1. Deductive and induction reasoning

2. Deductive reasoning

3. Syllogisms
Holmes reasoning is an example of a syllogism.

4. The Socrates Syllogism
All human beings are mortal
Socrates is a human being
Therefore Socrates is mortal
premises
Rationalism – A branch of philosophy which takes reason as the most important source of knowledge
conclusion

5. Syllogisms contain: Two premises and a conclusion
Three terms, each must occur twice (“Socrates”, “human”, “mortal”.)
Quantifiers, such as “all”, or “some” or “no” which tell us of the quantity being referred to
“TOK for the IB Diploma”, Richard van de Lagemaat, Cambridge

6. Another example
All boys like playing football.
Chris is a boy
Chris likes to play football.

7. Imagine that some strange planet exists where the premises are true
Truth and validity
An argument is valid if the conclusion follows logically from the premises.
All hippopotamuses eat cockroaches
Matthew is a hippopotamus
Therefore Matthew eats cockroaches
Both premises and conclusion are false, but the argument is valid.
Imagine that some strange planet exists where the premises are true

8. = Truth and validity All rats are teachers Mr Jones is a rat
Therefore Mr Jones is a teacher
Both premises are false and conclusion is true! (but the argument is still valid). =

9. Deductive reasoning and truth
Just because an argument is valid (Some IB students are from Russia, all Russians are good at drinking vodka, therefore some IB students are good at drinking vodka) does not mean that the conclusion is true.

10. Deductive reasoning and truth
For an argument to be true you must be able to answer “yes” to the following questions:

11. Deductive reasoning and truth
For an argument to be true you must be able to answer “yes” to the following questions:
Are the premises true?
Is the argument valid?

12. Socrates Socrates is a man All men are mortal
Therefore Socrates is mortal
The conclusion is only true if the premises are true.

13. Make up your own VALID syllogisms to illustrate each of the following;
2 true premises and a true conclusion
1 true premise, 1 false premise and a true conclusion
1 true premise, 1 false premise and a false conclusion
2 false premises and a true conclusion
2 false premises and a false conclusion

14. Deciding whether a syllogism is valid
Trying to decide if a syllogism is valid is not easy.
Venn diagrams can help (at last a good use for Venn diagrams!)

15. Deciding whether a syllogism is valid
Mmmmmmm…Vodka!
Some IB students are from Russia
All Russians are good at drinking vodka
Therefore some IB students are good at drinking vodka
Is this a valid argument?
IB students from Oslo International School

16. Using Venn diagrams Some IB students are from Russia
IB Students who are Russian
IB Students
Russians

17. Using Venn diagrams All Russians are good at drinking vodka
Good vodka drinkers
IB Students
Russians

18. Using Venn diagrams
Therefore some IB students are good at drinking vodka
Good vodka drinkers
IB Students
Russians

19. Another example
All As are Bs
All Bs are Cs
Therefore all Cs are As

20. Another example
All As are Bs A B

21. Another example
All Bs are Cs A B C

22. Another example Therefore all Cs are As The syllogism is not valid
These Cs are not As A B C
The syllogism is not valid

23. Now your turn
Using Venn diagrams in your notebooks, decide whether each of the following arguments is valid or invalid.

24. Valid or invalid All Norwegians eat hotdogs Felix eats hotdogs
Therefore Felix is Norwegian

25. Valid or invalid All Year 12 boys are brave
Some brave people are compassionate
Some Year 12 boys are compassionate

26. Valid or invalid Some politicians are frauds
Some frauds are not wealthy
Therefore some politicians are not wealthy

27. Valid or invalid All Americans have dogs
No good football players have dogs
Therefore no Americans are good football players

28. Valid or invalid All clever girls are red-headed
All red heads are rich
Therefore all clever girls are rich