Subcontrary and Subalternate Statements The second two - PDF document

Three Acts of the Mind Mental Act : Verbal Expression: • Simple • Term Apprehension • Proposition • Judgment • Syllogism • Deductive Inference Slide 7-1 Subcontrary and Subalternate Statements The second two relationships of opposition The Rule of Subcontraries The Third Law of Opposition The Rule of Subalterns The Fourth Law of Opposition Slide 7-2 1

The Second Two Relationships of Opposition Contradictory Contrary Subcontrary Subalternate Slide 7-3 Rule of Subcontraries Two statements are subcontrary if they are both particular statements that differ in quality. Slide 7-4 2

The Third Law of Opposition Subcontraries may at the same time both be true, but cannot at the same time both be false. Slide 7-5 The Third Law of Opposition an example: If “Some men are mortal” is false, then “Some men are not mortal cannot be false . Slide 7-6 3

Subcontrary Statements I: Some men are mortal O: Some men are not mortal Slide 7-7 Quantity and Quality of the Four Categorical Statements Quality Negative Affirmative Universal A contraries E Quantity Particular I subcontraries O Slide 7-8 4

The Rule of Subalterns Two statements are subalternate if they have the same quality, but differ in quantity. Slide 7-9 Subalternate Statements A: All men are mortal I: Some men are mortal Slide 7-10 5

Subalternate Statements E: No men are mortal O: Some men are not mortal Slide 7-11 The Fourth Law of Opposition Subalterns may both be true or both be false. If the particular is false, then the universal is false; if the universal is true, then the particular is true; otherwise, their status cannot be determined. Slide 7-12 6

The Fourth Law of Opposition: an example If we know that “All dogs are mammals” is true, then we know that “Some dogs are mammals” is true. But if we know “Some dogs are long-haired” is true, we will not therefore know that “All dogs are long- haired” is true. Slide 7-13 Quantity and Quality of the Four Categorical Statements Quality Negative Affirmative S S Universal A contraries E U U B B A Quantity A L L T T Particular I subcontraries O E E R R N N Slide 7-14 7

Subcontrary and Subalternate Statements The second two relationships of opposition The Rule of Subcontraries The Third Law of Opposition The Rule of Subalterns The Fourth Law of Opposition Slide 7-2 The Four Relationships of Opposition Contradictory Contrary Subcontrary Subalternate Slide 7-14 8