Deductive logic•What is it?

•How does it work?•Why does it matter?

All generalization

s are false, including this

one

You do not reason a man out

something that he was

not reasoned into

Critical reason is the

only alternative to violence

so far discovered.

Logic is the beginning of wisdom, not

the end

An example..Sherlock Holmes (the master of deductive logic) speakingto 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!”

The deductive reasoning..

Watchdogs bark at strangersThe Watchdog did not bark at the

thiefTherefore the thief was not a

stranger

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

• 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

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 any freshwater lakes.

So what is deductive reasoning?

• Any form of reasoning that moves from the general to the particular e.g.

• “All dogs are mammals• Fido is a dog• Therefore Fido….Is a mammal

Syllogisms• The kind of deductive argument that we just

looked at is known as a syllogism• A syllogism consists of:

1. Two premises and a conclusion2. Three terms, each of which occurs twice

(dogs, mammals, fido)3. Quantifiers such as ‘all, some or no’

Truth Vs Valid – which is this?

• All rocket scientists are stupid• Bill Gates is a rocket scientist• Therefore Bill Gates is stupid

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

WHAT ABOUT THIS ONE..

• All tacos are teachers• Mr. Wright is a taco• Therefore Mr. Wright is a Teacher

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

This one?...• All projectors require electricity• This classroom has a projector• Therefore this this classroom does not have a

projector

INVALID• The premises are both true• The conclusion is false• This is the one combination where the

argument MUST be invalid

DIY – make your own valid syllogisms

1. Two true premises and a true conclusion2. One true premise, one false premise and a

true conclusion3. One true premise, one false premise and a

false conclusion4. Two false premises and a true conclusion5. Two false premises and a false conclusion

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

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

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

Using Venn diagrams• Refer to the photocopied information… Venn

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

Enthymeme’s• Incomplete arguments that exclude a premise

because it is considered obvious/assumed.

Supply the missing premise for these enthymemes

1. Jenny goes to Oxford University, so she must be very intelligent

2. Drugs should be legalised because they only harm the addict

3. Graham is a politician, so he is probably lying.4. Cheerleading should be an olympic event

becauses cheerleaders compete, train and have a high level of physical fitness

5. Since it is natural to eat meat, there is nothing morally wrong with it

But where do our premises come from?

• INDUCTIVE REASONING…!• To be continued….

Bibliography• Much of this presentation is shamelessly

based upon material from the excellent TOK book by Richard van de Lagemaat – thanks go to him!