1 / 26

Logic 4

Logic 4. Aristotle’s Square of Opposition “How Statements Compare”. Statements can have a variety of relationships. Statements can be related these ways:. Equivalence Contradiction Independence Implication Sub-implication Contrary Sub-contrary. 1. Equivalence.

quinta
Download Presentation

Logic 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Logic 4 Aristotle’s Square of Opposition “How Statements Compare”

  2. Statements can have a variety of relationships.

  3. Statements can be related these ways: • Equivalence • Contradiction • Independence • Implication • Sub-implication • Contrary • Sub-contrary

  4. 1. Equivalence • When the 1st statement is true, the 2nd is true. • When the 1st statement is false, the 2nd is false. • The statements say the same thing, or are “equivalent.”

  5. Examples of Equivalence • No ENG11H students are lying teenagers. (E) • No lying teenagers are ENG11H students. (E) • No mendacious humans between 13 and 19 are students taking ENG11H. (E)

  6. 2. Contradiction • If we know the 1st statement is true, the 2nd must be false. • If we know the 1st statement is false, the 2nd must be true.

  7. Examples of Contradiction • No ENG11H students are liars. (E) • Some ENG11H students are liars. (I) • If the 1st is false, the 2nd must be true. If the 1st is true, the 2nd must be false.

  8. Examples of Contradiction • All ENG11H students are liars. (A) • Some ENG11H students are not liars. (O) • So…A and O are contradictory. So are E and I.

  9. 3. Independence • The 1st statement tells us nothing about the 2nd statement’s truth or falsehood. • All girls are liars. • All boys are liars.

  10. 4. Implication • From the truth of one statement, we can imply the truth of a second.

  11. Examples of Implication • All girls are liars. (A) • Some girls are liars. (I) • No girls are liars. (E) • Some girls are not liars. (O)

  12. Dangers of Implication! • However, if the 1st statement is false, we can’t assume the 2nd. • All girls are liars. (A) FALSE • Some girls are liars. (I) Maybe some, maybe none!

  13. Implication • So… A implies I when A is true. • And…E implies O when E is true.

  14. 5. Sub-Implication(implication in reverse) • From the falsehood of a statement, we can imply the falsehood of a 2nd statement. • Some teenagers are liars. (I) FALSE • All teenagers are liars. (A) also FALSE • Some teenagers are not mature. (O) FALSE • No teenagers are mature. (E) FALSE

  15. Sub-implication • So…I implies A when I is FALSE. • And…O implies E when O is FALSE.

  16. 6. Contrariety“contrary-ness” • Two statements are contrary when they both can’t be true, but both can be false. • No boys are liars. (E) • All boys are liars. (A)

  17. Contrariety • But…if it’s false that no boys are liars (E), we can’t assume that all boys are liars (A). • So, A and E are contrary.

  18. 7. Sub-Contrariety • Two statements are subcontrary when they can both be true, but they can’t both be false. • Some girls are polite. (I) • Some girls are not polite. (O)

  19. Sub-contrariety • So, I and O are sub-contrary.

  20. Exercise #1 • Let’s assume it is true that all S is P. • What other statements can we infer? • It is true that some S is P (I). (Implication) • It is false that some S is not P (O). (Contradiction) • It is false that no S is P (E). (Contrary)

  21. Exercise #2 • It is false that some Shakespeare plays have four acts. (I) • What can we infer? • It is false that all Shakespeare plays have four acts. (A) (sub-implication) • It is true that no Shakespeare plays have four acts. (E) (contradiction) • It is true that some Shakespeare plays do not have four acts. (O) (sub-contrary)

  22. Exercise #3 • It is true that some children are not fit. (O) • What can we infer? • It is false that all children are fit. (E) contradiction • We can’t infer the truth or falsehood of an I statement (Some children are fit), because it may also be the case that all/none of the children are fit. • We can’t infer the truth or falsehood of an E statement (No children are fit).

More Related