# Category:Categorical Statements

This category contains results about Categorical Statements.

Definitions specific to this category can be found in Definitions/Categorical Statements.

Let $S$ and $P$ be predicates.

A **categorical statement** is a statement that can be expressed in one of the following ways in natural language:

\((A)\) | $:$ | Universal Affirmative: | Every $S$ is $P$ | |||||

\((E)\) | $:$ | Universal Negative: | No $S$ is $P$ | |||||

\((I)\) | $:$ | Particular Affirmative: | Some $S$ is $P$ | |||||

\((O)\) | $:$ | Particular Negative: | Some $S$ is not $P$ |

## Pages in category "Categorical Statements"

The following 11 pages are in this category, out of 11 total.

### P

### U

- Universal Affirmative and Negative are both False iff Particular Affirmative and Negative are both True
- Universal Affirmative and Particular Negative are Contradictory
- Universal Affirmative and Universal Negative are Contrary iff First Predicate is not Vacuous
- Universal Affirmative implies Particular Affirmative iff First Predicate is not Vacuous
- Universal Negative implies Particular Negative iff First Predicate is not Vacuous