[FOM] Weak logic axioms

[martdowd at aol.com]

 Charlie Silver writes:


I’ve wondered why no one has expressed
the view that empty domains seem more mathematically appropriate, rather than
assuming first-order logic domains must be non-empty.



Whether the empty domain should be included depends on the context.  In classical FOL it must be excluded, so that some validities hold in all structures (e.g., $P(x)\rightarrow\exists x P(x)$.   In other contexts, such as universal algebra or open FOL, the empty structure is allowed.

- Martin Dowd

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