1. What is it? How does it work? Why does it matter?
You do not reason a man out of something that he was not reasoned into
All generalizations are false, including this one
Deductive logic
What is it?
How does it work?
Why does it matter?
Critical reason is the only alternative to violence so far discovered.
Logic is the beginning of wisdom, not the end

2. An example.. Sherlock Holmes (the master of deductive logic) speaking
to a police officer about the theft of an expensive racehorse…
Police Officer: “Holmes, does any one aspect of the crime strike you as significant?”
Holmes: “Yes, the curious incident of the dog in the night time”
Police Officer: “But the dog did nothing in the night time!”
Holmes: “That was the curious incident!”
What was Holmes’ reasoning?

3. The deductive reasoning..
Watchdogs bark at strangers The Watchdog did not bark at the thief Therefore the thief was not a stranger

4. More examples..
You know that you left your mobile phone either in your pocket or on your desk
Your mobile isn’t in your pocket
Therefore...
It must be on your desk

5. More examples..
You know that The West Lake in Hangzhou is a fresh water lake
You know that sharks cannot live in fresh water
Therefore...
There cannot be any sharks in the West Lake

6. The benefits?
You don’t have to check West Lake to know that there aren’t any sharks in it: deductive logic tells you that there are no sharks in the West Lake.
If...

7. So what is deductive reasoning?
Any form of reasoning that moves from the general to the particular e.g.
“All dogs are happy (general)
Fido is a dog (particular)
Therefore Fido….

8. Syllogisms
The kind of deductive argument that we just looked at is known as a syllogism
A syllogism consists of:
Two premises and a conclusion. One premise is Major (a generalisation: “All...” or “No...”); the other Minor (a particular example)
Three terms, each of which occurs twice (dogs, mammals, Fido)
Quantifiers such as ‘all, some or no’

9. Truth Vs Valid – which is this?
All rocket scientists are stupid
Bill Gates is a rocket scientist
Therefore Bill Gates is stupid

10. It is Valid! Both the PREMISES are false The CONCLUSION is false
Yet the ARGUMENT ITSELF IS VALID!

11. WHAT ABOUT THIS ONE? All tacos are teachers Mr Weatherell is a taco
Therefore Mr Weatherell is a teacher

12. Valid Both the premises are false But the conclusion is true
However the argument is still VALID

13. This one?... All toasters require electricity
This classroom has no toaster
Therefore this this classroom has no electricity

14. INVALID The premises are both true The conclusion is false
This is the one combination where the argument MUST be invalid

15. DIY – make your own valid syllogisms
Two true premises and a true conclusion
One true premise, one false premise and a false conclusion
Two false premises and a true conclusion
Two false premises and a false conclusion

16. Pure logic
Concerned merely with the structure of arguments, it doesn’t matter if the premises are false, or even meaningless!
All that matters is does the conclusion follow logically from the premises.
E.g. :
All blims are blams
Some blims are bloms
Therefore some blams are bloms

17. Aghhhh – my head hurts! Algebra in TOK!
All A’s are B’s
Some A’s are C’s
Therefore some B’s are C’s
IS THIS VALID OR INVALID?
UNDER WHAT CIRCUMSTANCES IS THIS TRUE?

18. What’s the point? Removes ‘belief bias’
Sometimes we tend to believe an argument is valid because we already agree with the conclusion
E.g. Democrats are in favour of free speech
Dictators are not Democrats
Therefore all dictators are opposed to free speech
This is NOT a valid argument

19. Using Venn diagrams
Venn diagrams can be a useful way of picturing a Syllogism and determining whether an argument if valid

20. Enthymeme’s
Incomplete arguments that exclude a premise because it is considered obvious/assumed.

21. Supply the missing premise for these enthymemes
Jenny goes to Oxford University, so she must be very intelligent
Drugs should be legalised because they only harm the addict
Graham is a politician, so he is probably lying.
Cheerleading should be an olympic event because cheerleaders compete, train and have a high level of physical fitness
Since it is natural to eat meat, there is nothing morally wrong with it

22. But where do our premises come from?
INDUCTIVE REASONING…!
To be continued….

23. Bibliography
Much of this presentation is shamelessly based upon material from the excellent TOK book by Richard van de Lagemaat – thanks go to him!