4 Categorical Propositions

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4 Categorical Propositions 4.5 Traditional Square of Opposition

Traditional Square of Opposition Contrary A E T T Contra dictory Subalternation Subalternation Contra dictory F F I O Subcontrary 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 E T T Contra dictory Subalternation Subalternation Contra dictory F F I O Subcontrary 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 E T T Contra dictory Subalternation Subalternation Contra dictory F F I O Subcontrary 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 E T T Contra dictory Subalternation Subalternation Contra dictory F F I O Subcontrary 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 non-existent 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’.