Affirming The Consequent

     1. If P, then Q.
     2. Q.
     3. Therefore, P
For several months, really for over a year as a background activity, I’ve been trying to answer the question, “Is there convincing evidence that one or more of the kings of Ugarit could read and write beyond the most elementary level?” Here’s the problem. I’ve found several lines of evidence that look very much like Qs and I have come to believe P. Formally, this is a deductive fallacy and on that basis, I should abandon the project.
But is it an inductive fallacy? If there were once an elephant in this room, I would expect to see elephant dung scattered around, the flooring would be damaged; various things in the room would be destroyed; if it were an adult elephant, the ceiling would be destroyed; the doorway to the room would be widened in a destructive way; and so forth. Now solely for the sake of argument, let’s assume I see (and smell) quite a bit of elephant dung in this room, the flooring is damaged, the furniture is broken and tossed around, the doorway is severally damaged, the ceiling is broken up and even the roof above it appears to have perforation patterns commensurate elephant tusk penetrations. Am I justified in believing that there was an elephant in this room even though I haven’t seen one or heard its trumpet? Before you say yes (or no), there are environmental considerations to take into account. No one has ever reported an elephant within twenty miles of this room that was not under the firm control of its human handler. The closest elephant permanently in residence lives about 40 miles away at the Los Angeles Zoo and there has been no news of an escape with one elephant last seen heading east. Now this doesn’t make it impossible that there has been an elephant in this room but it sure lowers the probability. On the other hand, if elephants regularly roamed our neighborhood and were will known to enter houses and hang out in studies then that would make it fairly likely that an elephant was here.
Is this the common plight of all who deal with severally underdetermined problems? All underdetermined problems? Realizing that mathematical statistical methodologies are not applicable, when has one gathered enough Qs to assert P with reasonable confidence that one is not making an inductive fallacy as well as a deductive one? How does one know? What environmental, contextual, factors would increase or decrease the probability of P, of my P?