and complexity theory. James Clerk Maxwell noted in the 1860's that even if two molecules were adjacent to one another in a hydrodynamic flow, they might find themselves in random places in the container after relatively short mixing times. He wrote:

When the state of things is such that an infinitely small variation of the present state will alter only by an infinitely small quantity the state at some future time, the condition of the system, whether at rest or in motion, is said to be stable; but when an infinitely small variation in the present state may bring about a finite difference in the state of the system in a finite time, the condition of the system is said to be unstable.

(Essay on Science and Free Will, 1873)

Maxwell may have been first, but certainly not the last, to connect this sensitivity to initial conditions to free will (e.g., John Eccles, with his "critically poised neurons.")

The real world is only approximately classical mechanical (obeying Newton's dynamical laws at all scales). At the small scales of atomic and molecular physics, the world is quantum mechanical. There is nothing corresponding to deterministic chaos in quantum physics. Deterministic chaos requires continuous motion to produce mathematical singularities and exponential non-linearity.

Despite their unpredictable and spontaneous "quantum jumps," the discrete states of the quantum world are more regular and stable than their classical analogues. Indeed, the long-term stability of quantum structures in their "ground states" is astonishing, as is the complete indistinguishability of elementary particles, which gives rise to extremely non-intuitive statistics. Finally, the long-term stability of quantum cooperative phenomena is evident in the ability of biological macromolecules to maintain (by error detection and correction) their information content over billions of years.

The desire to describe randomness and chance in the world with deterministic chaos resembles the view of Adolphe Quételet and Henry Thomas Buckle that statistical regularities in various physical and social phenomena are evidence of an underlying determinism. Is the motivation similar to that which seeks an intelligent designer behind biological evolution? It seems that the "antipathy to chance" observed by William James at the end of the nineteenth century is alive and well in the twenty-first.

Scholars at the Santa Fe Institute promote the self-organization aspects of complexity and chaos theories as assisting Darwin's theory of evolution. There is no doubt that in the early stages between non-living and living systems that auto-catalytic molecular evolution might provide one of the steps to biogenesis.

But some of these scholars think that complexity theory adds something that is not provided by the randomness of quantum physics. It may, but it does not provide the purpose (the teleonomy or entelechy) that appears when molecules first discover how to replicate themselves. And more important, it does not add any teleological purpose that pre-exists life.

Physical systems far from equilibrium use the flow of matter and energy from the environment through an open system to create and maintain information structures. In this respect, they resemble living systems, whaich are information structures, patterns, through which matter and energy flows. They do produce Prigogine's "order from chaos." But they are not information replicators and the information processors that evolve from the simplest organisms.

Atomic constraints such as the quantum-mechanical bonding of water molecules allow snow crystals to self-organize into spectacular forms, producing order from disorder. Besides crystals, there are whirlpools, Bénard convection cells, basalt columns, and soil polygons, all of which apparently violate the fundamental tendency toward equilibrium and disorder in the universe. These are processes that information philosophy calls ergodic. They can do this only because of the negative entropy flow from the Sun. They all are completely undirected and purposeless, like the formation of the galaxies, stars, and planets. They cannot add meaning to the universe.

Stuart Kauffman is perhaps the best known exponent of complexity as aiding natural selection.

The origin of life, rather than having been vastly improbable, is instead an expected collective property of complex systems of catalytic polymers and the molecules on which they act. Life, in a deep sense, crystallized as a collective self-reproducing metabolism in a space of possible organic reactions. If this is true, then the routes to life are many and its origin is profound yet simple.

While heretical, this new body of theory is robust in the sense that the conclusions hold for a wide variety of assumptions about prebiotic chemistry, about the kinds of polymers involved, and about the capacities of those polymers to catalyze reactions transforming either themselves or other, very similar polymers. It is also robust in leading to a fundamental new conclusion: Molecular systems, in principle, can both reproduce and evolve without having a genome in the familiar sense of a template-replicating molecular species. It is no small conclusion that heritable variation, and hence adaptive evolution, can occur in a self-reproducing molecular system lacking a genome. Since Darwin's theory of evolution, Mendel's discovery of the "atoms" of heredity, and Weismann 's theory of the germ plasm, biologists have argued that evolution requires a genome. False, I claim.

(The Origins of Order, 1993, p.285)

Kauffman's ideas about autocatalytic systems are shared by Terrence Deacon.

Kauffman thought that he might even discover "laws" of self-organization. In his 1995 book, At Home in the Universe, he identified the discovery of such laws as showing that human life followed directly from these pre-existing laws, which would replace the arbitrary and purposeless system of Darwinian natural selection.