Soft Causality is the causality we have in the physical world. It includes occasional quantum events, which are only probabilistic and statistical. This means that they are not strictly caused by prior events, although they may be causes of subsequent events. The ancients called such causes "causa sui," or self-caused causes. They depend on chance in the form of irreducible quantum indeterminacy. Soft Causality is not the strict deterministic causal chain that leads to the idea that there can be but one possible future for the universe.
Soft Causality is not the causal chain that leads back to an Aristotelian prime mover that some have identified with God. Nor is it the idea that information is a constant of nature, so the information available at the Big Bang is all that will exist at the end of the universe, as captured in the 73rd quatrain of Omar Khayyam's Rubaiyat, as translated by Edward Fitzgerald.
With Earth's first Clay, They did the Last Man knead,Soft Causality is not the deterministic laws of classical physics that allow Laplace's Demon to see all times past and future - sub specie aeternitatis.
Soft Causality is very simply the idea that most events are adequately determined by normal causes, but that some events are not precisely predictable from prior events. Their unpredictability leads us to call them uncaused events, which in turn become uncaused causes (causa sui) that start new causal chains. The unpredictability is usually of minor importance. Uncaused causes do not produce the kind of "miracles" normally associated with the idea of the causa sui in scholastic theology. But they do occasionally break the causal chain of strict determinism, without denying causality. Soft Causality gives us an Adequate Determinism.