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Syllogisms

Syllogisms. Formal Reasoning. Formal Reasoning. Concerned with “form” or structures Need have nothing to do with content or fact May use symbols (e.g., p , q , ζ , Þ). Following form …. As mentioned above, formal logic doesn’t have to have anything to do with the real world

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Syllogisms

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  1. Syllogisms Formal Reasoning

  2. Formal Reasoning • Concerned with “form” or structures • Need have nothing to do with content or fact • May use symbols (e.g., p, q, ζ, Þ)

  3. Following form … • As mentioned above, formal logic doesn’t have to have anything to do with the real world • “Validity” is about form, not fact • E.g., All heavenly bodies are made of milk The sun is a heavenly body The sun is made of milk

  4. Deductive and Inductive • Deductive • No new information • Conclusions are certain • Inductive • New information • Conclusions are probable Formal reasoning isdeductive

  5. Syllogism • Syn- together + logos, reason, discourse • Contains three (3) parts • Major premise • Minor premise • Conclusion • Three (3) syllogistic types here considered: • Categorical • Conditional • Disjunctive

  6. Categorical Syllogism • “All,”“None,” or “Some” syllogism • Sound example All freshmen are lazy (major premise) John is a freshman (minor premise) John is lazy (conclusion) • Faulty example Some freshmen are lazy John is a freshman John is lazy (maybe, maybe not)

  7. Categorical Syllogism • Better example of “some” All girls like Jane Austen Some students are girls Some students like Jane Austen (An unfounded generalization? You betcha. But it’s formally correct.)

  8. Conditional Syllogism • “If-then” syllogism • Antecedent • Consequent • E.g., If you go to school, you will learn something You go to school You will learn something

  9. Conditional Syllogism • Affirming the antecedent—saying the “if” condition did in fact occur If you go to school, you will learn something You go to school You will learn something

  10. Conditional Syllogism • Denying the consequent—saying the “then” part did not occur If you go to school, you will learn something You did not learn something You did not go to school

  11. Conditional Syllogism • Two (2) fallacies involved • Denying the antecedent • Affirming the consequent Denying the antecedent If you go to school, you will learn something You do not go to school You will not learn anything (Not necessarily! One may learn out of school)

  12. Conditional Syllogism Affirming the consequent If you go to school, you will learn something You learn something You go to school (Again, one may learn elsewhere)

  13. Disjunctive Syllogism • “Either-or” syllogism Either you like Star Wars or Star Trek You like Star Wars You don’t like Star Trek (Formally valid, but can’t we like both?)

  14. Limitations • Formal correctness insufficient to gain adherence • Precise language essential to analyzing and appraising arguments • Certainty cannot always be established • Reasoning does not always follow three-liner form

  15. Sources Consulted • Zarefsky, David. Argumentation: The Study of Effective Reasoning. 2nd Edition. The Great Courses. Chantilly, VA: The Teaching Company, 2005. • Pirie, Madsen. How to Win Every Argument: The Use and Abuse of Logic. London: Continuum, 2006.

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