Deductive logic

1. 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!”

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. 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 every single fresh water lake to know that there aren’t any sharks in it: deductive logic tells you that there are no sharks in the West Lake.

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

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 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!