In order to understand the meaning of Categorically False , one must understand the Categorical approach to defining crimes. Where there are two crimes that may be similar in nature, but defined differently in different areas (Such as "Burglary" and "Shoplifting") then one may or may not be the same as the other.For example, State X defines walking into a store in the middle of the day and stealing X amount of product from the shelf as "Burglary". State Y defines the same action as "Shoplifting". It is in a defense attorney's best interest to argue that this conviction, especially as it applies to Federal Law (enhancing sentences based on prior convictions), does not fall in the same category as a specified crime.So, in practice, it means that a reporter asking someone's opinion of whether or not the charges of " drug smuggling " to a relative are true. The interviewee would respond, "Those charges are categorically false ". Meaning, this person did something... but not defined in the way you just asked about.However, in popular culture, people using the phrase Categorically False simple mean "wholly untrue", which is incorrect.