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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

Syllogisms

Formal Reasoning

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
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

deductive and inductive
Deductive and Inductive
  • Deductive
    • No new information
    • Conclusions are certain
  • Inductive
    • New information
    • Conclusions are probable

Formal reasoning isdeductive

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

categorical syllogism1
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.)

conditional syllogism
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

conditional syllogism1
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

conditional syllogism2
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

conditional syllogism3
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)

conditional syllogism4
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)

disjunctive syllogism
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?)

limitations
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
sources consulted
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.