How does 'not' affect what we understand? Scientists find negation mitigates

Negation is not all that well understood even in formal settings.

When PROLOG introduced negation-as-failure, many logicians (Girard) were repulsed: how can failure to find a proof for a proposition P be considered a proof of the negation (not P)? Yet there are theories where this just "works" because P is about some inherently finite set of observations (not (John Doe is an employee)) is very much the failure of finding a record after consulting the employee database.

The different treatment of negation in intuitionistic logic and classical logic is another example. Intuitionistic logic is more precise than classical: a statement of classical logic logic can be translated into one of intuitionistic logic (eg Gödel-Gentzen) that is provable if and only if the original statement was provable.

Things like identity, equality, negation in real life reasoning seem to often be "good enough"/ fuzzy rather than rigorous applications of logic.

> But what about when we're told 'This coffee is not hot'? Does that mean we think it's cold?

I think it depends on your training and how you've studied to interpret statements with logical operators such as these.

If I interpret "not" as "anything but", and if the possibility space of "anything" includes more than one state (temperature, in the article's example), then "not hot" should be taken to mean "any temperature but hot".

'A team of scientists has now identified how our brains work to process phrases that include negation (i.e., 'not'), revealing that it mitigates rather than inverts meaning -- in other words, in our minds, negation merely reduces the temperature of our coffee and does not make it 'cold.' '