Exact(1)
One theological expert was enraged that I did not mention the "reincarnation" of Christ, while another was shocked that the beautiful verses of the Bible might have a literal meaning: "to criticise the opening line of Psalm 19 – 'The heavens declare the glory of the Lord' – for empty logic is a strangely wooden way of reading poetry" (the New Statesman).
Similar(7)
Logics for non-strict functions must be positive because in a negative or neutral logic empty-termed atomic formulas, such as f 1, 1/0) = 1, cannot be true.
(Which could be extended to "less self, more fulfillment". The more you're emptied out, runs the logic of Kyoto, the more you're ready to be filled up).
For more discussion of logic with an empty domain see (Quine 1954) and (Williamson 1999).
For a sound and complete proof system for logic with an empty domain, see (Tennant 1990).
That's as rule bound as any other kind of rule and as empty of any kind of logic of consequence.
For Quine first-order predicate logic excludes the empty domain: its valid formulas are those that come out true under all interpretations of the non-logical symbols over all non-empty domains.
In modern predicate logic, problems with empty terms arise primarily from the use of singular terms like "the fountain of youth" or "the Loch Ness monster" that refer to nothing or at least to no real object.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com