As I said in a previous part of this thread, the rules of logic are as arbitrary (by definition) as they are paramount, and often diverge from natural language logic: https://news.ycombinator.com/item?id=42365222#42368661
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I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic.
The fact that we compact these edge cases into arbitrary truth values is just for ease of computing.
This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.
This addresses my previous reply to you, thanks. I wonder though if there's a problem in that common natural language is inherently limited to common concepts. Scientists famously use confusing language in their papers but they're writing for people who use the same language so it's OK. For example, they use "consistent with zero" to mean "might be zero" even though a common-language reader can interpret it as "not zero". I suppose logicians use "or" to mean inclusive or in their papers too.
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I mean, it's important to remember that the axioms of first-order logic are arbitrary. We could easily argue that the truth value of an empty group is undecidable, and that would better correlate to natural language logic.
The fact that we compact these edge cases into arbitrary truth values is just for ease of computing.
This is also relevant to the arbitrary choice of the 'inclusive or' as a default over an 'exclusive or', which most people use in natural language.