How Should We Evaluate Abstractions?

One of our recent participants asked me about this topic and it well deserves a thread. I recall in our podcast years ago that I consciously pulled back from some earlier statements that were probably too sweeping in viewing abstractions negatively. My current view is that it's certainly not abstractions as a concept that are across-the-board suspect, but those abstractions which are formed without any connection to evidence from the senses, anticipations, and feelings. But we can probably do a lot better than that than clarifying a proper Epicurean attitude toward classes of abstractions.

Here's the question that was presented:

I'm interested in how we can determine whether a given abstraction is useful or not. For example, mathematics cannot be understood through the senses. It is abstract in a sense, but it is helpful in describing the world. I'm interested in the criteria for considering given abstractions valuable or not.

Anyone have thoughts to add to the conversation?

One additional thought to add to this is that I would recommend anyone interested in this issue to check out what Norman DeWitt has to say in emphasizing Epicurus' commitment to deductive reasoning.

While atoms are not abstractions, we don't have any direct ability to see or touch them directly, so the inferences we draw about them and how they operate are certainly abstract to a degree, and I think this is what the topic is largely about.

Are "abstractions" the same as "concepts?" If so, we certainly do conceptual reasoning all the time, and I think the question is whether those concepts are supported by evidence of the sensations, anticipations, and feelings (such as when we base our inferences about atoms on things we can see and touch and smell etc.)

This note will also serve as a reminder that after we complete Tusculan Disputations we're going to at least visit Philodemus' "On Signs/On Methods Of Inference" which is directly related to this topic.