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

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
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.