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Understanding Deductive and Inductive Arguments with Venn Diagrams

This lesson explores the concepts of induction and deduction through a detailed examination of Venn diagrams and syllogisms. Induction involves drawing generalized conclusions from specific instances, while deduction draws specific conclusions from general premises. We'll illustrate categorical and hypothetical syllogisms, discuss Modus Ponens and Modus Tollens, and identify common fallacies. Additionally, we'll practice creating dilemmas and applying these concepts in real-life situations. Reinforce your understanding by completing homework assignments that encourage critical thinking and logical reasoning.

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Understanding Deductive and Inductive Arguments with Venn Diagrams

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Presentation Transcript

  1. Deductive argument

  2. Let’s Review.

  3. Induction vs. deduction • Induction: inference of a generalized conclusion from particular instances  • Deduction: inference in which the conclusion about particulars follows necessarily from general or universal premises

  4. Note #1:you are going to hate today’s lesson.

  5. Note #2:don’t worry about names. Just try to think with venn diagrams.

  6. Part I:venn diagrams with overlap

  7. First we draw the venn diagram.

  8. Categorical syllogism • All p are q. • All q are r. • Therefore all p are r. • All Boston folk are from Massachusetts. • All Massachusetts folk are from America. • All Boston folk are from America.

  9. Hypothetical syllogism • If p, then q. • If q, then r. • Therefore, if p, then r. • If Sam is from Boston, then he is from Massachusetts. • If he is from Massachusetts, then he is from America. • Therefore, if Sam is from Boston, then he is from America.

  10. What’s the relationship? They’re basically the same.

  11. Next we find out where we are in the venn diagram.

  12. Modus ponendo ponens • If p, then q. • P. • Therefore q. • If it is a dog, then it is a mammal. • It is a dog. • Therefore it is a mammal.

  13. Modus tollendo tollens (Contrapositive) • If p, then q. • Not q. • Therefore p. • If it is a dog, then it is a mammal. • It is not a mammal. • Therefore it is not a dog.

  14. Fallacy test!!!

  15. Converse fallacy(Affirming the consequent) • If p, then q. • Q. • Therefore p. • If it is a dog, then it is a mammal. • It is a mammal. • Therefore it is a dog. What if it’s a bear? Bears are mammals.

  16. Inverse fallacy(Denying the antecedent) • If p, then q. • Not p. • Therefore not q. • If it is a dog, then it is a mammal. • It is not a dog. • Therefore it is not a mammal. What if it’s a bear? Bears are mammals.

  17. Finally we put it all together.

  18. Put it all together! • If p, then q. • If q, then r. • Therefore, if p, then r. • P. • Therefore r. • If it is a dog, then it is a mammal. • If it is a mammal, then it is an animal. • Therefore, if it is a dog, then it is an animal. • It is a dog. • Therefore it is an animal.

  19. Part II:venn diagrams without overlap

  20. Note #3:each of these arguments has a contrapositive version. But we’re going to focus on the positive.

  21. First we draw the venn diagram.

  22. [constructive] Dilemma • Either p or q. • If p, then r. • If q, then s. • Therefore either r or s. • Abdulhaye’s first language is either Darija or Tashlhit. • If Abdulhaye’s first language is Darija, then he is Arab. • If Abdulhaye’s first language is Tashlhit, then he is Tamazight. • Therefore Abdulhaye is either Arab or Tamazight.

  23. Let’s create some dilemmas!

  24. Next we find out where we are in the venn diagram.

  25. Modus Tollendo Ponens(Disjunctive Syllogism) • Either p or q. • Not p. • Therefore q. • Abdulhaye’s first language is either Darija or Tashlhit. • It is not Darija. • Therefore it is Tashlhit.

  26. Finally we put it all together.

  27. Put it all together! • Either p or q. • If p, then r. • If q, then s. • Therefore either r or s. • Not p. • Therefore q. • Either we legalize prostitution or we keep it illegal. • If we legalize prostitution, we would be breaking Islamic law! • If we keep prostitution illegal, we maintain our Islamic values. • Therefore either we break Islamic law or we remain Islamic. • Let’s not break Islamic law by legalizing prostitution. • Therefore let’s remain Islamic by keeping it illegal.

  28. Note #4:Be wary of false dilemmas and “Reductions to the Absurd.”

  29. Rework your dilemmas

  30. Using both types of argument at the same time

  31. Read Chapter 5 in The Debater’s Guide.For tomorrow, prove using deduction... Homework.

  32. Homework • Prove by creating your own hypothetical syllogism and modus ponendo ponens: It is wrong for a man to have more than one wife. • Prove by creating your own dilemma and modus tollendo ponens: Morocco should be friends with North Korea. • Draw Venn diagrams for your arguments in (1) and (2). • What is wrong with this argument?... If the government cuts taxes, then the economy will improve. The economy improved. Therefore the government cut taxes • If the government invests in education, then more Moroccans have access to education. Does this mean that government investment causes the increase in access? • Make an analogy between the human body and human society.

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