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> I've been trying to look for my old logic book, but I can't seem to find it.

My first formal logic book was "Discrete Mathematics and Its Applications 7th Edition" by Kenneth Rosen. It covered the basics like DeMorgan's Law, Modus Pollens, Modus Tollens, sets, cardinality, conjunctions, bijections, proofs, relations (reflexive, symmetric, antisymmetric, transitive), big-O notation, etc.
My second formal logic class used "Foundations Of Computing" by Charles Allison. That class focused on things like on Deterministic Finite Automata, Regular Expressions, Grammars, Pushdown Automata, Turing Machines, reductions, etc.

> One possible explanation is that I am not as good at communicating as I think I am. Another possible explanation is that the receiving party is in denial.

The first explanation is also sometimes due to the complexity of English. It's a horrible language that is full of ambiguity and colloquial repurposing. So when you use a word, it may mean something else to the person you are talking to. The second explanation is amplified because people will not admit that they are in denial. Some will even "nod along", making you think they agree with foundational components of your logic, but later expose that they disagree on some fundamental part.

> I don't suppose you'd be willing to give me a quick refresher in identifying circular logic?

Circular logic is evident when one of your left-hand-side (LHS) propositional variables is present in the RHS of a subsequent proposition. To avoid circular logic, I go to great lengths to keep my propositions as pure as possible. But sometimes I let English ambiguities creep in and ruin my comments.

So if a logic sequence start with p→q, if we ever see p appear on the RHS of any proposition later on, we should be suspect of circular logic.

The shape of the Earth and Gravity should not present a circular logic problem. This is because the shape of the Earth is dependant on gravity, but gravity does not depend on the shape of the Earth. I would be interested in hearing about any uses of circular logic that are prevalent in RE discussions. Sadly, there are plenty of idiots in both RE and FE camps. And it seems that the less that one knows about a subject, the louder they shout. So I'm sure you have heard ignorant globies spew forth falsehoods. And I would be happy to correct any you have heard.

Feel free to DM me that article. But it may take me a day or two to budget the time to read it.

> You are one of the more polite folks on here and certainly one of the most well reasoned.

Likewise. This is how I wish every interaction between RE and FE advocates would pan out.