Everything that happens is followed by something else which depends on it by causal necessity. Likewise, everything that happens is preceded by something with which it is causally connected. For nothing exists or has come into being in the cosmos without a cause. The universe will be disrupted and disintegrate into pieces and cease to be a unity functioning as a single system, if any uncaused movement is introduced into it.

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

In addition, 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)

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 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.

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.