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THE SQUARE OF OPPOSITION
The Square of Opposition
Angelica Garcia
West Coast University
PHIL 341: Critical Reasoning
Dr. Burt Stillar
August 2, 2020

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THE SQUARE OF OPPOSITION
We may not know how vital categorical logic is in our daily lives. Established by Aristotle
in the fourth century, this terminology has become a means of essentially breaking down
arguments. According to Critical Thinking, categorical logic means "logic based on the relations
of inclusion and exclusion among classes" (Moore & Parker, 2017). In other words, it is used to
clarify and analyze deductive arguments. This form of logic is used to break down claims by
placing them into categories and converting them into simpler standard-form. (Categorical
Logic, 2020). While there are many ways to categorized claims, there are four main types of
sentences that can be translated into statements called A, E, I, O claims. Upon interpreting the
claims and placing them into their sections, we are then able to use the square of opposition to
identify a particular claim. Subsequently, the square of opposition was created to better
coordinate such statements, to describe the interaction between each of them, and to determine if
the syllogism is correct. (The Editors of Encyclopaedia Britannica, 2013). This paper would
define and describe important terms and concepts, explain the mechanism behind them, describe
the four categories and their interaction with each other, and include an example of how to turn
an argument into a standard format claim that can be utilized in the square of opposition to
support or refute a statement.
Category is a classification or grouping with closely related features, and logic is the
analysis of rational and irrational reasoning. Together, categorical logic is the analysis and
implementation of the rules of reasoning that applies to a class that comes under the same group.
Proposition is a statement that may be true or false. Categorical propositions are proposals which
reveal the simplified relation between both a subject and a predicate. The categorical
propositions involve four components: a subject, a predicate, a copula, and a quantity expression.
Categorical logic is based on the four main standard-forms of categorical propositions which are

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THE SQUARE OF OPPOSITION
A, E, I, O claims. (Introduction to Logic: Translation of Propositions, 2020). Those four types of
claims are the universal statement (A), the universal negative statement (E), the particular
affirmative statement (I), and the particular negative statement (O). Statements in (A) group are
in the form of “All ___ are ___.” Whereas (E) statements occur in the form of “No ___ are ___.”
While (I) statements are placed in the form of
“Some ___ are ___.” Ultimately, statements in the
category (O) are rendered in the form of “Some__are not ___.” Words within the blank spaces
are considered terms, which can only be nouns or nouns phrases. In the first blank, it should be
the subject term, and in the second blank the predicate term. (Murray & Kujundizic, 2005).

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