It would appear that logical justification can only arise byway of induction. The observer cannot claim knowledge based upon his observations. The next rock to go into the box could be gold, or any other substance. This then, is the logical flaw in induction. Induction is logically inconsistent in that the number of possible cases which might be observed is infinite and no number of observed cases which give the same result can therefore increase the probability of that result occurring in the next observed case, because no number can make a dent on infinity.
Probability remains zero.
The solution I would like to offer for consideration came to me as a result of long contemplation of Zeno's paradoxes, in particular, the paradox known as The Stadium . In attempting to resolve the paradox, I found an approach which I believe may be useful in tackling the problem of induction. Zeno's logical paradox is derived from the artificial nature of measuring distance based on number. Numbers are infinite, but that does not mean that there are an infinite number of discrete points in space. The mistake arises from an erroneous belief in the actuality of logical fictions , invented to help us to deal with the world.