Not sure if there is something wrong in my brain but I have not been able to understand the hate against NULL. To me the three value logic feels very natural and just clicks. Lately I have been dipping my toes into Alteryx, which treats empty values in a way that definitely does not correspond to 'normal' NULL logic in databases and it feels very much like a constraint on building my workflows.
If a NULL were just a value in 3-valued logic, it could have been OK. However, that's not how it works out. Consider the following (that should be equivalent if NULL is just like Maybe in True-Maybe-False logic):
SELECT null AND true;
SELECT bool_and(column1) FROM (VALUES (null::bool),(true)) AS foo;
In PostgreSQL the first query produces NULL, while the second produces TRUE. Yet, it's also possible to get NULL as a result of aggregating values with bool_and:
SELECT bool_and(column1) FROM (VALUES (null::bool),(null::bool)) AS foo;
You are mixing two concepts here: 3VL and how most aggregates work in SQL: the drop NULL values before doing their work. That's why the first BOOL_AND example only sees one value, thus returning true.
