4 Categorical Propositions
4.5 Traditional Square of Opposition
Traditional Square of Opposition
Contrary
A
T
E
T
Subalternation
Subalternation
F
I
F
Subcontrary
O
Supposing one proposition is true (or false), you can tell the truth value of its
opposite, and quite a bit more …
Traditional Square of Opposition
Contrary
A
T
E
T
Subalternation
Subalternation
F
I
F
Subcontrary
O
Contrary propositions (A and E propositions) cannot both be true, though
both can be false (and at least one IS false)
Traditional Square of Opposition
Contrary
A
T
E
T
Subalternation
Subalternation
F
I
F
Subcontrary
O
Subcontrary propositions (I and O propositions) cannot both be false, though
they can both be true (and at least one IS true)
Traditional Square of Opposition
Contrary
A
T
E
T
Subalternation
Subalternation
F
I
F
Subcontrary
O
Subalternation: truth flows downward, falsehood flows upward (if an I or O
propositions is false, then so is the proposition above it)
Traditional Square of Opposition
Terminology for the traditional square:
Undetermined truth value =df occurs if the truth value of a given proposition
cannot be determined using another proposition, its truth value (truth or
falsehood), and the rules of the square
Illicit contrary =df inferring via the contrariety relation the truth value of an A or E
proposition that is undetermined
Illicit subcontrary =df inferring via the subcontrariety relation the truth value of
an I or O proposition that is undetermined
Illicit subalternation =df inferring any proposition (A E I or O) via a subalternation
relation that is undetermined
Existential Fallacies
• Existential fallacy in the traditional square =df
using contrary, subcontrary, and
subalternation with propositions about nonexistent things.
• Existential fallacy in the Boolean square =df
when our argument is invalid merely because
a universal premise is interpreted as having
existential import.
Conditional Validity
When the validity of an argument depends on the
existence of the subject matter.
All redheads in this class are expelled students.
Therefore, some redheads in this class are expelled
students.
Valid only if there are redheads in this class … and
so ‘conditionally valid’.