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

Negation is not all that well understood even in formal settings.<p>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 &quot;works&quot; 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.<p>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.<p>Things like identity, equality, negation in real life reasoning seem to often be &quot;good enough&quot;&#x2F; fuzzy rather than rigorous applications of logic.

&gt; But what about when we&#x27;re told &#x27;This coffee is not hot&#x27;? Does that mean we think it&#x27;s cold?<p>I think it depends on your training and how you&#x27;ve studied to interpret statements with logical operators such as these.<p>If I interpret &quot;not&quot; as &quot;anything but&quot;, and if the possibility space of &quot;anything&quot; includes more than one state (temperature, in the article&#x27;s example), then &quot;not hot&quot; should be taken to mean &quot;any temperature but hot&quot;.

&#x27;A team of scientists has now identified how our brains work to process phrases that include negation (i.e., &#x27;not&#x27;), 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 &#x27;cold.&#x27; &#x27;