The “Square of Opposition”
In On Interpretation, Aristotle spells out the relationships of contradiction for sentences with universal subjects as follows:
| | Affirmation | Denial |
| Universal | Every A is B | No A is B |
| Particular | Some A is B | Not every A is B |
Simple as it appears, this table raises important difficulties of interpretation (for a thorough discussion, see the entry on the square of opposition).
In the Prior Analytics, Aristotle adopts a somewhat artificial way of expressing predications:
instead of saying “X is predicated of Y” he says “X belongs (huparchei) to Y”.
This should really be regarded as a technical expression.
The verb huparchein usually means either “begin” or “exist, be present”, and Aristotle’s usage appears to be a development of this latter use.