The Square of Opposition The Square of opposition has categorical statements at its corners: Those categorical statements help us make syllogisms, like this one: All Socrateses are men. All men are mortal. Therefore, all Socrateses are mortal. We test syllogisms for validity with Venn diagrams or with the Rules of Validity. We will need to be able to convert statements into categorical form. The sun is shining. A: All things like the sun are shining things. Fred can sing. A: All things like Fred are singers. Some people cannot play the guitar. O: Some people are not guitar players. Napoleon was a great general. A: All things like Napoleon are great generals. Some statements share important characteristics. A & E statements are Universals. I & O statements are Particulars. A & I statements are Affirmatives. E & O statements are Negatives. In the Modern Square of Opposition, the only relationship that holds between statements is that of Contradictories. A & O statements are Contradictories to each other. I & E statements are also Contradictories to each other.

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