Miracles, induction, and retrodiction

According to the principle of induction, we can retroengineer the past from the present. There's a chain of events leading up to the present. Antecedent states produce subsequent states. The same causes produce the same effects. Since that's repeatable, if we're familiar with the process, we can retrace an effect back through intervening stages to the originating cause. 

For instance, when I see an adult human, I know how he got to that point. I can run it backwards from adulthood through adolescence, childhood, gestation, and conception. 

All things being equal, that's a generally reliable inference. However, miracles pose an exception to induction. A classic miracle (in contrast to a coincidence miracle) is causally discontinuous with the past. A miracle isn't uncaused, but it's not the result of a causal chain. Rather, a miracle results from the introduction an anomalous cause outside the ordinary chain of events. It represents a break in the causal continuum. The continuum resumes after the break, taking the miracle as a new starting-point. 

For instance, suppose a person suffers from a naturally irreversible degenerative condition. Suppose he undergoes miraculous healing. That outcome can't be retrodicted from his prior condition. 

In the case of miracles, induction hits a wall. When the subsequent course of events is the result of a miracle, inductive inference can't go further back than the miracle. It can't reconstruct the past before the miracle occurred, because the post-miraculous state is not a product of the pre-miraculous state. Induction can only take you from the present to as far back in time as the precipitating miracle. It can't jump over that to the other side, because the chain of events prior to the miracle is a dead-end. The prior chain of events terminated with the miracle, which represents a new beginning. 

This raises a potential problem regarding past-oriented sciences (e.g. cosmology, historical geology, paleontology, evolution). If miracles occur in the past, are they even detectable? What's the scope of any particular miracle to reset the status quo? That limits our ability to reconstruct the past.