Elayne and i have been having some discussions which I think are going to lead back to the material in "On Methods of Inference" ("OMOI") and I would like to tackle the task of identifying "Just What Is The Argument Presented in On Methods of Inference?" In other words, before getting into the details, can we at least begin to get a handle on what the argument was about?
The primary source material I have found most helpful on OMOI is the book by Phillip and Estelle De Lacy. Their introduction and their endnotes are extensive and I think bring some degree of clarity to a very complex topic, but even with all those notes is difficult to get a handle on what the issues were, and what the Epicurean position was on those issues. So in the following excerpts and comments I am going to try to make a start at grasping the big picture, and I hope others will see what they can do to help.
First, I think I have identified two key paragraphs in the introduction which purport to be a summary of the main issues of the work. Unfortunately the meaning of the terminology in them about "contraposition" and "common and particular signs" is not immediately clear, but at least this gives us a place to start. In the end, it appears to me that we're ultimately after a formula by which we can decide how to attack things for which there is no direct evidence. In other words - in legal terms - we are talking about the proper method of using circumstantial evidence, and when (if ever) it is possible to state a conclusion with confidence based on evidence that is only circumstantial. This material, and the excerpts that follow, begin on page 13 of the text.
I am going to read more and enter more comments on this thread, but if someone already has a command of this material and wants to try to shortcircuit the need for a deep dive into this subject, please feel free to jump in and save us all some time!
Failing that, I think this is an issue that underlays a great deal of Epicurean philosophy, and explains how it differs from competing philosophies, and also probably explains how different people who consider themselves to be within the Epicurean tradition can find themselves reaching different conclusions based on much the same evidence. I don't want to distract @Susan Hill from her current project, but I think the issues involved here are going to have a deep impact on how we should understand the conclusions of Epicurus on divinity as well as on many other matters.
So from here let's go further and see what we can read from the signs.