Aristotle laid out the principles of his logic in his writing Περὶ Ἑρμηνείας, in Latin De Interpretatione, in English On Exposition. It is a graphical representation of the relations between propositions that guarantee their truth. If philosophers and scientists would internalise the logical rules in Aristotle’s square of opposition, a lot of misunderstandings would be prevented. SEE: The Square of Opposition as a Whiteboard animation
Basics of the Square of Opposition of Aristotle
0:06 A proposition (e.g. “All Greeks are men.”) consists of a subject (“Greeks”) and a predicate (“men”).
The four types of propositions are:
Universal positive (“All Greeks are men.”, abbreviated “aGM”),
Universal negative (“No Greeks are men.”, abbreviated “nGM”),
Particular positive (“Some Greeks are men.”, abbreviated “sGM”) and
Particular negative (“Some Greeks are not men”, abbreviated “sGnM”).
1:38 Contradiction (Aristotle)
Universal positive and particular negative, as well as universal negative and particular positive are contradictory. They can’t both be true and can’t both be false at the same time.
1:59 Contraries (Aristotle)
Universal positive and Universal negative propositions are contraries. They can’t both be true, but can both be false at the same time.
2:15 Subcontraries (Aristotle)
Particular positive and Particular negative propositions are subcontraries. They can’t both be false, but can both be true at the same time.
2:35 Implication (Aristotle)
Implied propositions (particular positive and particular negative) are true, when their implying propositions (universal positive and universal negative) are true.
2:55 Counter Indication (Aristotle)
Universal propositions (positive and negative respectively) are false, when their particular propositions (positive and negative respectively) are false.
3:19 Converse propositions (Aristotle)
In converse propositions, subjects (e.g. Greeks) and predicates (e.g. men) can be switched without altering the proposition’s truth.
Converse Propositions are:
“No Greeks are men” and
“Some Greeks are men”.
so it is also true that
“No men are Greeks” as well as
“Some men are Greeks”.
3:44 Complements (Aristotle)
A complement of a subject or predicate is everything that it is not.
E.g. “all that is not a man” and “all that is not a Greek”.
3:58 Contrapositive propositions (Aristotle)
In contrapositive propositions (“all Greeks are men” and “some Greeks are not men”), if the subjects’ and predicates’ complements are switched, the proposition retains its truth.