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Syllogisms Formal Reasoning

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**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)

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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

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**Deductive and Inductive**

No new information Conclusions are certain Inductive New information Conclusions are probable Formal reasoning is deductive

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**Syllogism Syn- together + logos, reason, discourse**

Contains three (3) parts Major premise Minor premise Conclusion Three (3) syllogistic types here considered: Categorical Conditional Disjunctive

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**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)

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**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.)

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**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

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**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

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**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

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**Conditional Syllogism**

Two (2) fallacies involved Denying the antecedent Affirming the consequent 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)

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**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)

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**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?)

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**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

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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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Reasoning -deductive versus inductive reasoning -two basic types of deductive reasoning task: conditional (propositional) and syllogistic.

Reasoning -deductive versus inductive reasoning -two basic types of deductive reasoning task: conditional (propositional) and syllogistic.

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