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Symbolic Logic Book V Syllogisms

Book V – Syllogisms Introduction Problems in Syllogisms Determining Conclusions Evaluating Conclusions

Introduction Syllogism: A trio of Biliteral Propositions All six terms are Species of the same Genus Every two of them contain between them a pair of codivisional Classes The three Propositions are so related that, if the first two are true, the third must be true

Introduction Syllogism: The first two Propositions are Premises The third Proposition is the Conclusion The Pair of Codivisional Terms in the Premises are “Eliminands” The other two Pairs are “Retinends”

Introduction An example:

Introduction An example:

Problems in Syllogisms: Determining a Conclusion The Rules: Determine the Univ Construct a Dictionary (label your variables) Translate the Premises into abstract form Represent them on a Triliteral Diagram Determine a Biliteral Conclusion Translate the Conclusion into concrete form

Problems in Syllogisms: Determining a Conclusion No son of mine is dishonest. People always treat an honest man with respect. Conclusion?

Problems in Syllogisms: Determining a Conclusion No son of mine is dishonest. People always treat an honest man with respect. Conclusion? Univ = “men” No sons of mine are dishonest men. All honest men are men treated with respect. Determine a Univ and rewrite the Premises (if necessary)

Problems in Syllogisms: Determining a Conclusion No sons of mine are dishonest men. All honest men are men treated with respect. Conclusion? M = honest (the common term) X = sons of mine Y = treated with respect Construct a Dictionary

Problems in Syllogisms: Determining a Conclusion No sons of mine are dishonest men. All honest men are men treated with respect. Conclusion? No X are M’ All M are Y Translate the Premises into abstract form

Problems in Syllogisms: Determining a Conclusion No X are M’ All M are Y Conclusion? Represent the Premises on the Triliteral diagram

Problems in Syllogisms: Determining a Conclusion Determine a Biliteral Conclusion Conclusion: No X are Y’

Problems in Syllogisms: Determining a Conclusion P: No X are M’ P: All M are Y C: No X are Y’ Translate the Conclusion into concrete form No son of mine is dishonest. People always treat an honest man with respect. No son of mine ever fails to be treated with respect.

Problems in Syllogisms: Determining a Conclusion All girls get good grades. Lazy students fail. Conclusion?

Problems in Syllogisms: Determining a Conclusion All girls get good grades. Lazy students fail. Conclusion? Univ = “students” All female students are students who get good grades. All lazy students are students who fail. Determine a Univ and rewrite the Premises (if necessary)

Problems in Syllogisms: Determining a Conclusion All female students are students who get good grades. All lazy students are students who fail. Conclusion? M = pass (good grades) (the common term) X = female students Y = lazy students Construct a Dictionary

Problems in Syllogisms: Determining a Conclusion All female students are students who get good grades. All lazy students are students who fail. Conclusion? All X are M All Y are M’ Translate the Premises into abstract form

Problems in Syllogisms: Determining a Conclusion P: All X are M P: All Y are M’ Conclusion? Represent the Premises on the Triliteral diagram (“No” statements first!)

Problems in Syllogisms: Determining a Conclusion Determine a Biliteral Conclusion Conclusion (2): All X are Y’, All Y are X’

Problems in Syllogisms: Determining a Conclusion P: All X are M P: All Y are M’ C: All X are Y’, All Y are X’ Translate the Conclusion into concrete form All girls get good grades. Lazy students fail. All girls are hardworking, all lazy students are boys.

Problems in Syllogisms: Evaluating a Conclusion The Rules: Follow the rules for determining a Conclusion from your given Premises. If there is no Conclusion, say so. If there is a Conclusion, compare it with the proposed Conclusion.

Problems in Syllogisms: Evaluating a Conclusion P: All soldiers are strong. P: All soldiers are brave. C: Some strong men are brave.

Problems in Syllogisms: Evaluating a Conclusion P: All soldiers are strong. P: All soldiers are brave. C: Some strong men are brave. Univ = “men” M = soldiers, X = strong, Y = brave Follow the rules for determining a Conclusion

Problems in Syllogisms: Determining a Conclusion P: All soldiers are strong. P: All soldiers are brave. C: Some strong men are brave. All M are X All M are Y Follow the rules for determining a Conclusion Conclusion: Some X are Y

Problems in Syllogisms: Determining a Conclusion C: Some strong men are brave. Compare the deduced Conclusion with the proposed Conclusion Conclusion: Some X are Y Some strong men are brave. They match!

Problems in Syllogisms: Evaluating a Conclusion P: I enjoy country music. P: When I enjoy something, I wish to expose other people to it. C: I wish to expose other people to some country music.

Problems in Syllogisms: Evaluating a Conclusion P: I enjoy country music. P: When I enjoy something, I wish to expose other people to it. C: I wish to expose other people to some country music. Univ = “things” M = enjoy, X = country music, Y = expose other people Follow the rules for determining a Conclusion

Problems in Syllogisms: Determining a Conclusion P: I enjoy country music. P: When I enjoy something, I wish to expose other people to it. C: I wish to expose other people to some country music. All X are M All M are Y Follow the rules for determining a Conclusion Conclusion: All X are Y

Problems in Syllogisms: Determining a Conclusion C: I wish to expose other people to some country music. Compare the deduced Conclusion with the proposed Conclusion Conclusion: All Y are X I wish to expose people to all country music. The proposed Conclusion is incomplete.

That’s All, Folks! Your assignment for next week: Complete the worksheet Have a great weekend!